Determine if two triangles overlap: Difference between revisions
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Revision as of 21:34, 25 January 2021
You are encouraged to solve this task according to the task description, using any language you may know.
Determining if two triangles in the same plane overlap is an important topic in collision detection.
- Task
Determine which of these pairs of triangles overlap in 2D:
- (0,0),(5,0),(0,5) and (0,0),(5,0),(0,6)
- (0,0),(0,5),(5,0) and (0,0),(0,5),(5,0)
- (0,0),(5,0),(0,5) and (-10,0),(-5,0),(-1,6)
- (0,0),(5,0),(2.5,5) and (0,4),(2.5,-1),(5,4)
- (0,0),(1,1),(0,2) and (2,1),(3,0),(3,2)
- (0,0),(1,1),(0,2) and (2,1),(3,-2),(3,4)
Optionally, see what the result is when only a single corner is in contact (there is no definitive correct answer):
- (0,0),(1,0),(0,1) and (1,0),(2,0),(1,1)
Ada
<lang ada> WITH Ada.Text_IO; USE Ada.Text_IO;
PROCEDURE Main IS
TYPE Vertex IS MOD 3;
TYPE Point IS ARRAY (0 .. 1) OF Float;
TYPE Triangle IS ARRAY (Vertex) OF Point;
TYPE Triangle_Vertices IS ARRAY (0 .. 5) OF Float;
FUNCTION Same_Side (A, B, M, N : Point) RETURN Boolean IS
FUNCTION Aff (U : Point) RETURN Float IS
((B (1) - A (1)) * (U (0) - A (0)) + (A (0) - B (0)) * (U (1) - A (1)));
BEGIN
RETURN Aff (M) * Aff (N) >= 0.0;
END Same_Side;
FUNCTION In_Side (T1 , T2 : Triangle) RETURN Boolean IS
(FOR ALL V IN Vertex =>
(FOR Some P OF T2 => Same_Side (T1 (V + 1), T1 (V + 2), T1 (V), P)));
FUNCTION Overlap (T1, T2 : Triangle) RETURN Boolean IS
(In_Side (T1, T2) AND THEN In_Side (T2, T1));
FUNCTION "+" (T : Triangle_Vertices) RETURN Triangle IS
((T (0), T (1)), (T (2), T (3)), (T (4), T (5)));
PROCEDURE Put (T1, T2 : Triangle_Vertices) IS
BEGIN
Put_Line (Overlap (+T1, +T2)'Img);
END Put;
BEGIN
Put ((0.0, 0.0, 5.0, 0.0, 0.0, 5.0), (0.0, 0.0, 5.0, 0.0, 0.0, 6.0)); Put ((0.0, 0.0, 0.0, 5.0, 5.0, 0.0), (0.0, 0.0, 0.0, 5.0, 5.0, 0.0)); Put ((0.0, 0.0, 5.0, 0.0, 0.0, 5.0), (-10.0, 0.0, -5.0, 0.0, -1.0, 6.0)); Put ((0.0, 0.0, 5.0, 0.0, 2.5, 5.0), (0.0, 4.0, 2.5, -1.0, 5.0, 4.0)); Put ((0.0, 0.0, 1.0, 1.0, 0.0, 2.0), (2.0, 1.0, 3.0, 0.0, 3.0, 2.0)); Put ((0.0, 0.0, 1.0, 1.0, 0.0, 2.0), (2.0, 1.0, 3.0, -2.0, 3.0, 4.0)); Put ((0.0, 0.0, 1.0, 0.0, 0.0, 1.0), (1.0, 0.0, 2.0, 0.0, 1.0, 1.0));
END Main; </lang>
- Output:
true true false true false false true
ALGOL W
... with different output format (based on Modula 2). <lang algolw>begin % determine if two triangles overlap %
record Point ( real x, y );
record Triangle ( reference(Point) p1, p2, p3 );
procedure WritePoint ( reference(Point) value p ) ;
writeon( r_w := 3, r_d := 1, r_format := "A", s_w := 0, "(", x(p), ", ", y(p), ")" );
procedure WriteTriangle ( reference(Triangle) value t ) ;
begin
WritePoint( p1(t) );
writeon( ", " );
WritePoint( p2(t) );
writeon( ", " );
WritePoint( p3(t) )
end WriteTriangle ;
real procedure Det2D ( reference(Triangle) value t ) ;
( ( x(p1(t)) * ( y(p2(t)) - y(p3(t)) ) )
+ ( x(p2(t)) * ( y(p3(t)) - y(p1(t)) ) )
+ ( x(p3(t)) * ( y(p1(t)) - y(p2(t)) ) )
);
procedure CheckTriWinding ( reference(Triangle) value t ; logical value allowReversed ) ;
begin
real detTri;
detTri := Det2D(t);
if detTri < 0.0 then begin
if allowReversed then begin
reference(Point) a;
a := p3(t);
p3(t) := p2(t);
p2(t) := a
end
else begin
write( "triangle has wrong winding direction" );
assert( false )
end
end if_detTri_lt_0
end CheckTriWinding ;
logical procedure BoundaryCollideChk( reference(Triangle) value t ; real value eps ) ; Det2D( t ) < eps ;
logical procedure BoundaryDoesntCollideChk( reference(Triangle) value t ; real value eps ) ; Det2D( t ) <= eps ;
logical procedure TriTri2D( reference(Triangle) value t1, t2 ; real value eps ; logical value allowReversed, onBoundary ) ;
begin
logical procedure ChkEdge( reference(Triangle) value t ) ;
if onBoundary then % Points on the boundary are considered as colliding %
BoundaryCollideChk( t, eps )
else % Points on the boundary are not considered as colliding %
BoundaryDoesntCollideChk( t, eps )
;
reference(Point) array lp1, lp2 ( 0 :: 2 );
logical overlap;
overlap := true;
% Triangles must be expressed anti-clockwise %
CheckTriWinding( t1, allowReversed );
CheckTriWinding( t2, allowReversed );
lp1( 0 ) := p1(t1); lp1( 1 ) := p2(t1); lp1( 2 ) := p3(t1);
lp2( 0 ) := p1(t2); lp2( 1 ) := p2(t2); lp2( 2 ) := p3(t2);
% for each edge E of t1 %
for i := 0 until 2 do begin
integer j;
j := ( i + 1 ) rem 3;
% Check all points of t2 lay on the external side of edge E. %
% if they do, the triangles do not overlap. %
if ChkEdge( Triangle( lp1( i ), lp1( j ), lp2( 0 ) ) )
and ChkEdge( Triangle( lp1( i ), lp1( j ), lp2( 1 ) ) )
and ChkEdge( Triangle( lp1( i ), lp1( j ), lp2( 2 ) ) )
then begin
overlap := false;
goto return
end
end for_i ;
% for each edge E of t2 %
for i := 0 until 2 do begin
integer j;
j := ( i + 1 ) rem 3;
% Check all points of t1 lay on the external side of edge E. %
% if they do, the triangles do not overlap. %
if ChkEdge( Triangle( lp2( i ), lp2( j ), lp1( 0 ) ) )
and ChkEdge( Triangle( lp2( i ), lp2( j ), lp1( 1 ) ) )
and ChkEdge( Triangle( lp2( i ), lp2( j ), lp1( 2 ) ) )
then begin
overlap := false;
goto return
end
end for_i;
% if we get here, The triangles overlap %
return: overlap
end TriTri2D ;
procedure CheckOverlap( reference(Triangle) value t1, t2
; real value eps
; logical value allowReversed, onBoundary
) ;
begin
write( "Triangles " );
WriteTriangle( t1 );
writeon( " and " );
WriteTriangle( t2 );
writeon( if TriTri2D( t1, t2, eps, allowReversed, onBoundary ) then " overlap" else " do not overlap" );
end CheckOverlap ;
begin % main %
reference(Triangle) t1, t2;
t1 := Triangle( Point( 0.0, 0.0 ), Point( 5.0, 0.0 ), Point( 0.0, 5.0 ) );
t2 := Triangle( Point( 0.0, 0.0 ), Point( 5.0, 0.0 ), Point( 0.0, 6.0 ) );
CheckOverlap( t1, t2, 0.0, false, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 0.0, 5.0 ), Point( 5.0, 0.0 ) );
t2 := Triangle( Point( 0.0, 0.0 ), Point( 0.0, 5.0 ), Point( 5.0, 0.0 ) );
CheckOverlap(t1, t2, 0.0, true, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 5.0, 0.0 ), Point( 0.0, 5.0 ) );
t2 := Triangle( Point( -10.0, 0.0 ), Point( -5.0, 0.0 ), Point( -1.0, 6.0 ) );
CheckOverlap( t1, t2, 0.0, false, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 5.0, 0.0 ), Point( 2.5, 5.0 ) );
t2 := Triangle( Point( 0.0, 4.0 ), Point( 2.5, -1.0 ), Point( 5.0, 4.0 ) );
CheckOverlap( t1, t2, 0.0, false, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 1.0, 1.0 ), Point( 0.0, 2.0 ) );
t2 := Triangle( Point( 2.0, 1.0 ), Point( 3.0, 0.0 ), Point( 3.0, 2.0 ) );
CheckOverlap( t1, t2, 0.0, false, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 1.0, 1.0 ), Point( 0.0, 2.0 ) );
t2 := Triangle( Point( 2.0, 1.0 ), Point( 3.0, -2.0 ), Point( 3.0, 4.0 ) );
CheckOverlap( t1, t2, 0.0, false, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 1.0, 0.0 ), Point( 0.0, 1.0 ) );
t2 := Triangle( Point( 1.0, 0.0 ), Point( 2.0, 0.0 ), Point( 1.0, 1.1 ) );
CheckOverlap( t1, t2, 0.0, false, true );
t1 := Triangle( Point( 0.0, 0.0 ), Point( 1.0, 0.0 ), Point( 0.0, 1.0 ) );
t2 := Triangle( Point( 1.0, 0.0 ), Point( 2.0, 0.0 ), Point( 1.0, 1.1 ) );
CheckOverlap( t1, t2, 0.0, false, false );
end
end.</lang>
- Output:
Triangles (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and (0.0, 0.0), (5.0, 0.0), (0.0, 6.0) overlap Triangles (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) and (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) overlap Triangles (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and (-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0) do not overlap Triangles (0.0, 0.0), (5.0, 0.0), (2.5, 5.0) and (0.0, 4.0), (2.5, -1.0), (5.0, 4.0) overlap Triangles (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and (2.0, 1.0), (3.0, 0.0), (3.0, 2.0) do not overlap Triangles (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and (2.0, 1.0), (3.0, -2.0), (3.0, 4.0) do not overlap Triangles (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) overlap Triangles (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) do not overlap
AutoHotkey
<lang AutoHotkey>TrianglesIntersect(T1, T2){ ; T1 := [[x1,y1],[x2,y2],[x3,y3]] , T2 :=[[x4,y4],[x5,y5],[x6,y6]] counter := 0 for i, Pt in T1 counter += PointInTriangle(Pt, T2) ; check if any coordinate of triangle 1 is inside triangle 2 for i, Pt in T2 counter += PointInTriangle(Pt, T1) ; check if any coordinate of triangle 2 is inside triangle 1 ; check if sides of triangle 1 intersect with sides of triangle 2 counter += LinesIntersect([t1.1,t1.2],[t2.1,t2.2]) ? 1 : 0 counter += LinesIntersect([t1.1,t1.3],[t2.1,t2.2]) ? 1 : 0 counter += LinesIntersect([t1.2,t1.3],[t2.1,t2.2]) ? 1 : 0
counter += LinesIntersect([t1.1,t1.2],[t2.1,t2.3]) ? 1 : 0 counter += LinesIntersect([t1.1,t1.3],[t2.1,t2.3]) ? 1 : 0 counter += LinesIntersect([t1.2,t1.3],[t2.1,t2.3]) ? 1 : 0
counter += LinesIntersect([t1.1,t1.2],[t2.2,t2.3]) ? 1 : 0 counter += LinesIntersect([t1.1,t1.3],[t2.2,t2.3]) ? 1 : 0 counter += LinesIntersect([t1.2,t1.3],[t2.2,t2.3]) ? 1 : 0 return (counter>3) ; 3 points inside or 1 point inside and 2 lines intersect or 3 lines intersect } PointInTriangle(pt, Tr){ ; pt:=[x,y] , Tr := [[x1,y1],[x2,y2],[x3,y3]] v1 := Tr.1, v2 := Tr.2, v3 := Tr.3
d1 := sign(pt, v1, v2) d2 := sign(pt, v2, v3) d3 := sign(pt, v3, v1) has_neg := (d1 < 0) || (d2 < 0) || (d3 < 0) has_pos := (d1 > 0) || (d2 > 0) || (d3 > 0) return !(has_neg && has_pos)
} sign(p1, p2, p3){
return (p1.1 - p3.1) * (p2.2 - p3.2) - (p2.1 - p3.1) * (p1.2 - p3.2)
} LinesIntersect(L1, L2){ ; L1 := [[x1,y1],[x2,y2]] , L2 := [[x3,y3],[x4,y4]] x1 := L1[1,1], y1 := L1[1,2] x2 := L1[2,1], y2 := L1[2,2] x3 := L2[1,1], y3 := L2[1,2] x4 := L2[2,1], y4 := L2[2,2] x := ((x1*y2-y1*x2)*(x3-x4) - (x1-x2)*(x3*y4-y3*x4)) / ((x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)) y := ((x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)) / ((x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)) if (x<>"" && y<>"") && isBetween(x, x1, x2) && isBetween(x, x3, x4) && isBetween(y, y1, y2) && isBetween(y, y3, y4) return 1 } isBetween(x, p1, p2){ return !((x>p1 && x>p2) || (x<p1 && x<p2)) }</lang> Examples:<lang AutoHotkey>result := "" result .= TrianglesIntersect([[0,0],[5,0],[0,5]], [[0,0],[5,0],[0,6]]) "`n" result .= TrianglesIntersect([[0,0],[0,5],[5,0]], [[0,0],[0,5],[5,0]]) "`n" result .= TrianglesIntersect([[0,0],[5,0],[0,5]], [[-10,0],[-5,0],[-1,6]])"`n" result .= TrianglesIntersect([[0,0],[5,0],[2.5,5]], [[0,4],[2.5,-1],[5,4]]) "`n" result .= TrianglesIntersect([[0,0],[1,1],[0,2]], [[2,1],[3,0],[3,2]]) "`n" result .= TrianglesIntersect([[0,0],[1,1],[0,2]], [[2,1],[3,-2],[3,4]]) "`n" result .= TrianglesIntersect([[0,0],[1,0],[0,1]], [[1,0],[2,0],[1,1]]) "`n" MsgBox % result return</lang>
Outputs:
1 1 0 1 0 0 1
C
<lang c>#include <errno.h>
- include <stdbool.h>
- include <stdio.h>
- include <stdlib.h>
typedef struct {
double x, y;
} Point;
double det2D(const Point * const p1, const Point * const p2, const Point * const p3) {
return p1->x * (p2->y - p3->y)
+ p2->x * (p3->y - p1->y)
+ p3->x * (p1->y - p2->y);
}
void checkTriWinding(Point * p1, Point * p2, Point * p3, bool allowReversed) {
double detTri = det2D(p1, p2, p3);
if (detTri < 0.0) {
if (allowReversed) {
double t = p3->x;
p3->x = p2->x;
p2->x = t;
t = p3->y;
p3->y = p2->y;
p2->y = t;
} else {
errno = 1;
}
}
}
bool boundaryCollideChk(const Point *p1, const Point *p2, const Point *p3, double eps) {
return det2D(p1, p2, p3) < eps;
}
bool boundaryDoesntCollideChk(const Point *p1, const Point *p2, const Point *p3, double eps) {
return det2D(p1, p2, p3) <= eps;
}
bool triTri2D(Point t1[], Point t2[], double eps, bool allowReversed, bool onBoundary) {
bool(*chkEdge)(Point*, Point*, Point*, double); int i;
// Triangles must be expressed anti-clockwise
checkTriWinding(&t1[0], &t1[1], &t1[2], allowReversed);
if (errno != 0) {
return false;
}
checkTriWinding(&t2[0], &t2[1], &t2[2], allowReversed);
if (errno != 0) {
return false;
}
if (onBoundary) {
// Points on the boundary are considered as colliding
chkEdge = boundaryCollideChk;
} else {
// Points on the boundary are not considered as colliding
chkEdge = boundaryDoesntCollideChk;
}
//For edge E of trangle 1,
for (i = 0; i < 3; ++i) {
int j = (i + 1) % 3;
//Check all points of trangle 2 lay on the external side of the edge E. If
//they do, the triangles do not collide.
if (chkEdge(&t1[i], &t1[j], &t2[0], eps) &&
chkEdge(&t1[i], &t1[j], &t2[1], eps) &&
chkEdge(&t1[i], &t1[j], &t2[2], eps)) {
return false;
}
}
//For edge E of trangle 2,
for (i = 0; i < 3; i++) {
int j = (i + 1) % 3;
//Check all points of trangle 1 lay on the external side of the edge E. If
//they do, the triangles do not collide.
if (chkEdge(&t2[i], &t2[j], &t1[0], eps) &&
chkEdge(&t2[i], &t2[j], &t1[1], eps) &&
chkEdge(&t2[i], &t2[j], &t1[2], eps))
return false;
}
//The triangles collide return true;
}
int main() {
{
Point t1[] = { {0, 0}, {5, 0}, {0, 5} };
Point t2[] = { {0, 0}, {5, 0}, {0, 6} };
printf("%d,true\n", triTri2D(t1, t2, 0.0, false, true));
}
{
Point t1[] = { {0, 0}, {0, 5}, {5, 0} };
Point t2[] = { {0, 0}, {0, 5}, {5, 0} };
printf("%d,true\n", triTri2D(t1, t2, 0.0, true, true));
}
{
Point t1[] = { {0, 0}, {5, 0}, {0, 5} };
Point t2[] = { {-10, 0}, {-5, 0}, {-1, 6} };
printf("%d,false\n", triTri2D(t1, t2, 0.0, false, true));
}
{
Point t1[] = { {0, 0}, {5, 0}, {2.5, 5} };
Point t2[] = { {0, 4}, {2.5, -1}, {5, 4} };
printf("%d,true\n", triTri2D(t1, t2, 0.0, false, true));
}
{
Point t1[] = { {0, 0}, {1, 1}, {0, 2} };
Point t2[] = { {2, 1}, {3, 0}, {3, 2} };
printf("%d,false\n", triTri2D(t1, t2, 0.0, false, true));
}
{
Point t1[] = { {0, 0}, {1, 1}, {0, 2} };
Point t2[] = { {2, 1}, {3, -2}, {3, 4} };
printf("%d,false\n", triTri2D(t1, t2, 0.0, false, true));
}
//Barely touching
{
Point t1[] = { {0, 0}, {1, 0}, {0, 1} };
Point t2[] = { {1, 0}, {2, 0}, {1, 1} };
printf("%d,true\n", triTri2D(t1, t2, 0.0, false, true));
}
//Barely touching
{
Point t1[] = { {0, 0}, {1, 0}, {0, 1} };
Point t2[] = { {1, 0}, {2, 0}, {1, 1} };
printf("%d,false\n", triTri2D(t1, t2, 0.0, false, false));
}
return EXIT_SUCCESS;
}</lang>
- Output:
1,true 1,true 0,false 1,true 0,false 0,false 1,true 0,false
C#
<lang csharp>using System; using System.Collections.Generic;
namespace TriangleOverlap {
class Triangle {
public Tuple<double, double> P1 { get; set; }
public Tuple<double, double> P2 { get; set; }
public Tuple<double, double> P3 { get; set; }
public Triangle(Tuple<double, double> p1, Tuple<double, double> p2, Tuple<double, double> p3) {
P1 = p1;
P2 = p2;
P3 = p3;
}
public double Det2D() {
return P1.Item1 * (P2.Item2 - P3.Item2)
+ P2.Item1 * (P3.Item2 - P1.Item2)
+ P3.Item1 * (P3.Item1 - P2.Item2);
}
public void CheckTriWinding(bool allowReversed) {
var detTri = Det2D();
if (detTri < 0.0) {
if (allowReversed) {
var a = P3;
P3 = P2;
P2 = a;
} else {
throw new Exception("Triangle has wrong winding direction");
}
}
}
public bool BoundaryCollideChk(double eps) {
return Det2D() < eps;
}
public bool BoundaryDoesntCollideChk(double eps) {
return Det2D() <= eps;
}
public override string ToString() {
return string.Format("Triangle: {0}, {1}, {2}", P1, P2, P3);
}
}
class Program {
static bool BoundaryCollideChk(Triangle t, double eps) {
return t.BoundaryCollideChk(eps);
}
static bool BoundaryDoesntCollideChk(Triangle t, double eps) {
return t.BoundaryDoesntCollideChk(eps);
}
static bool TriTri2D(Triangle t1, Triangle t2, double eps = 0.0, bool allowReversed = false, bool onBoundary = true) {
// Triangles must be expressed anti-clockwise
t1.CheckTriWinding(allowReversed);
t2.CheckTriWinding(allowReversed);
// 'onBoundary' determines whether points on boundary are considered as colliding or not
var chkEdge = onBoundary
? (Func<Triangle, double, bool>)BoundaryCollideChk
: BoundaryDoesntCollideChk;
List<Tuple<double, double>> lp1 = new List<Tuple<double, double>>() { t1.P1, t1.P2, t1.P3 };
List<Tuple<double, double>> lp2 = new List<Tuple<double, double>>() { t2.P1, t2.P2, t2.P3 };
// for each edge E of t1
for (int i = 0; i < 3; i++) {
var j = (i + 1) % 3;
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(new Triangle(lp1[i], lp1[j], lp2[0]), eps) &&
chkEdge(new Triangle(lp1[i], lp1[j], lp2[1]), eps) &&
chkEdge(new Triangle(lp1[i], lp1[j], lp2[2]), eps)) {
return false;
}
}
// for each edge E of t2
for (int i = 0; i < 3; i++) {
var j = (i + 1) % 3;
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(new Triangle(lp2[i], lp2[j], lp1[0]), eps) &&
chkEdge(new Triangle(lp2[i], lp2[j], lp1[1]), eps) &&
chkEdge(new Triangle(lp2[i], lp2[j], lp1[2]), eps)) {
return false;
}
}
// The triangles overlap
return true;
}
static void Overlap(Triangle t1, Triangle t2, double eps = 0.0, bool allowReversed = false, bool onBoundary = true) {
if (TriTri2D(t1, t2, eps, allowReversed, onBoundary)) {
Console.WriteLine("overlap");
} else {
Console.WriteLine("do not overlap");
}
}
static void Main(string[] args) {
var t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(5.0, 0.0), new Tuple<double, double>(0.0, 5.0));
var t2 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(5.0, 0.0), new Tuple<double, double>(0.0, 6.0));
Console.WriteLine("{0} and\n{1}", t1, t2);
Overlap(t1, t2);
Console.WriteLine();
// need to allow reversed for this pair to avoid exception
t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(0.0, 5.0), new Tuple<double, double>(5.0, 0.0));
t2 = t1;
Console.WriteLine("{0} and\n{1}", t1, t2);
Overlap(t1, t2, 0.0, true);
Console.WriteLine();
t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(5.0, 0.0), new Tuple<double, double>(0.0, 5.0));
t2 = new Triangle(new Tuple<double, double>(-10.0, 0.0), new Tuple<double, double>(-5.0, 0.0), new Tuple<double, double>(-1.0, 6.0));
Console.WriteLine("{0} and\n{1}", t1, t2);
Overlap(t1, t2);
Console.WriteLine();
t1.P3 = new Tuple<double, double>(2.5, 5.0);
t2 = new Triangle(new Tuple<double, double>(0.0, 4.0), new Tuple<double, double>(2.5, -1.0), new Tuple<double, double>(5.0, 4.0));
Console.WriteLine("{0} and\n{1}", t1, t2);
Overlap(t1, t2);
Console.WriteLine();
t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(1.0, 1.0), new Tuple<double, double>(0.0, 2.0));
t2 = new Triangle(new Tuple<double, double>(2.0, 1.0), new Tuple<double, double>(3.0, 0.0), new Tuple<double, double>(3.0, 2.0));
Console.WriteLine("{0} and\n{1}", t1, t2);
Overlap(t1, t2);
Console.WriteLine();
t2 = new Triangle(new Tuple<double, double>(2.0, 1.0), new Tuple<double, double>(3.0, -2.0), new Tuple<double, double>(3.0, 4.0));
Console.WriteLine("{0} and\n{1}", t1, t2);
Overlap(t1, t2);
Console.WriteLine();
t1 = new Triangle(new Tuple<double, double>(0.0, 0.0), new Tuple<double, double>(1.0, 0.0), new Tuple<double, double>(0.0, 1.0));
t2 = new Triangle(new Tuple<double, double>(1.0, 0.0), new Tuple<double, double>(2.0, 0.0), new Tuple<double, double>(1.0, 1.1));
Console.WriteLine("{0} and\n{1}", t1, t2);
Console.WriteLine("which have only a single corner in contact, if boundary points collide");
Overlap(t1, t2);
Console.WriteLine();
Console.WriteLine("{0} and\n{1}", t1, t2);
Console.WriteLine("which have only a single corner in contact, if boundary points do not collide");
Overlap(t1, t2, 0.0, false, false);
}
}
}</lang>
- Output:
Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (0, 0), (5, 0), (0, 6) overlap Triangle: (0, 0), (0, 5), (5, 0) and Triangle: (0, 0), (0, 5), (5, 0) overlap Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (-10, 0), (-5, 0), (-1, 6) do not overlap Triangle: (0, 0), (5, 0), (2.5, 5) and Triangle: (0, 4), (2.5, -1), (5, 4) overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, 0), (3, 2) do not overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, -2), (3, 4) do not overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1.1) which have only a single corner in contact, if boundary points collide do not overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
C++
<lang cpp>#include <vector>
- include <iostream>
- include <stdexcept>
using namespace std;
typedef std::pair<double, double> TriPoint;
inline double Det2D(TriPoint &p1, TriPoint &p2, TriPoint &p3) { return +p1.first*(p2.second-p3.second) +p2.first*(p3.second-p1.second) +p3.first*(p1.second-p2.second); }
void CheckTriWinding(TriPoint &p1, TriPoint &p2, TriPoint &p3, bool allowReversed) { double detTri = Det2D(p1, p2, p3); if(detTri < 0.0) { if (allowReversed) { TriPoint a = p3; p3 = p2; p2 = a; } else throw std::runtime_error("triangle has wrong winding direction"); } }
bool BoundaryCollideChk(TriPoint &p1, TriPoint &p2, TriPoint &p3, double eps) { return Det2D(p1, p2, p3) < eps; }
bool BoundaryDoesntCollideChk(TriPoint &p1, TriPoint &p2, TriPoint &p3, double eps) { return Det2D(p1, p2, p3) <= eps; }
bool TriTri2D(TriPoint *t1, TriPoint *t2, double eps = 0.0, bool allowReversed = false, bool onBoundary = true) { //Trangles must be expressed anti-clockwise CheckTriWinding(t1[0], t1[1], t1[2], allowReversed); CheckTriWinding(t2[0], t2[1], t2[2], allowReversed);
bool (*chkEdge)(TriPoint &, TriPoint &, TriPoint &, double) = NULL; if(onBoundary) //Points on the boundary are considered as colliding chkEdge = BoundaryCollideChk; else //Points on the boundary are not considered as colliding chkEdge = BoundaryDoesntCollideChk;
//For edge E of trangle 1, for(int i=0; i<3; i++) { int j=(i+1)%3;
//Check all points of trangle 2 lay on the external side of the edge E. If //they do, the triangles do not collide. if (chkEdge(t1[i], t1[j], t2[0], eps) && chkEdge(t1[i], t1[j], t2[1], eps) && chkEdge(t1[i], t1[j], t2[2], eps)) return false; }
//For edge E of trangle 2, for(int i=0; i<3; i++) { int j=(i+1)%3;
//Check all points of trangle 1 lay on the external side of the edge E. If //they do, the triangles do not collide. if (chkEdge(t2[i], t2[j], t1[0], eps) && chkEdge(t2[i], t2[j], t1[1], eps) && chkEdge(t2[i], t2[j], t1[2], eps)) return false; }
//The triangles collide return true; }
int main() { {TriPoint t1[] = {TriPoint(0,0),TriPoint(5,0),TriPoint(0,5)}; TriPoint t2[] = {TriPoint(0,0),TriPoint(5,0),TriPoint(0,6)}; cout << TriTri2D(t1, t2) << "," << true << endl;}
{TriPoint t1[] = {TriPoint(0,0),TriPoint(0,5),TriPoint(5,0)}; TriPoint t2[] = {TriPoint(0,0),TriPoint(0,5),TriPoint(5,0)}; cout << TriTri2D(t1, t2, 0.0, true) << "," << true << endl;}
{TriPoint t1[] = {TriPoint(0,0),TriPoint(5,0),TriPoint(0,5)}; TriPoint t2[] = {TriPoint(-10,0),TriPoint(-5,0),TriPoint(-1,6)}; cout << TriTri2D(t1, t2) << "," << false << endl;}
{TriPoint t1[] = {TriPoint(0,0),TriPoint(5,0),TriPoint(2.5,5)}; TriPoint t2[] = {TriPoint(0,4),TriPoint(2.5,-1),TriPoint(5,4)}; cout << TriTri2D(t1, t2) << "," << true << endl;}
{TriPoint t1[] = {TriPoint(0,0),TriPoint(1,1),TriPoint(0,2)}; TriPoint t2[] = {TriPoint(2,1),TriPoint(3,0),TriPoint(3,2)}; cout << TriTri2D(t1, t2) << "," << false << endl;}
{TriPoint t1[] = {TriPoint(0,0),TriPoint(1,1),TriPoint(0,2)}; TriPoint t2[] = {TriPoint(2,1),TriPoint(3,-2),TriPoint(3,4)}; cout << TriTri2D(t1, t2) << "," << false << endl;}
//Barely touching {TriPoint t1[] = {TriPoint(0,0),TriPoint(1,0),TriPoint(0,1)}; TriPoint t2[] = {TriPoint(1,0),TriPoint(2,0),TriPoint(1,1)}; cout << TriTri2D(t1, t2, 0.0, false, true) << "," << true << endl;}
//Barely touching {TriPoint t1[] = {TriPoint(0,0),TriPoint(1,0),TriPoint(0,1)}; TriPoint t2[] = {TriPoint(1,0),TriPoint(2,0),TriPoint(1,1)}; cout << TriTri2D(t1, t2, 0.0, false, false) << "," << false << endl;}
}</lang>
- Output:
1,1 1,1 0,0 1,1 0,0 0,0 1,1 0,0
D
<lang D>import std.stdio; import std.typecons;
alias Pair = Tuple!(real, real);
struct Triangle {
Pair p1; Pair p2; Pair p3;
void toString(scope void delegate(const(char)[]) sink) const {
import std.format;
sink("Triangle: ");
formattedWrite!"%s"(sink, p1);
sink(", ");
formattedWrite!"%s"(sink, p2);
sink(", ");
formattedWrite!"%s"(sink, p3);
}
}
auto det2D(Triangle t) {
return t.p1[0] *(t.p2[1] - t.p3[1])
+ t.p2[0] *(t.p3[1] - t.p1[1])
+ t.p3[0] *(t.p1[1] - t.p2[1]);
}
void checkTriWinding(Triangle t, bool allowReversed) {
auto detTri = t.det2D();
if (detTri < 0.0) {
if (allowReversed) {
auto a = t.p3;
t.p3 = t.p2;
t.p2 = a;
} else {
throw new Exception("Triangle has wrong winding direction");
}
}
}
auto boundaryCollideChk(Triangle t, real eps) {
return t.det2D() < eps;
}
auto boundaryDoesntCollideChk(Triangle t, real eps) {
return t.det2D() <= eps;
}
bool triTri2D(Triangle t1, Triangle t2, real eps = 0.0, bool allowReversed = false, bool onBoundary = true) {
// Triangles must be expressed anti-clockwise checkTriWinding(t1, allowReversed); checkTriWinding(t2, allowReversed); // 'onBoundary' determines whether points on boundary are considered as colliding or not auto chkEdge = onBoundary ? &boundaryCollideChk : &boundaryDoesntCollideChk; auto lp1 = [t1.p1, t1.p2, t1.p3]; auto lp2 = [t2.p1, t2.p2, t2.p3];
// for each edge E of t1
foreach (i; 0..3) {
auto j = (i + 1) % 3;
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(Triangle(lp1[i], lp1[j], lp2[0]), eps) &&
chkEdge(Triangle(lp1[i], lp1[j], lp2[1]), eps) &&
chkEdge(Triangle(lp1[i], lp1[j], lp2[2]), eps)) {
return false;
}
}
// for each edge E of t2
foreach (i; 0..3) {
auto j = (i + 1) % 3;
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(Triangle(lp2[i], lp2[j], lp1[0]), eps) &&
chkEdge(Triangle(lp2[i], lp2[j], lp1[1]), eps) &&
chkEdge(Triangle(lp2[i], lp2[j], lp1[2]), eps)) {
return false;
}
}
// The triangles overlap return true;
}
void overlap(Triangle t1, Triangle t2, real eps = 0.0, bool allowReversed = false, bool onBoundary = true) {
if (triTri2D(t1, t2, eps, allowReversed, onBoundary)) {
writeln("overlap");
} else {
writeln("do not overlap");
}
}
void main() {
auto t1 = Triangle(Pair(0.0, 0.0), Pair(5.0, 0.0), Pair(0.0, 5.0)); auto t2 = Triangle(Pair(0.0, 0.0), Pair(5.0, 0.0), Pair(0.0, 6.0)); writeln(t1, " and\n", t2); overlap(t1, t2); writeln;
// need to allow reversed for this pair to avoid exception t1 = Triangle(Pair(0.0, 0.0), Pair(0.0, 5.0), Pair(5.0, 0.0)); t2 = t1; writeln(t1, " and\n", t2); overlap(t1, t2, 0.0, true); writeln;
t1 = Triangle(Pair(0.0, 0.0), Pair(5.0, 0.0), Pair(0.0, 5.0)); t2 = Triangle(Pair(-10.0, 0.0), Pair(-5.0, 0.0), Pair(-1.0, 6.0)); writeln(t1, " and\n", t2); overlap(t1, t2); writeln;
t1.p3 = Pair(2.5, 5.0); t2 = Triangle(Pair(0.0, 4.0), Pair(2.5, -1.0), Pair(5.0, 4.0)); writeln(t1, " and\n", t2); overlap(t1, t2); writeln;
t1 = Triangle(Pair(0.0, 0.0), Pair(1.0, 1.0), Pair(0.0, 2.0)); t2 = Triangle(Pair(2.0, 1.0), Pair(3.0, 0.0), Pair(3.0, 2.0)); writeln(t1, " and\n", t2); overlap(t1, t2); writeln;
t2 = Triangle(Pair(2.0, 1.0), Pair(3.0, -2.0), Pair(3.0, 4.0)); writeln(t1, " and\n", t2); overlap(t1, t2); writeln;
t1 = Triangle(Pair(0.0, 0.0), Pair(1.0, 0.0), Pair(0.0, 1.0));
t2 = Triangle(Pair(1.0, 0.0), Pair(2.0, 0.0), Pair(1.0, 1.1));
writeln(t1, " and\n", t2);
writeln("which have only a single corner in contact, if boundary points collide");
overlap(t1, t2);
writeln;
writeln(t1, " and\n", t2);
writeln("which have only a single corner in contact, if boundary points do not collide");
overlap(t1, t2, 0.0, false, false);
}</lang>
- Output:
Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(5, 0), Tuple!(real, real)(0, 5) and Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(5, 0), Tuple!(real, real)(0, 6) overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(0, 5), Tuple!(real, real)(5, 0) and Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(0, 5), Tuple!(real, real)(5, 0) overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(5, 0), Tuple!(real, real)(0, 5) and Triangle: Tuple!(real, real)(-10, 0), Tuple!(real, real)(-5, 0), Tuple!(real, real)(-1, 6) do not overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(5, 0), Tuple!(real, real)(2.5, 5) and Triangle: Tuple!(real, real)(0, 4), Tuple!(real, real)(2.5, -1), Tuple!(real, real)(5, 4) overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(1, 1), Tuple!(real, real)(0, 2) and Triangle: Tuple!(real, real)(2, 1), Tuple!(real, real)(3, 0), Tuple!(real, real)(3, 2) do not overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(1, 1), Tuple!(real, real)(0, 2) and Triangle: Tuple!(real, real)(2, 1), Tuple!(real, real)(3, -2), Tuple!(real, real)(3, 4) do not overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(1, 0), Tuple!(real, real)(0, 1) and Triangle: Tuple!(real, real)(1, 0), Tuple!(real, real)(2, 0), Tuple!(real, real)(1, 1.1) which have only a single corner in contact, if boundary points collide overlap Triangle: Tuple!(real, real)(0, 0), Tuple!(real, real)(1, 0), Tuple!(real, real)(0, 1) and Triangle: Tuple!(real, real)(1, 0), Tuple!(real, real)(2, 0), Tuple!(real, real)(1, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
F#
<lang fsharp>open System
type Point = double * double type Triangle = Point * Point * Point
let Det2D (t:Triangle) =
let (p1, p2, p3) = t let (p1x, p1y) = p1 let (p2x, p2y) = p2 let (p3x, p3y) = p3
p1x * (p2y - p3y) + p2x * (p3y - p1y) + p3x * (p1y - p2y)
let CheckTriWinding allowReversed t =
let detTri = Det2D t
if detTri < 0.0 then
if allowReversed then
let (p1, p2, p3) = t
(p1, p3, p2)
else
raise (Exception "Triangle has wrong winding direction")
else
t
let boundaryCollideChk eps t =
(Det2D t) < eps
let boundaryDoesntCollideChk eps t =
(Det2D t) <= eps
let TriTri2D eps allowReversed onBoundary t1 t2 =
// Triangles must be expressed anti-clockwise let t3 = CheckTriWinding allowReversed t1 let t4 = CheckTriWinding allowReversed t2
// 'onBoundary' determines whether points on boundary are considered as colliding or not let chkEdge = if onBoundary then boundaryCollideChk else boundaryDoesntCollideChk let (t1p1, t1p2, t1p3) = t3 let (t2p1, t2p2, t2p3) = t4
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge eps (t1p1, t1p2, t2p1)) && (chkEdge eps (t1p1, t1p2, t2p2)) && (chkEdge eps (t1p1, t1p2, t2p3)) then
false
else if (chkEdge eps (t1p2, t1p3, t2p1)) && (chkEdge eps (t1p2, t1p3, t2p2)) && (chkEdge eps (t1p2, t1p3, t2p3)) then
false
else if (chkEdge eps (t1p3, t1p1, t2p1)) && (chkEdge eps (t1p3, t1p1, t2p2)) && (chkEdge eps (t1p3, t1p1, t2p3)) then
false
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
else if (chkEdge eps (t2p1, t2p2, t1p1)) && (chkEdge eps (t2p1, t2p2, t1p2)) && (chkEdge eps (t2p1, t2p2, t1p3)) then
false
else if (chkEdge eps (t2p2, t2p3, t1p1)) && (chkEdge eps (t2p2, t2p3, t1p2)) && (chkEdge eps (t2p2, t2p3, t1p3)) then
false
else if (chkEdge eps (t2p3, t2p1, t1p1)) && (chkEdge eps (t2p3, t2p1, t1p2)) && (chkEdge eps (t2p3, t2p1, t1p3)) then
false
else
// The triangles overlap
true
let Print t1 t2 =
Console.WriteLine("{0} and\n{1}\n{2}\n", t1, t2, if TriTri2D 0.0 false true t1 t2 then "overlap" else "do not overlap")
[<EntryPoint>] let main _ =
let t1 = ((0.0, 0.0), (5.0, 0.0), (0.0, 5.0)) let t2 = ((0.0, 0.0), (5.0, 0.0), (0.0, 6.0)) Print t1 t2
let t3 = ((0.0, 0.0), (0.0, 5.0), (5.0, 0.0))
Console.WriteLine("{0} and\n{1}\n{2}\n", t3, t3, if TriTri2D 0.0 true true t3 t3 then "overlap (reversed)" else "do not overlap")
let t4 = ((0.0, 0.0), (5.0, 0.0), (0.0, 5.0)) let t5 = ((-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0)) Print t4 t5
let t6 = ((0.0, 0.0), (5.0, 0.0), (2.5, 5.0)) let t7 = ((0.0, 4.0), (2.5, -1.0), (5.0, 4.0)) Print t6 t7
let t8 = ((0.0, 0.0), (1.0, 1.0), (0.0, 2.0))
let t9 = ((2.0, 1.0), (3.0, 0.0), (3.0, 2.0))
Print t8 t9
let t10 = ((2.0, 1.0), (3.0, -2.0), (3.0, 4.0))
Print t8 t10
let t11 = ((0.0, 0.0), (1.0, 0.0), (0.0, 1.0))
let t12 = ((1.0, 0.0), (2.0, 0.0), (1.0, 1.1))
printfn "The following triangles which have only a single corner in contact, if boundary points collide"
Print t11 t12
Console.WriteLine("{0} and\n{1}\nwhich have only a single corner in contact, if boundary points do not collide\n{2}", t11, t12, if TriTri2D 0.0 false false t11 t12 then "overlap" else "do not overlap")
0 // return an integer exit code</lang>
- Output:
((0, 0), (5, 0), (0, 5)) and ((0, 0), (5, 0), (0, 6)) overlap ((0, 0), (0, 5), (5, 0)) and ((0, 0), (0, 5), (5, 0)) overlap (reversed) ((0, 0), (5, 0), (0, 5)) and ((-10, 0), (-5, 0), (-1, 6)) do not overlap ((0, 0), (5, 0), (2.5, 5)) and ((0, 4), (2.5, -1), (5, 4)) overlap ((0, 0), (1, 1), (0, 2)) and ((2, 1), (3, 0), (3, 2)) do not overlap ((0, 0), (1, 1), (0, 2)) and ((2, 1), (3, -2), (3, 4)) do not overlap The following triangles which have only a single corner in contact, if boundary points collide ((0, 0), (1, 0), (0, 1)) and ((1, 0), (2, 0), (1, 1.1)) overlap ((0, 0), (1, 0), (0, 1)) and ((1, 0), (2, 0), (1, 1.1)) which have only a single corner in contact, if boundary points do not collide do not overlap
FreeBASIC
<lang freebasic>#macro min(x,y)
Iif(x>y,y,x)
- endmacro
- macro max(x,y)
Iif(x>y,x,y)
- endmacro
type pnt 'typedef for a point
x as double y as double
end type
type edg 'typedef for an edge
p1 as pnt p2 as pnt
end type
function point_in_tri( r as pnt, a as pnt, b as pnt, c as pnt ) as boolean
'uses barycentric coordinates to determine whether point r is in the triangle defined by a, b, c dim as double k = ((b.y - c.y)*(a.x - c.x) + (c.x - b.x)*(a.y - c.y)) dim as double v = ((b.y - c.y)*(r.x - c.x) + (c.x - b.x)*(r.y - c.y)) / k dim as double w = ((c.y - a.y)*(r.x - c.x) + (a.x - c.x)*(r.y - c.y)) / k dim as double z = 1 - v- w if v<0 or v>1 then return false if w<0 or w>1 then return false if z<0 or z>1 then return false return true
end function
function bbox_overlap( a1 as pnt, a2 as pnt, b1 as pnt, b2 as pnt) as boolean
dim as double a1x = min(a1.x, a2.x), a1y = min(a1.y, a2.y) dim as double a2x = max(a1.x, a2.x), a2y = max(a1.y, a2.y) dim as double b1x = min(b1.x, b2.x), b1y = min(b1.y, b2.y) dim as double b2x = max(b1.x, b2.x), b2y = max(b1.y, b2.y) if a1x > b2x or b1x > a2x then return false if a1y > b2y or b2y > a2y then return false return true
end function
function ccw( a as pnt, b as pnt, c as pnt) as double
return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y)
end function
function line_intersect( a as edg, b as edg ) as boolean
if ccw(a.p1, a.p2, b.p1)*ccw(a.p1, a.p2, b.p2) > 0 then return false if ccw(b.p1, b.p2, a.p1)*ccw(b.p1, b.p2, a.p2) > 0 then return false if not bbox_overlap( a.p1, a.p2, b.p1, b.p2 ) then return false return true
end function
function triangle_overlap( a() as pnt, b() as pnt ) as boolean
'if two triangles overlap then either a corner of one triangle is inside
'the other OR an edge of one triangle intersects an edge of the other.
dim as uinteger i, j
dim as edg c, d
for i = 0 to 2
if point_in_tri( a(i), b(0), b(1), b(2) ) then return true
if point_in_tri( b(i), a(0), a(1), a(2) ) then return true
c.p1.x = a(i).x
c.p1.y = a(i).y
c.p2.x = a((i+1) mod 3).x
c.p2.y = a((i+1) mod 3).y
for j = 0 to 2
d.p1.x = b(i).x
d.p1.y = b(i).y
d.p2.x = b((i+1) mod 3).x
d.p2.y = b((i+1) mod 3).y
if line_intersect( c, d ) then return true
next j
next i
return 00
end function
data 0,0 , 5,0 , 0,5 , 0,0 , 5,0 , 0,6 data 0,0 , 0,5 , 5,0 , 0,0 , 0,5 , 5,0 data 0,0 , 5,0 , 0,5 , -10,0 , -5,0 , -1,6 data 0,0 , 5,0 , 2.5,5 , 0,4 , 2.5,-1 , 5,4 data 0,0 , 1,1 , 0,2 , 2,1 , 3,0 , 3,2 data 0,0 , 1,1 , 0,2 , 2,1 , 3,-2 , 3,4 data 0,0 , 1,0 , 0,1 , 1,0 , 2,0 , 1,1
dim as uinteger t, i dim as pnt a(0 to 2), b(0 to 2)
for t = 1 to 7
for i = 0 to 2
read a(i).x, a(i).y
next i
for i = 0 to 2
read b(i).x, b(i).y
next i
print triangle_overlap( a(), b() )
next t </lang>
- Output:
true true false true false false true
Go
<lang go>package main
import "fmt"
type point struct {
x, y float64
}
func (p point) String() string {
return fmt.Sprintf("(%.1f, %.1f)", p.x, p.y)
}
type triangle struct {
p1, p2, p3 point
}
func (t *triangle) String() string {
return fmt.Sprintf("Triangle %s, %s, %s", t.p1, t.p2, t.p3)
}
func (t *triangle) det2D() float64 {
return t.p1.x * (t.p2.y - t.p3.y) +
t.p2.x * (t.p3.y - t.p1.y) +
t.p3.x * (t.p1.y - t.p2.y)
}
func (t *triangle) checkTriWinding(allowReversed bool) {
detTri := t.det2D()
if detTri < 0.0 {
if allowReversed {
a := t.p3
t.p3 = t.p2
t.p2 = a
} else {
panic("Triangle has wrong winding direction.")
}
}
}
func boundaryCollideChk(t *triangle, eps float64) bool {
return t.det2D() < eps
}
func boundaryDoesntCollideChk(t *triangle, eps float64) bool {
return t.det2D() <= eps
}
func triTri2D(t1, t2 *triangle, eps float64, allowReversed, onBoundary bool) bool {
// Triangles must be expressed anti-clockwise. t1.checkTriWinding(allowReversed) t2.checkTriWinding(allowReversed)
// 'onBoundary' determines whether points on boundary are considered as colliding or not.
var chkEdge func (*triangle, float64) bool
if onBoundary {
chkEdge = boundaryCollideChk
} else {
chkEdge = boundaryDoesntCollideChk
}
lp1 := [3]point{t1.p1, t1.p2, t1.p3}
lp2 := [3]point{t2.p1, t2.p2, t2.p3}
// for each edge E of t1
for i := 0; i < 3; i++ {
j := (i + 1) % 3
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
tri1 := &triangle{lp1[i], lp1[j], lp2[0]}
tri2 := &triangle{lp1[i], lp1[j], lp2[1]}
tri3 := &triangle{lp1[i], lp1[j], lp2[2]}
if chkEdge(tri1, eps) && chkEdge(tri2, eps) && chkEdge(tri3, eps) {
return false
}
}
// for each edge E of t2
for i := 0; i < 3; i++ {
j := (i + 1) % 3
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
tri1 := &triangle{lp2[i], lp2[j], lp1[0]}
tri2 := &triangle{lp2[i], lp2[j], lp1[1]}
tri3 := &triangle{lp2[i], lp2[j], lp1[2]}
if chkEdge(tri1, eps) && chkEdge(tri2, eps) && chkEdge(tri3, eps) {
return false
}
}
// The triangles overlap. return true
}
func iff(cond bool, s1, s2 string) string {
if cond {
return s1
}
return s2
}
func main() {
t1 := &triangle{point{0.0, 0.0}, point{5.0, 0.0}, point{0.0, 5.0}}
t2 := &triangle{point{0.0, 0.0}, point{5.0, 0.0}, point{0.0, 6.0}}
fmt.Printf("%s and\n%s\n", t1, t2)
overlapping := triTri2D(t1, t2, 0.0, false, true)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
// Need to allow reversed for this pair to avoid panic.
t1 = &triangle{point{0.0, 0.0}, point{0.0, 5.0}, point{5.0, 0.0}}
t2 = t1
fmt.Printf("\n%s and\n%s\n", t1, t2)
overlapping = triTri2D(t1, t2, 0.0, true, true)
fmt.Println(iff(overlapping, "overlap (reversed)", "do not overlap"))
t1 = &triangle{point{0.0, 0.0}, point{5.0, 0.0}, point{0.0, 5.0}}
t2 = &triangle{point{-10.0, 0.0}, point{-5.0, 0.0}, point{-1.0, 6.0}}
fmt.Printf("\n%s and\n%s\n", t1, t2)
overlapping = triTri2D(t1, t2, 0.0, false, true)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
t1.p3 = point{2.5, 5.0}
t2 = &triangle{point{0.0, 4.0}, point{2.5, -1.0}, point{5.0, 4.0}}
fmt.Printf("\n%s and\n%s\n", t1, t2)
overlapping = triTri2D(t1, t2, 0.0, false, true)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
t1 = &triangle{point{0.0, 0.0}, point{1.0, 1.0}, point{0.0, 2.0}}
t2 = &triangle{point{2.0, 1.0}, point{3.0, 0.0}, point{3.0, 2.0}}
fmt.Printf("\n%s and\n%s\n", t1, t2)
overlapping = triTri2D(t1, t2, 0.0, false, true)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
t2 = &triangle{point{2.0, 1.0}, point{3.0, -2.0}, point{3.0, 4.0}}
fmt.Printf("\n%s and\n%s\n", t1, t2)
overlapping = triTri2D(t1, t2, 0.0, false, true)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
t1 = &triangle{point{0.0, 0.0}, point{1.0, 0.0}, point{0.0, 1.0}}
t2 = &triangle{point{1.0, 0.0}, point{2.0, 0.0}, point{1.0, 1.1}}
fmt.Printf("\n%s and\n%s\n", t1, t2)
println("which have only a single corner in contact, if boundary points collide")
overlapping = triTri2D(t1, t2, 0.0, false, true)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
fmt.Printf("\n%s and\n%s\n", t1, t2)
fmt.Println("which have only a single corner in contact, if boundary points do not collide")
overlapping = triTri2D(t1, t2, 0.0, false, false)
fmt.Println(iff(overlapping, "overlap", "do not overlap"))
}</lang>
- Output:
Same as Kotlin entry.
Groovy
<lang groovy>import java.util.function.BiFunction
class TriangleOverlap {
private static class Pair {
double first
double second
Pair(double first, double second) {
this.first = first
this.second = second
}
@Override
String toString() {
return String.format("(%s, %s)", first, second)
}
}
private static class Triangle {
Pair p1, p2, p3
Triangle(Pair p1, Pair p2, Pair p3) {
this.p1 = p1
this.p2 = p2
this.p3 = p3
}
@Override
String toString() {
return String.format("Triangle: %s, %s, %s", p1, p2, p3)
}
}
private static double det2D(Triangle t) {
Pair p1 = t.p1
Pair p2 = t.p2
Pair p3 = t.p3
return p1.first * (p2.second - p3.second) + p2.first * (p3.second - p1.second) + p3.first * (p1.second - p2.second)
}
private static void checkTriWinding(Triangle t, boolean allowReversed) {
double detTri = det2D(t)
if (detTri < 0.0) {
if (allowReversed) {
Pair a = t.p3
t.p3 = t.p2
t.p2 = a
} else throw new RuntimeException("Triangle has wrong winding direction")
}
}
private static boolean boundaryCollideChk(Triangle t, double eps) {
return det2D(t) < eps
}
private static boolean boundaryDoesntCollideChk(Triangle t, double eps) {
return det2D(t) <= eps
}
private static boolean triTri2D(Triangle t1, Triangle t2) {
return triTri2D(t1, t2, 0.0, false, true)
}
private static boolean triTri2D(Triangle t1, Triangle t2, double eps, boolean allowedReversed) {
return triTri2D(t1, t2, eps, allowedReversed, true)
}
private static boolean triTri2D(Triangle t1, Triangle t2, double eps, boolean allowedReversed, boolean onBoundary) {
// Triangles must be expressed anti-clockwise
checkTriWinding(t1, allowedReversed)
checkTriWinding(t2, allowedReversed)
// 'onBoundary' determines whether points on boundary are considered as colliding or not
BiFunction<Triangle, Double, Boolean> chkEdge = onBoundary ? TriangleOverlap.&boundaryCollideChk : TriangleOverlap.&boundaryDoesntCollideChk
Pair[] lp1 = [t1.p1, t1.p2, t1.p3]
Pair[] lp2 = [t2.p1, t2.p2, t2.p3]
// for each edge E of t1
for (int i = 0; i < 3; ++i) {
int j = (i + 1) % 3
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge.apply(new Triangle(lp1[i], lp1[j], lp2[0]), eps) &&
chkEdge.apply(new Triangle(lp1[i], lp1[j], lp2[1]), eps) &&
chkEdge.apply(new Triangle(lp1[i], lp1[j], lp2[2]), eps)) return false
}
// for each edge E of t2
for (int i = 0; i < 3; ++i) {
int j = (i + 1) % 3
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge.apply(new Triangle(lp2[i], lp2[j], lp1[0]), eps) &&
chkEdge.apply(new Triangle(lp2[i], lp2[j], lp1[1]), eps) &&
chkEdge.apply(new Triangle(lp2[i], lp2[j], lp1[2]), eps)) return false
}
// The triangles overlap
return true
}
static void main(String[] args) {
Triangle t1 = new Triangle(new Pair(0.0, 0.0), new Pair(5.0, 0.0), new Pair(0.0, 5.0))
Triangle t2 = new Triangle(new Pair(0.0, 0.0), new Pair(5.0, 0.0), new Pair(0.0, 6.0))
printf("%s and\n%s\n", t1, t2)
if (triTri2D(t1, t2)) {
println("overlap")
} else {
println("do not overlap")
}
// need to allow reversed for this pair to avoid exception
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(0.0, 5.0), new Pair(5.0, 0.0))
t2 = t1
printf("\n%s and\n%s\n", t1, t2)
if (triTri2D(t1, t2, 0.0, true)) {
println("overlap (reversed)")
} else {
println("do not overlap")
}
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(5.0, 0.0), new Pair(0.0, 5.0))
t2 = new Triangle(new Pair(-10.0, 0.0), new Pair(-5.0, 0.0), new Pair(-1.0, 6.0))
printf("\n%s and\n%s\n", t1, t2)
if (triTri2D(t1, t2)) {
println("overlap")
} else {
println("do not overlap")
}
t1.p3 = new Pair(2.5, 5.0)
t2 = new Triangle(new Pair(0.0, 4.0), new Pair(2.5, -1.0), new Pair(5.0, 4.0))
printf("\n%s and\n%s\n", t1, t2)
if (triTri2D(t1, t2)) {
println("overlap")
} else {
println("do not overlap")
}
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(1.0, 1.0), new Pair(0.0, 2.0))
t2 = new Triangle(new Pair(2.0, 1.0), new Pair(3.0, 0.0), new Pair(3.0, 2.0))
printf("\n%s and\n%s\n", t1, t2)
if (triTri2D(t1, t2)) {
println("overlap")
} else {
println("do not overlap")
}
t2 = new Triangle(new Pair(2.0, 1.0), new Pair(3.0, -2.0), new Pair(3.0, 4.0))
printf("\n%s and\n%s\n", t1, t2)
if (triTri2D(t1, t2)) {
println("overlap")
} else {
println("do not overlap")
}
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(1.0, 0.0), new Pair(0.0, 1.0))
t2 = new Triangle(new Pair(1.0, 0.0), new Pair(2.0, 0.0), new Pair(1.0, 1.1))
printf("\n%s and\n%s\n", t1, t2)
println("which have only a single corner in contact, if boundary points collide")
if (triTri2D(t1, t2)) {
println("overlap")
} else {
println("do not overlap")
}
printf("\n%s and\n%s\n", t1, t2)
println("which have only a single corner in contact, if boundary points do not collide")
if (triTri2D(t1, t2, 0.0, false, false)) {
println("overlap")
} else {
println("do not overlap")
}
}
}</lang>
- Output:
Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 6.0) overlap Triangle: (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) and Triangle: (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) overlap (reversed) Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle: (-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0) do not overlap Triangle: (0.0, 0.0), (5.0, 0.0), (2.5, 5.0) and Triangle: (0.0, 4.0), (2.5, -1.0), (5.0, 4.0) overlap Triangle: (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle: (2.0, 1.0), (3.0, 0.0), (3.0, 2.0) do not overlap Triangle: (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle: (2.0, 1.0), (3.0, -2.0), (3.0, 4.0) do not overlap Triangle: (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle: (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points collide overlap Triangle: (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle: (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
Java
<lang Java>import java.util.function.BiFunction;
public class TriangleOverlap {
private static class Pair {
double first;
double second;
Pair(double first, double second) {
this.first = first;
this.second = second;
}
@Override
public String toString() {
return String.format("(%s, %s)", first, second);
}
}
private static class Triangle {
Pair p1, p2, p3;
Triangle(Pair p1, Pair p2, Pair p3) {
this.p1 = p1;
this.p2 = p2;
this.p3 = p3;
}
@Override
public String toString() {
return String.format("Triangle: %s, %s, %s", p1, p2, p3);
}
}
private static double det2D(Triangle t) {
Pair p1 = t.p1;
Pair p2 = t.p2;
Pair p3 = t.p3;
return p1.first * (p2.second - p3.second)
+ p2.first * (p3.second - p1.second)
+ p3.first * (p1.second - p2.second);
}
private static void checkTriWinding(Triangle t, boolean allowReversed) {
double detTri = det2D(t);
if (detTri < 0.0) {
if (allowReversed) {
Pair a = t.p3;
t.p3 = t.p2;
t.p2 = a;
} else throw new RuntimeException("Triangle has wrong winding direction");
}
}
private static boolean boundaryCollideChk(Triangle t, double eps) {
return det2D(t) < eps;
}
private static boolean boundaryDoesntCollideChk(Triangle t, double eps) {
return det2D(t) <= eps;
}
private static boolean triTri2D(Triangle t1, Triangle t2) {
return triTri2D(t1, t2, 0.0, false, true);
}
private static boolean triTri2D(Triangle t1, Triangle t2, double eps, boolean allowedReversed) {
return triTri2D(t1, t2, eps, allowedReversed, true);
}
private static boolean triTri2D(Triangle t1, Triangle t2, double eps, boolean allowedReversed, boolean onBoundary) {
// Triangles must be expressed anti-clockwise
checkTriWinding(t1, allowedReversed);
checkTriWinding(t2, allowedReversed);
// 'onBoundary' determines whether points on boundary are considered as colliding or not
BiFunction<Triangle, Double, Boolean> chkEdge = onBoundary ? TriangleOverlap::boundaryCollideChk : TriangleOverlap::boundaryDoesntCollideChk;
Pair[] lp1 = new Pair[]{t1.p1, t1.p2, t1.p3};
Pair[] lp2 = new Pair[]{t2.p1, t2.p2, t2.p3};
// for each edge E of t1
for (int i = 0; i < 3; ++i) {
int j = (i + 1) % 3;
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge.apply(new Triangle(lp1[i], lp1[j], lp2[0]), eps) &&
chkEdge.apply(new Triangle(lp1[i], lp1[j], lp2[1]), eps) &&
chkEdge.apply(new Triangle(lp1[i], lp1[j], lp2[2]), eps)) return false;
}
// for each edge E of t2
for (int i = 0; i < 3; ++i) {
int j = (i + 1) % 3;
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge.apply(new Triangle(lp2[i], lp2[j], lp1[0]), eps) &&
chkEdge.apply(new Triangle(lp2[i], lp2[j], lp1[1]), eps) &&
chkEdge.apply(new Triangle(lp2[i], lp2[j], lp1[2]), eps)) return false;
}
// The triangles overlap
return true;
}
public static void main(String[] args) {
Triangle t1 = new Triangle(new Pair(0.0, 0.0), new Pair(5.0, 0.0), new Pair(0.0, 5.0));
Triangle t2 = new Triangle(new Pair(0.0, 0.0), new Pair(5.0, 0.0), new Pair(0.0, 6.0));
System.out.printf("%s and\n%s\n", t1, t2);
if (triTri2D(t1, t2)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
// need to allow reversed for this pair to avoid exception
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(0.0, 5.0), new Pair(5.0, 0.0));
t2 = t1;
System.out.printf("\n%s and\n%s\n", t1, t2);
if (triTri2D(t1, t2, 0.0, true)) {
System.out.println("overlap (reversed)");
} else {
System.out.println("do not overlap");
}
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(5.0, 0.0), new Pair(0.0, 5.0));
t2 = new Triangle(new Pair(-10.0, 0.0), new Pair(-5.0, 0.0), new Pair(-1.0, 6.0));
System.out.printf("\n%s and\n%s\n", t1, t2);
if (triTri2D(t1, t2)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
t1.p3 = new Pair(2.5, 5.0);
t2 = new Triangle(new Pair(0.0, 4.0), new Pair(2.5, -1.0), new Pair(5.0, 4.0));
System.out.printf("\n%s and\n%s\n", t1, t2);
if (triTri2D(t1, t2)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(1.0, 1.0), new Pair(0.0, 2.0));
t2 = new Triangle(new Pair(2.0, 1.0), new Pair(3.0, 0.0), new Pair(3.0, 2.0));
System.out.printf("\n%s and\n%s\n", t1, t2);
if (triTri2D(t1, t2)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
t2 = new Triangle(new Pair(2.0, 1.0), new Pair(3.0, -2.0), new Pair(3.0, 4.0));
System.out.printf("\n%s and\n%s\n", t1, t2);
if (triTri2D(t1, t2)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
t1 = new Triangle(new Pair(0.0, 0.0), new Pair(1.0, 0.0), new Pair(0.0, 1.0));
t2 = new Triangle(new Pair(1.0, 0.0), new Pair(2.0, 0.0), new Pair(1.0, 1.1));
System.out.printf("\n%s and\n%s\n", t1, t2);
System.out.println("which have only a single corner in contact, if boundary points collide");
if (triTri2D(t1, t2)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
System.out.printf("\n%s and\n%s\n", t1, t2);
System.out.println("which have only a single corner in contact, if boundary points do not collide");
if (triTri2D(t1, t2, 0.0, false, false)) {
System.out.println("overlap");
} else {
System.out.println("do not overlap");
}
}
}</lang>
- Output:
Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 6.0) overlap Triangle: (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) and Triangle: (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) overlap (reversed) Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle: (-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0) do not overlap Triangle: (0.0, 0.0), (5.0, 0.0), (2.5, 5.0) and Triangle: (0.0, 4.0), (2.5, -1.0), (5.0, 4.0) overlap Triangle: (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle: (2.0, 1.0), (3.0, 0.0), (3.0, 2.0) do not overlap Triangle: (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle: (2.0, 1.0), (3.0, -2.0), (3.0, 4.0) do not overlap Triangle: (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle: (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points collide overlap Triangle: (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle: (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
Julia
Module: <lang julia>module Triangles
using LinearAlgebra
export AntiClockwise, Both, StrictCheck, MildCheck
abstract type Widing end struct AntiClockwise <: Widing end struct Both <: Widing end
function _check_triangle_winding(t, widing::AntiClockwise)
trisq = fill!(Matrix{eltype(t)}(undef, 3, 3), 1)
trisq[:, 1:2] .= t
det(trisq) < 0 && throw(ArgumentError("triangle has wrong winding direction"))
return trisq
end
function _check_triangle_winding(t, widing::Both)
trisq = fill!(Matrix{eltype(t)}(undef, 3, 3), 1)
trisq[:, 1:2] .= t
if det(trisq) < 0
tmp = trisq[2, :]
trisq[2, :] .= trisq[1, :]
trisq[1, :] .= tmp
end
return trisq
end
abstract type OnBoundaryCheck end struct StrictCheck <: OnBoundaryCheck end struct MildCheck <: OnBoundaryCheck end
_checkedge(::StrictCheck, x, ϵ) = det(x) < ϵ _checkedge(::MildCheck, x, ϵ) = det(x) ≤ ϵ
function overlap(T₁, T₂, onboundary::OnBoundaryCheck=MildCheck(),; ϵ=0.0, widing::Widing=AntiClockwise())
# Trangles must be expressed anti-clockwise T₁ = _check_triangle_winding(T₁, widing) T₂ = _check_triangle_winding(T₂, widing)
edge = similar(T₁)
for (A, B) in ((T₁, T₂), (T₂, T₁)), i in 1:3
circshift!(edge, A, (i, 0))
@views if all(_checkedge(onboundary, vcat(edge[1:2, :], B[r, :]'), ϵ) for r in 1:3)
return false
end
end
return true
end
end # module Triangles</lang>
Main: <lang julia>using .Triangles
t1 = [0 0; 5 0; 0 5] t2 = [0 0; 5 0; 0 6] @show Triangles.overlap(t1, t2)
t1 = [0 0; 0 5; 5 0] t2 = [0 0; 0 6; 5 0] @show Triangles.overlap(t1, t2, widing=Both())
t1 = [0 0; 5 0; 0 5] t2 = [-10 0; -5 0; -1 6] @show Triangles.overlap(t1, t2)
t1 = [0 0; 5 0; 2.5 5] t2 = [0 4; 2.5 -1; 5 4] @show Triangles.overlap(t1, t2)
t1 = [0 0; 1 1; 0 2] t2 = [2 1; 3 0; 3 2] @show Triangles.overlap(t1, t2)
t1 = [0 0; 1 1; 0 2] t2 = [2 1; 3 -2; 3 4] @show Triangles.overlap(t1, t2)
- Barely touching
t1 = [0 0; 1 0; 0 1] t2 = [1 0; 2 0; 1 1] @show Triangles.overlap(t1, t2, StrictCheck())
- Barely touching
t1 = [0 0; 1 0; 0 1] t2 = [1 0; 2 0; 1 1] @show Triangles.overlap(t1, t2, MildCheck())</lang>
- Output:
Triangles.overlap(t1, t2) = true Triangles.overlap(t1, t2, widing=Both()) = true Triangles.overlap(t1, t2) = false Triangles.overlap(t1, t2) = true Triangles.overlap(t1, t2) = false Triangles.overlap(t1, t2) = false Triangles.overlap(t1, t2, StrictCheck()) = true Triangles.overlap(t1, t2, MildCheck()) = false
Kotlin
<lang scala>// version 1.1.0
typealias Point = Pair<Double, Double>
data class Triangle(var p1: Point, var p2: Point, var p3: Point) {
override fun toString() = "Triangle: $p1, $p2, $p3"
}
fun det2D(t: Triangle): Double {
val (p1, p2, p3) = t
return p1.first * (p2.second - p3.second) +
p2.first * (p3.second - p1.second) +
p3.first * (p1.second - p2.second)
}
fun checkTriWinding(t: Triangle, allowReversed: Boolean) {
val detTri = det2D(t)
if (detTri < 0.0) {
if (allowReversed) {
val a = t.p3
t.p3 = t.p2 t.p2 = a
}
else throw RuntimeException("Triangle has wrong winding direction")
}
}
fun boundaryCollideChk(t: Triangle, eps: Double) = det2D(t) < eps
fun boundaryDoesntCollideChk(t: Triangle, eps: Double) = det2D(t) <= eps
fun triTri2D(t1: Triangle, t2: Triangle, eps: Double = 0.0,
allowReversed: Boolean = false, onBoundary: Boolean = true): Boolean {
// Triangles must be expressed anti-clockwise
checkTriWinding(t1, allowReversed)
checkTriWinding(t2, allowReversed)
// 'onBoundary' determines whether points on boundary are considered as colliding or not
val chkEdge = if (onBoundary) ::boundaryCollideChk else ::boundaryDoesntCollideChk
val lp1 = listOf(t1.p1, t1.p2, t1.p3)
val lp2 = listOf(t2.p1, t2.p2, t2.p3)
// for each edge E of t1
for (i in 0 until 3) {
val j = (i + 1) % 3
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(Triangle(lp1[i], lp1[j], lp2[0]), eps) &&
chkEdge(Triangle(lp1[i], lp1[j], lp2[1]), eps) &&
chkEdge(Triangle(lp1[i], lp1[j], lp2[2]), eps)) return false
}
// for each edge E of t2
for (i in 0 until 3) {
val j = (i + 1) % 3
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(Triangle(lp2[i], lp2[j], lp1[0]), eps) &&
chkEdge(Triangle(lp2[i], lp2[j], lp1[1]), eps) &&
chkEdge(Triangle(lp2[i], lp2[j], lp1[2]), eps)) return false
}
// The triangles overlap return true
}
fun main(args: Array<String>) {
var t1 = Triangle(0.0 to 0.0, 5.0 to 0.0, 0.0 to 5.0)
var t2 = Triangle(0.0 to 0.0, 5.0 to 0.0, 0.0 to 6.0)
println("$t1 and\n$t2")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
// need to allow reversed for this pair to avoid exception
t1 = Triangle(0.0 to 0.0, 0.0 to 5.0, 5.0 to 0.0)
t2 = t1
println("\n$t1 and\n$t2")
println(if (triTri2D(t1, t2, 0.0, true)) "overlap (reversed)" else "do not overlap")
t1 = Triangle(0.0 to 0.0, 5.0 to 0.0, 0.0 to 5.0)
t2 = Triangle(-10.0 to 0.0, -5.0 to 0.0, -1.0 to 6.0)
println("\n$t1 and\n$t2")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t1.p3 = 2.5 to 5.0
t2 = Triangle(0.0 to 4.0, 2.5 to -1.0, 5.0 to 4.0)
println("\n$t1 and\n$t2")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t1 = Triangle(0.0 to 0.0, 1.0 to 1.0, 0.0 to 2.0)
t2 = Triangle(2.0 to 1.0, 3.0 to 0.0, 3.0 to 2.0)
println("\n$t1 and\n$t2")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t2 = Triangle(2.0 to 1.0, 3.0 to -2.0, 3.0 to 4.0)
println("\n$t1 and\n$t2")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t1 = Triangle(0.0 to 0.0, 1.0 to 0.0, 0.0 to 1.0)
t2 = Triangle(1.0 to 0.0, 2.0 to 0.0, 1.0 to 1.1)
println("\n$t1 and\n$t2")
println("which have only a single corner in contact, if boundary points collide")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
println("\n$t1 and\n$t2")
println("which have only a single corner in contact, if boundary points do not collide")
println(if (triTri2D(t1, t2, 0.0, false, false)) "overlap" else "do not overlap")
}</lang>
- Output:
Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 6.0) overlap Triangle: (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) and Triangle: (0.0, 0.0), (0.0, 5.0), (5.0, 0.0) overlap (reversed) Triangle: (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle: (-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0) do not overlap Triangle: (0.0, 0.0), (5.0, 0.0), (2.5, 5.0) and Triangle: (0.0, 4.0), (2.5, -1.0), (5.0, 4.0) overlap Triangle: (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle: (2.0, 1.0), (3.0, 0.0), (3.0, 2.0) do not overlap Triangle: (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle: (2.0, 1.0), (3.0, -2.0), (3.0, 4.0) do not overlap Triangle: (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle: (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points collide overlap Triangle: (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle: (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
Lambdatalk
<lang scheme> Here we present a rasterized version based on a single function "isInside".
1) isInside
Given A, B, C, P is in the triangle ABC if the three cross-products PA^PB, PB^PC and PC^PA are of equal sign.
{def isInside
{lambda {:a :b :c :p}
{let { {:ax {car :a}} {:ay {cdr :a}}
{:bx {car :b}} {:by {cdr :b}}
{:cx {car :c}} {:cy {cdr :c}}
{:px {car :p}} {:py {cdr :p}}
} {let { {:w1 {- {* {- :px :ax} {- :cy :ay}}
{* {- :cx :ax} {- :py :ay}} }}
{:w2 {- {* {- :px :bx} {- :ay :by}}
{* {- :ax :bx} {- :py :by}} }}
{:w3 {- {* {- :px :cx} {- :by :cy}}
{* {- :bx :cx} {- :py :cy}} }}
} {or {and {>= :w1 0} {>= :w2 0} {>= :w3 0}}
{and {< :w1 0} {< :w2 0} {< :w3 0}}} }}}}
-> isInside
2) overlapping
For every points in the rectangle surrounding two given triangles we compute the number of points inside both. If it is null they don't overlap.
{def overlap
{def overlap.row
{lambda {:p0 :p1 :p2 :q0 :q1 :q2 :w :h :y}
{S.map {{lambda {:p0 :p1 :p2 :q0 :q1 :q2 :qp}
{if {and {isInside :p0 :p1 :p2 :qp}
{isInside :q0 :q1 :q2 :qp}}
then x else}} :p0 :p1 :p2 :q0 :q1 :q2}
{S.map {{lambda {:y :x} {cons :x :y}} :y}
{S.serie :w :h} }}}}
{lambda {:p0 :p1 :p2 :q0 :q1 :q2 :w :h}
{S.length {S.map {overlap.row :p0 :p1 :p2 :q0 :q1 :q2 :w :h}
{S.serie :w :h}} }}}
-> overlap
Given coordonnees will just be scaled to become integers, here miltiplied by 10
{overlap {cons 0 0} {cons 50 0} {cons 0 50}
{cons 0 0} {cons 50 0} {cons 0 60} 0 60} -> 1326
{overlap {cons 0 0} {cons 0 50} {cons 50 0}
{cons 0 0} {cons 0 50} {cons 50 0} 0 50} -> 1176
{overlap {cons 0 0} {cons 50 0} {cons 0 50}
{cons -100 0} {cons -50 0} {cons -10 60} 100 60} -> 0
{overlap {cons 0 0} {cons 50 0} {cons 25 50}
{cons 0 40} {cons 25 -10} {cons 50 40} -10 50} -> 831
{overlap {cons 0 0} {cons 10 10} {cons 0 20}
{cons 20 10} {cons 30 0} {cons 30 20} 0 20} -> 0
{overlap {cons 0 0} {cons 10 10} {cons 0 20}
{cons 20 10} {cons 30 -20} {cons 40 40} -20 40} -> 0
{overlap {cons 0 0} {cons 10 0} {cons 0 10}
{cons 10 0} {cons 20 0} {cons 10 10} 0 20} -> 1
3) plot
The first triangle is plotted with 1s, the second with 2s,
the intersection with 3s, else with dots.
{def plot
{def plot.row
{lambda {:p0 :p1 :p2 :q0 :q1 :q2 :w :h :y}
{br}{S.replace \s by in
{S.map {{lambda {:p0 :p1 :p2 :q0 :q1 :q2 :qp}
{let { {:isinp {isInside :p0 :p1 :p2 :qp}}
{:isinq {isInside :q0 :q1 :q2 :qp}}
} {if {and :isinp :isinq} then 3
else {if :isnp then 1
else {if :isnq then 2
else .}}} }} :p0 :p1 :p2 :q0 :q1 :q2}
{S.map {{lambda {:y :x} {cons :x :y}} :y}
{S.serie :w :h} }}} }}
{lambda {:p0 :p1 :p2 :q0 :q1 :q2 :w :h}
{S.map {plot.row :p0 :p1 :p2 :q0 :q1 :q2 :w :h}
{S.serie :w :h}} }}
-> plot
{plot {cons 0 0} {cons 30 0} {cons 30 30}
{cons 5 10} {cons 25 10} {cons 5 25} 0 30}
->
1111111111111111111111111111111 .111111111111111111111111111111 ..11111111111111111111111111111 ...1111111111111111111111111111 ....111111111111111111111111111 .....11111111111111111111111111 ......1111111111111111111111111 .......111111111111111111111111 ........11111111111111111111111 .........1111111111111111111111 .....22222333333333333333311111 .....22222233333333333331111111 .....22222223333333333311111111 .....22222222333333333111111111 .....22222222233333311111111111 .....22222222223333111111111111 .....22222222222331111111111111 .....22222222222.11111111111111 .....2222222222...1111111111111 .....222222222.....111111111111 .....2222222........11111111111 .....222222..........1111111111 .....22222............111111111 .....222...............11111111 .....22.................1111111 .....2...................111111 ..........................11111 ...........................1111 ............................111 .............................11 ..............................1 </lang>
Lua
<lang lua>function det2D(p1,p2,p3)
return p1.x * (p2.y - p3.y)
+ p2.x * (p3.y - p1.y)
+ p3.x * (p1.y - p2.y)
end
function checkTriWinding(p1,p2,p3,allowReversed)
local detTri = det2D(p1,p2,p3)
if detTri < 0.0 then
if allowReversed then
local t = p3
p3 = p2
p2 = t
else
error("triangle has wrong winding direction")
end
end
return nil
end
function boundaryCollideChk(p1,p2,p3,eps)
return det2D(p1,p2,p3) < eps
end
function boundaryDoesntCollideChk(p1,p2,p3,eps)
return det2D(p1,p2,p3) <= eps
end
function triTri2D(t1,t2,eps,allowReversed,onBoundary)
eps = eps or 0.0 allowReversed = allowReversed or false onBoundary = onBoundary or true
-- triangles must be expressed anti-clockwise checkTriWinding(t1[1], t1[2], t1[3], allowReversed) checkTriWinding(t2[1], t2[2], t2[3], allowReversed)
local chkEdge
if onBoundary then
-- points on the boundary are considered as colliding
chkEdge = boundaryCollideChk
else
-- points on the boundary are not considered as colliding
chkEdge = boundaryDoesntCollideChk
end
-- for edge E of triangle 1
for i=0,2 do
local j = (i+1)%3
-- check all points of triangle 2 lay on the external side of the edge E.
-- If they do, the triangles do not collide
if chkEdge(t1[i+1], t1[j+1], t2[1], eps) and
chkEdge(t1[i+1], t1[j+1], t2[2], eps) and
chkEdge(t1[i+1], t1[j+1], t2[3], eps) then
return false
end
end
-- for edge E of triangle 2
for i=0,2 do
local j = (i+1)%3
-- check all points of triangle 1 lay on the external side of the edge E.
-- If they do, the triangles do not collide
if chkEdge(t2[i+1], t2[j+1], t1[1], eps) and
chkEdge(t2[i+1], t2[j+1], t1[2], eps) and
chkEdge(t2[i+1], t2[j+1], t1[3], eps) then
return false
end
end
-- the triangles collide return true
end
function formatTri(t)
return "Triangle: ("..t[1].x..", "..t[1].y
.."), ("..t[2].x..", "..t[2].y
.."), ("..t[3].x..", "..t[3].y..")"
end
function overlap(t1,t2,eps,allowReversed,onBoundary)
if triTri2D(t1,t2,eps,allowReversed,onBoundary) then
return "overlap\n"
else
return "do not overlap\n"
end
end
-- Main local t1 = {{x=0,y=0},{x=5,y=0},{x=0,y=5}} local t2 = {{x=0,y=0},{x=5,y=0},{x=0,y=6}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2))
t1 = {{x=0,y=0},{x=0,y=5},{x=5,y=0}} t2 = {{x=0,y=0},{x=0,y=5},{x=5,y=0}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2,0.0,true))
t1 = {{x=0,y=0},{x=5,y=0},{x=0,y=5}} t2 = {{x=-10,y=0},{x=-5,y=0},{x=-1,y=6}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2))
t1 = {{x=0,y=0},{x=5,y=0},{x=2.5,y=5}} t2 = {{x=0,y=4},{x=2.5,y=-1},{x=5,y=4}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2))
t1 = {{x=0,y=0},{x=1,y=1},{x=0,y=2}} t2 = {{x=2,y=1},{x=3,y=0},{x=3,y=2}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2))
t1 = {{x=0,y=0},{x=1,y=1},{x=0,y=2}} t2 = {{x=2,y=1},{x=3,y=-2},{x=3,y=4}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2))
-- Barely touching t1 = {{x=0,y=0},{x=1,y=0},{x=0,y=1}} t2 = {{x=1,y=0},{x=2,y=0},{x=1,y=1}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2,0.0,false,true))
-- Barely touching local t1 = {{x=0,y=0},{x=1,y=0},{x=0,y=1}} local t2 = {{x=1,y=0},{x=2,y=0},{x=1,y=1}} print(formatTri(t1).." and") print(formatTri(t2)) print(overlap(t1,t2,0.0,false,false))</lang>
- Output:
Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (0, 0), (5, 0), (0, 6) overlap Triangle: (0, 0), (0, 5), (5, 0) and Triangle: (0, 0), (0, 5), (5, 0) overlap Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (-10, 0), (-5, 0), (-1, 6) do not overlap Triangle: (0, 0), (5, 0), (2.5, 5) and Triangle: (0, 4), (2.5, -1), (5, 4) overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, 0), (3, 2) do not overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, -2), (3, 4) do not overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1) overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1) overlap
Modula-2
<lang modula2>MODULE Overlap; FROM EXCEPTIONS IMPORT AllocateSource,ExceptionSource,GetMessage,RAISE; FROM LongStr IMPORT RealToFixed; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
TYPE
Point = RECORD
x,y : LONGREAL;
END;
Triangle = RECORD
p1,p2,p3 : Point;
END;
VAR
TextWinExSrc : ExceptionSource;
PROCEDURE WritePoint(p : Point); VAR buf : ARRAY[0..31] OF CHAR; BEGIN
WriteString("(");
RealToFixed(p.x, 2, buf);
WriteString(buf);
WriteString(", ");
RealToFixed(p.y, 2, buf);
WriteString(buf);
WriteString(")")
END WritePoint;
PROCEDURE WriteTriangle(t : Triangle); BEGIN
WriteString("Triangle: ");
WritePoint(t.p1);
WriteString(", ");
WritePoint(t.p2);
WriteString(", ");
WritePoint(t.p3)
END WriteTriangle;
PROCEDURE Det2D(p1,p2,p3 : Point) : LONGREAL; BEGIN
RETURN p1.x * (p2.y - p3.y)
+ p2.x * (p3.y - p1.y)
+ p3.x * (p1.y - p2.y)
END Det2D;
PROCEDURE CheckTriWinding(VAR p1,p2,p3 : Point; allowReversed : BOOLEAN); VAR
detTri : LONGREAL; t : Point;
BEGIN
detTri := Det2D(p1, p2, p3);
IF detTri < 0.0 THEN
IF allowReversed THEN
t := p3;
p3 := p2;
p2 := t
ELSE
RAISE(TextWinExSrc, 0, "triangle has wrong winding direction")
END
END
END CheckTriWinding;
PROCEDURE BoundaryCollideChk(p1,p2,p3 : Point; eps : LONGREAL) : BOOLEAN; BEGIN
RETURN Det2D(p1, p2, p3) < eps
END BoundaryCollideChk;
PROCEDURE BoundaryDoesntCollideChk(p1,p2,p3 : Point; eps : LONGREAL) : BOOLEAN; BEGIN
RETURN Det2D(p1, p2, p3) <= eps
END BoundaryDoesntCollideChk;
PROCEDURE TriTri2D(t1,t2 : Triangle; eps : LONGREAL; allowReversed,onBoundary : BOOLEAN) : BOOLEAN; TYPE
Points = ARRAY[0..2] OF Point;
VAR
chkEdge : PROCEDURE(Point, Point, Point, LONGREAL) : BOOLEAN; lp1,lp2 : Points; i,j : CARDINAL;
BEGIN
(* Triangles must be expressed anti-clockwise *) CheckTriWinding(t1.p1, t1.p2, t1.p3, allowReversed); CheckTriWinding(t2.p1, t2.p2, t2.p3, allowReversed);
(* 'onBoundary' determines whether points on boundary are considered as colliding or not *)
IF onBoundary THEN
chkEdge := BoundaryCollideChk
ELSE
chkEdge := BoundaryDoesntCollideChk
END;
lp1 := Points{t1.p1, t1.p2, t1.p3};
lp2 := Points{t2.p1, t2.p2, t2.p3};
(* for each edge E of t1 *)
FOR i:=0 TO 2 DO
j := (i + 1) MOD 3;
(* Check all points of t2 lay on the external side of edge E.
If they do, the triangles do not overlap. *)
IF chkEdge(lp1[i], lp1[j], lp2[0], eps)
AND chkEdge(lp1[i], lp1[j], lp2[1], eps)
AND chkEdge(lp1[i], lp1[j], lp2[2], eps)
THEN
RETURN FALSE
END
END;
(* for each edge E of t2 *)
FOR i:=0 TO 2 DO
j := (i + 1) MOD 3;
(* Check all points of t1 lay on the external side of edge E.
If they do, the triangles do not overlap. *)
IF chkEdge(lp2[i], lp2[j], lp1[0], eps)
AND chkEdge(lp2[i], lp2[j], lp1[1], eps)
AND chkEdge(lp2[i], lp2[j], lp1[2], eps)
THEN
RETURN FALSE
END
END;
(* The triangles overlap *) RETURN TRUE
END TriTri2D;
PROCEDURE CheckOverlap(t1,t2 : Triangle; eps : LONGREAL; allowReversed,onBoundary : BOOLEAN); BEGIN
WriteTriangle(t1);
WriteString(" and");
WriteLn;
WriteTriangle(t2);
WriteLn;
IF TriTri2D(t1, t2, eps, allowReversed, onBoundary) THEN
WriteString("overlap")
ELSE
WriteString("do not overlap")
END;
WriteLn
END CheckOverlap;
(* main *) VAR
t1,t2 : Triangle;
BEGIN
t1 := Triangle{{0.0,0.0},{5.0,0.0},{0.0,5.0}};
t2 := Triangle{{0.0,0.0},{5.0,0.0},{0.0,6.0}};
CheckOverlap(t1, t2, 0.0, FALSE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{0.0,5.0},{5.0,0.0}};
t2 := Triangle{{0.0,0.0},{0.0,5.0},{5.0,0.0}};
CheckOverlap(t1, t2, 0.0, TRUE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{5.0,0.0},{0.0,5.0}};
t2 := Triangle{{-10.0,0.0},{-5.0,0.0},{-1.0,6.0}};
CheckOverlap(t1, t2, 0.0, FALSE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{5.0,0.0},{2.5,5.0}};
t2 := Triangle{{0.0,4.0},{2.5,-1.0},{5.0,4.0}};
CheckOverlap(t1, t2, 0.0, FALSE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{1.0,1.0},{0.0,2.0}};
t2 := Triangle{{2.0,1.0},{3.0,0.0},{3.0,2.0}};
CheckOverlap(t1, t2, 0.0, FALSE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{1.0,1.0},{0.0,2.0}};
t2 := Triangle{{2.0,1.0},{3.0,-2.0},{3.0,4.0}};
CheckOverlap(t1, t2, 0.0, FALSE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{1.0,0.0},{0.0,1.0}};
t2 := Triangle{{1.0,0.0},{2.0,0.0},{1.0,1.1}};
CheckOverlap(t1, t2, 0.0, FALSE, TRUE);
WriteLn;
t1 := Triangle{{0.0,0.0},{1.0,0.0},{0.0,1.0}};
t2 := Triangle{{1.0,0.0},{2.0,0.0},{1.0,1.1}};
CheckOverlap(t1, t2, 0.0, FALSE, FALSE);
WriteLn;
ReadChar
END Overlap.</lang>
Nim
<lang Nim>import strformat
type Point = tuple[x, y: float]
type Triangle = array[3, Point]
func `$`(p: Point): string =
fmt"({p.x:.1f}, {p.y:.1f})"
func `$`(t: Triangle): string =
fmt"Triangle {t[0]}, {t[1]}, {t[2]}"
func det2D(t: Triangle): float =
t[0].x * (t[1].y - t[2].y) + t[1].x * (t[2].y - t[0].y) + t[2].x * (t[0].y - t[1].y)
func checkTriWinding(t: var Triangle; allowReversed: bool) =
let det = t.det2D()
if det < 0:
if allowReversed:
swap t[1], t[2]
else:
raise newException(ValueError, "Triangle has wrong winding direction.")
func boundaryCollideChk(t: Triangle; eps: float): bool =
t.det2D() < eps
func boundaryDoesntCollideChk(t: Triangle; eps: float): bool =
t.det2D() <= eps
func triTri2D(t1, t2: var Triangle; eps = 0.0;
allowReversed = false; onBoundary = true): bool =
# Triangles must be expressed anti-clockwise. t1.checkTriWinding(allowReversed) t2.checkTriWinding(allowReversed)
# "onBoundary" determines whether points on boundary are considered as colliding or not. let chkEdge = if onBoundary: boundaryCollideChk else: boundaryDoesntCollideChk
# For each edge E of t1.
for i in 0..2:
let j = (i + 1) mod 3
# Check that all points of t2 lay on the external side of edge E.
# If they do, the triangles do not overlap.
if chkEdge([t1[i], t1[j], t2[0]], eps) and
chkEdge([t1[i], t1[j], t2[1]], eps) and
chkEdge([t1[i], t1[j], t2[2]], eps):
return false
# For each edge E of t2.
for i in 0..2:
let j = (i + 1) mod 3
# Check that all points of t1 lay on the external side of edge E.
# If they do, the triangles do not overlap.
if chkEdge([t2[i], t2[j], t1[0]], eps) and
chkEdge([t2[i], t2[j], t1[1]], eps) and
chkEdge([t2[i], t2[j], t1[2]], eps):
return false
# The triangles overlap. result = true
when isMainModule:
var t1: Triangle = [(0.0, 0.0), (5.0, 0.0), (0.0, 5.0)] var t2: Triangle = [(0.0, 0.0), (5.0, 0.0), (0.0, 6.0)] echo t1, " and\n", t2 var overlapping = triTri2D(t1, t2, 0, false, true) echo if overlapping: "overlap\n" else: "do not overlap\n"
# Need to allow reversed for this pair to avoid exception. t1 = [(0.0, 0.0), (5.0, 0.0), (5.0, 0.0)] t2 = t1 echo t1, " and\n", t2 overlapping = triTri2D(t1, t2, 0, true, true) echo if overlapping: "overlap (reversed)\n" else: "do not overlap\n"
t1 = [(0.0, 0.0), (5.0, 0.0), (0.0, 5.0)] t2 = [(-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0)] echo t1, " and\n", t2 overlapping = triTri2D(t1, t2, 0, false, true) echo if overlapping: "overlap\n" else: "do not overlap\n"
t1[2] = (2.5, 5.0) t2 = [(0.0, 4.0), (2.5, -1.0), (5.0, 4.0)] echo t1, " and\n", t2 overlapping = triTri2D(t1, t2, 0, false, true) echo if overlapping: "overlap\n" else: "do not overlap\n"
t1 = [(0.0, 0.0), (1.0, 1.0), (0.0, 2.0)] t2 = [(2.0, 1.0), (3.0, 0.0), (3.0, 2.0)] echo t1, " and\n", t2 overlapping = triTri2D(t1, t2, 0, false, true) echo if overlapping: "overlap\n" else: "do not overlap\n"
t2 = [(2.0, 1.0), (3.0, -2.0), (3.0, 4.0)] echo t1, " and\n", t2 overlapping = triTri2D(t1, t2, 0, false, true) echo if overlapping: "overlap\n" else: "do not overlap\n"
t1 = [(0.0, 0.0), (1.0, 0.0), (0.0, 1.0)] t2 = [(1.0, 0.0), (2.0, 0.0), (1.0, 1.1)] echo t1, " and\n", t2 echo "which have only a single corner in contact, if boundary points collide" overlapping = triTri2D(t1, t2, 0, false, true) echo if overlapping: "overlap\n" else: "do not overlap\n"
echo t1, " and\n", t2 echo "which have only a single corner in contact, if boundary points do not collide" overlapping = triTri2D(t1, t2, 0, false, false) echo if overlapping: "overlap\n" else: "do not overlap\n"</lang>
- Output:
Triangle (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle (0.0, 0.0), (5.0, 0.0), (0.0, 6.0) overlap Triangle (0.0, 0.0), (5.0, 0.0), (5.0, 0.0) and Triangle (0.0, 0.0), (5.0, 0.0), (5.0, 0.0) overlap (reversed) Triangle (0.0, 0.0), (5.0, 0.0), (0.0, 5.0) and Triangle (-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0) do not overlap Triangle (0.0, 0.0), (5.0, 0.0), (2.5, 5.0) and Triangle (0.0, 4.0), (2.5, -1.0), (5.0, 4.0) overlap Triangle (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle (2.0, 1.0), (3.0, 0.0), (3.0, 2.0) do not overlap Triangle (0.0, 0.0), (1.0, 1.0), (0.0, 2.0) and Triangle (2.0, 1.0), (3.0, -2.0), (3.0, 4.0) do not overlap Triangle (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points collide overlap Triangle (0.0, 0.0), (1.0, 0.0), (0.0, 1.0) and Triangle (1.0, 0.0), (2.0, 0.0), (1.0, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
ooRexx
<lang oorexx>/*--------------------------------------------------------------------
- Determine if two triangles overlap
- Fully (?) tested with integer coordinates of the 6 corners
- This was/is an exercise with ooRexx
- Removed the fraction arithmetic
- -------------------------------------------------------------------*/
Parse Version v
oid='trioo.txt'; 'erase' oid Call o v case=0 cc=0 Call trio_test '0 0 4 0 0 4 1 1 2 1 1 2' Call trio_test '0 0 0 6 8 3 8 0 8 8 0 3' Call trio_test '0 0 0 2 2 0 0 0 4 0 0 6' /* The task's specified input */ Call trio_test '0 0 5 0 0 5 0 0 5 0 0 6' Call trio_test '0 0 0 5 5 0 0 0 0 5 5 0' Call trio_test '0 0 5 0 0 5 -10 0 -5 0 -1 6' Call trio_test '0 0 5 0 2.5 5 0 4 2.5 -1 5 4' Call trio_test '0 0 1 1 0 2 2 1 3 0 3 2' Call trio_test '0 0 1 1 0 2 2 1 3 -2 3 4' Call trio_test '0 0 1 0 0 1 1 0 2 0 1 1' Exit /* Other test cases */ Call trio_test '0 0 0 4 4 0 0 2 2 2 2 0' Call trio_test '0 0 0 5 5 0 0 0 0 5 5 0' Call trio_test '0 0 0 5 5 0 0 0 0 5 7 0' Call trio_test '0 0 1 0 0 1 1 0 2 0 1 1' Call trio_test '0 0 1 1 0 2 2 1 3 0 3 2' Call trio_test '0 0 1 1 0 2 2 1 3 -2 3 4' Call trio_test '0 0 2 0 2 2 3 3 5 3 5 5' Call trio_test '0 0 2 0 2 3 0 0 2 0 2 3' Call trio_test '0 0 4 0 0 4 0 2 2 0 2 2' Call trio_test '0 0 4 0 0 4 1 1 2 1 1 2' Call trio_test '0 0 5 0 0 2 5 0 8 0 4 8' Call trio_test '0 0 5 0 0 5 0 0 5 0 0 6' Call trio_test '0 0 5 0 0 5 -10 0 -5 0 -1 6' Call trio_test '0 0 5 0 0 5 -5 0 -1 6 -3 0' Call trio_test '0 0 5 0 3 5 0 4 3 -1 5 4' Call trio_test '0 0 6 0 4 6 1 1 4 2 7 1' Call trio_test '0 1 0 4 2 2 3 1 3 4 5 2' Call trio_test '1 0 3 0 2 2 1 3 3 3 2 2' Call trio_test '1 0 3 0 2 2 1 3 3 3 2 5' Call trio_test '1 1 4 2 7 1 0 0 8 0 4 8' Call trio_test '2 0 2 6 1 8 0 1 0 5 8 3' Call trio_test '0 0 4 0 0 4 1 1 2 1 1 2' Say case 'cases tested' Say cc Exit
trio_test: Parse Arg tlist cc+=1 tlist=space(tlist) tl1=tlist ; Call trio_t tl1 tl2=reversex(tlist) ; Call trio_t tl2 tl3= tl=tlist Do While tl<>
Parse Var tl x y tl
tl3=tl3 y x
End
Call trio_t tl3
tl4=reversex(tl3) ; Call trio_t tl4 tl5=subword(tl4,7) subword(tl4,1,6) ; Call trio_t tl5 tl6=subword(tl5,7) subword(tl5,1,6) ; Call trio_t tl6 Return
trio_t: Parse Arg tlist tlist=space(tlist) Say tlist case+=1 Parse Arg ax ay bx by cx cy dx dy ex ey fx fy /*---------------------------------------------------------------------
- First build the objects needed
- --------------------------------------------------------------------*/
a=.point~new(ax,ay); b=.point~new(bx,by); c=.point~new(cx,cy) d=.point~new(dx,dy); e=.point~new(ex,ey); f=.point~new(fx,fy) abc=.triangle~new(a,b,c) def=.triangle~new(d,e,f) Call o 'Triangle: ABC:' abc ,1 Call o 'Edges of ABC:'; Do i=1 To 3; Call o ' 'abc~edge(i); End Call o 'Triangle: DEF:' def ,1 Call o 'Edges of DEF:'; Do i=1 To 3; Call o ' 'def~edge(i); End pixl=' ' Do i=1 To 3
pixl=pixl abc~draw(i,'O') pixl=pixl def~draw(i,'*') End
res=0 fc=0 touch=0 bordl= Do i=1 To 3
p1=abc~point(i)
p2=def~point(i)
Do j=1 To 3
e1=abc~edge(j)
e2=def~edge(j)
If e1~contains(p2) Then Do
Call o e1 'contains' p2
ps=p2~string
If wordpos(ps,bordl)=0 Then Do
bordl=bordl ps
touch+=1
End
End
Else
Call o e1 'does not contain' p2 i j
If e2~contains(p1) Then Do
Call o e2 'contains' p1
ps=p1~string
If wordpos(ps,bordl)=0 Then Do
bordl=bordl ps
touch+=1
End
End
Else
Call o e2 'does not contain' p1
End
End
wb=words(bordl) /* how many of them? */ If wb>0 Then
Call o 'Corner(s) that touch the other triangle:' bordl,1
/*---------------------------------------------------------------------
- How many of them are corners of both triangles
- --------------------------------------------------------------------*/
m=0 cmatch= do i=1 To 3
If wordpos(abc~point(i),bordl)>0 &,
wordpos(abc~point(i),def)>0 Then Do
cmatch=cmatch abc~point(i)
m+=1
End
End
/*---------------------------------------------------------------------
- With two or three touching corners we show the result and return
- --------------------------------------------------------------------*/
Select
When wb=3 Then Do /* all three touch */
Call draw(pixl)
Select
When m=3 Then
Call o 'Triangles are identical',1
When m=2 Then
Call o 'Triangles have an edge in common:' cmatch,1
Otherwise
Call o 'Triangles overlap and touch on' bordl,1
End
Call o ,1
-- Pull .
Return
End
When wb=2 Then Do /* two of them match */
Call draw(pixl)
If m=2 Then
Call o 'Triangles have an edge in common:' cmatch,1
Else
Call o 'Triangles overlap and touch on' bordl,1
Call o
-- Pull .
Return
End
When wb=1 Then Do /* one of them matches */
Call o 'Triangles touch on' bordl,1 /* other parts may overlap */
Call o ' we analyze further',1
End
Otherwise /* we know nothing yet */
Nop
End
/*---------------------------------------------------------------------
- Now we look for corners of abc that are within the triangle def
- --------------------------------------------------------------------*/
in_def=0 Do i=1 To 3
p=abc~point(i) Call o 'p ='p Call o 'def='def If def~contains(p) &, wordpos(p,bordl)=0 Then Do Call o def 'contains' p in_def+=1 End End
If in_def=3 Then Do
Call o abc 'is fully contained in' def,1 Call o ,1 Call draw(pixl) fc=1 End
res=(in_def>0) /*---------------------------------------------------------------------
- Now we look for corners of def that are within the triangle abc
- --------------------------------------------------------------------*/
If res=0 Then Do
in_abc=0
If res=0 Then Do
Do i=1 To 3
p=def~point(i)
Call o 'p ='p
Call o 'def='def
If abc~contains(p) &,
wordpos(p,bordl)=0 Then Do
Call o abc 'contains' p
in_abc+=1
End
End
End
If in_abc=3 Then Do
Call o def 'is fully contained in' abc,1
Call o ,1
Call draw(pixl)
fc=1
End
res=(in_abc>0)
End
/*---------------------------------------------------------------------
- Now we check if some edge of abc crosses any edge of def
- --------------------------------------------------------------------*/
If res=0 Then Do
Do i=1 To 3
Do j=1 To 3
e1=abc~edge(i); Call o 'e1='e1
e2=def~edge(j); Call o 'e2='e2
Call o 'crossing???'
res=e1~crosses(e2)
If res Then Do
End
If res Then
Call o 'edges cross'
Else
Call o 'edges dont cross'
End
End
End
If fc=0 Then Do /* no fully contained */
Call draw(pixl)
If res=0 Then /* no overlap */
If wb=1 Then /* but one touching corner */
call o abc 'and' def 'dont overlap but touch on' bordl,1
Else
call o abc 'and' def 'dont overlap',1
Else /* overlap */
If wb>0 Then /* one touching corner */
call o abc 'and' def 'overlap and touch on' bordl,1
Else
call o abc 'and' def 'overlap',1
Call o ,1
-- Pull .
End
Return
/*---------------------------------------------------------------------
- And here are all the classes and methods needed:
- point init, x, y, string
- triangle init, point, edge, contains, string
- edge init, p1, p2, kdx, contains, crosses, string
- --------------------------------------------------------------------*/
- class point public
- attribute x
- attribute y
- method init
expose x y use arg x,y
- method string
expose x y
return "("||x","y")"
- class triangle public
- method init
expose point edge use arg p1,p2,p3 point=.array~new point[1]=p1 point[2]=p2 point[3]=p3 edge=.array~new Do i=1 To 3 ia=i+1; If ia=4 Then ia=1 edge[i]=.edge~new(point[i],point[ia]) End
- method point
expose point use arg n Return point[n]
- method edge
expose edge use arg n Return edge[n]
- method contains
expose point edge
use arg pp
Call o self
Call o 'pp='pp
xmin=1.e9
ymin=1.e9
xmax=-1.e9
ymax=-1.e9
Do i=1 To 3
e=edge[i]
Parse Value e~kdx With ka.i da.i xa.i
Call o show_g(ka.i,da.i,xa.i)
p1=e~p1
p2=e~p2
xmin=min(xmin,p1~x,p2~x)
xmax=max(xmax,p1~x,p2~x)
ymin=min(ymin,p1~y,p2~y)
ymax=max(ymax,p1~y,p2~y)
End
If pp~x<xmin|pp~x>xmax|pp~y<ymin|pp~y>ymax Then
res=0
Else Do
e=edge[1]
e2=edge[2]
p1=e2~p1
p2=e2~p2
Call o 'e:' e
Select
When ka.1='*' Then Do
y2=ka.2*pp~x+da.2
y3=ka.3*pp~x+da.3
res=between(y2,pp~y,y3)
End
When ka.2='*' Then Do
y2=ka.1*pp~x+da.1
res=between(p1~y,y2,p2~y)
End
Otherwise Do
dap=pp~y-ka.1*pp~x
If ka.3='*' Then
x3=xa.3
Else
x3=(da.3-dap)/(ka.1-ka.3)
x2=(da.2-dap)/(ka.1-ka.2)
res=between(x2,pp~x,x3)
End
End
End
Return res
- method string
expose point ol= Do p over point ol=ol p~string End return ol
- method draw
expose point Use Arg i,c p=self~point(i) Return p~x p~y c
- class edge public
- method init
expose edge p1 p2 use arg p1,p2 edge=.array~new edge[1]=p1 edge[2]=p2
- method p1
expose edge p1 p2 return p1
- method p2
expose edge p1 p2 return p2
- method kdx
expose edge p1 p2
x1=p1~x
y1=p1~y
x2=p2~x
y2=p2~y
If x1=x2 Then Do
Parse Value '*' '-' x1 With ka da xa
Call o show_g(ka,da,xa)
End
Else Do
ka=(y2-y1)/(x2-x1)
da=y2-ka*x2
xa='*'
End
Return ka da xa
- method contains
Use Arg p
p1=self~p1
p2=self~p2
parse Value self~kdx With k d x
If k='*' Then Do
res=(p~x=p1~x)&between(p1~y,p~y,p2~y,'I')
End
Else Do
ey=k*p~x+d
res=(ey=p~y)&between(p1~x,p~x,p2~x,'I')
End
If res Then Call o self 'contains' p
Else Call o self 'does not contain' p
Return res
- method crosses
expose p1 p2
Use Arg e
q1=e~p1
q2=e~p2
Call o 'Test if' e 'crosses' self
Call o self~kdx
Call o e~kdx
Parse Value self~kdx With ka da xa; Call o ka da xa
Call o show_g(ka,da,xa)
Parse Value e~kdx With kb db xb; Call o kb db xb
Call o show_g(kb,db,xb)
Call o 'ka='ka
Call o 'kb='kb
Select
When ka='*' Then Do
If kb='*' Then Do
res=(xa=xb)
End
Else Do
Call o 'kb='kb 'xa='||xa 'db='db
yy=kb*xa+db
res=between(q1~y,yy,q2~y)
End
End
When kb='*' Then Do
yy=ka*xb+da
res=between(p1~y,yy,p2~y)
End
When ka=kb Then Do
If da=db Then Do
If min(p1~x,p2~x)>max(q1~x,q2~x) |,
min(q1~x,q2~x)>max(p1~x,p2~x) Then
res=0
Else Do
res=1
End
End
Else
res=0
End
Otherwise Do
x=(db-da)/(ka-kb)
y=ka*x+da
Call o 'cross:' x y
res=between(p1~x,x,p2~x)
End
End
Return res
- method string
expose edge p1 p2 ol=p1~string'-'p2~string return ol
- routine between /* check if a number is between two others */
Use Arg a,x,b,inc Call o 'between:' a x b Parse Var a anom '/' adenom Parse Var x xnom '/' xdenom Parse Var b bnom '/' bdenom If adenom= Then adenom=1 If xdenom= Then xdenom=1 If bdenom= Then bdenom=1 aa=anom*xdenom*bdenom xx=xnom*adenom*bdenom bb=bnom*xdenom*adenom If inc='I' Then res=sign(xx-aa)<>sign(xx-bb) Else res=sign(xx-aa)<>sign(xx-bb) & (xx-aa)*(xx-bb)<>0 Call o a x b 'res='res Return res
- routine show_g /* show a straight line's forula */
/*---------------------------------------------------------------------
- given slope, y-distance, and (special) x-value
- compute y=k*x+d or, if a vertical line, k='*'; x=c
- --------------------------------------------------------------------*/
Use Arg k,d,x
Select
When k='*' Then res='x='||x /* vertical line */
When k=0 Then res='y='d /* horizontal line */
Otherwise Do /* ordinary line */
Select
When k=1 Then res='y=x'dd(d)
When k=-1 Then res='y=-x'dd(d)
Otherwise res='y='k'*x'dd(d)
End
End
End
Return res
- routine dd /* prepare a displacement for presenting it in show_g */
/*---------------------------------------------------------------------
- prepare y-distance for display
- --------------------------------------------------------------------*/
Use Arg dd Select When dd=0 Then dd= /* omit dd if it's zero */ When dd<0 Then dd=dd /* use dd as is (-value) */ Otherwise dd='+'dd /* prepend '+' to positive dd */ End Return dd
- routine o /* debug output */
Use Arg txt,say If say=1 Then Say txt oid='trioo.txt' Return lineout(oid,txt)
- routine draw
Use Arg pixl
Return /* remove to see the triangle corners */
Say 'pixl='pixl
pix.=' '
Do While pixl<>
Parse Var pixl x y c pixl
x=2*x+16; y=2*y+4
If pix.x.y=' ' Then
pix.x.y=c
Else
pix.x.y='+'
End
Do j= 20 To 0 By -1
ol=
Do i=0 To 40
ol=ol||pix.i.j
End
Say ol
End
Return
- routine reversex
Use Arg list n=words(list) res=word(list,n) Do i=n-1 to 1 By -1 res=res word(list,i) End Return res </lang>
- Output:
0 0 4 0 0 4 1 1 2 1 1 2 Triangle: ABC: (0,0) (4,0) (0,4) Triangle: DEF: (1,1) (2,1) (1,2) (1,1) (2,1) (1,2) is fully contained in (0,0) (4,0) (0,4) 2 1 1 2 1 1 4 0 0 4 0 0 Triangle: ABC: (2,1) (1,2) (1,1) Triangle: DEF: (4,0) (0,4) (0,0) (2,1) (1,2) (1,1) is fully contained in (4,0) (0,4) (0,0) 1 2 2 1 1 1 0 4 4 0 0 0 Triangle: ABC: (1,2) (2,1) (1,1) Triangle: DEF: (0,4) (4,0) (0,0) (1,2) (2,1) (1,1) is fully contained in (0,4) (4,0) (0,0) 0 0 0 4 4 0 1 1 1 2 2 1 Triangle: ABC: (0,0) (0,4) (4,0) Triangle: DEF: (1,1) (1,2) (2,1) (1,1) (1,2) (2,1) is fully contained in (0,0) (0,4) (4,0) 1 1 1 2 2 1 0 0 0 4 4 0 Triangle: ABC: (1,1) (1,2) (2,1) Triangle: DEF: (0,0) (0,4) (4,0) (1,1) (1,2) (2,1) is fully contained in (0,0) (0,4) (4,0) 0 0 0 4 4 0 1 1 1 2 2 1 Triangle: ABC: (0,0) (0,4) (4,0) Triangle: DEF: (1,1) (1,2) (2,1) (1,1) (1,2) (2,1) is fully contained in (0,0) (0,4) (4,0) 0 0 0 6 8 3 8 0 8 8 0 3 Triangle: ABC: (0,0) (0,6) (8,3) Triangle: DEF: (8,0) (8,8) (0,3) Corner(s) that touch the other triangle: (0,3) (8,3) Triangles overlap and touch on (0,3) (8,3) 3 0 8 8 0 8 3 8 6 0 0 0 Triangle: ABC: (3,0) (8,8) (0,8) Triangle: DEF: (3,8) (6,0) (0,0) Corner(s) that touch the other triangle: (3,8) (3,0) Triangles overlap and touch on (3,8) (3,0) 0 3 8 8 8 0 8 3 0 6 0 0 Triangle: ABC: (0,3) (8,8) (8,0) Triangle: DEF: (8,3) (0,6) (0,0) Corner(s) that touch the other triangle: (8,3) (0,3) Triangles overlap and touch on (8,3) (0,3) 0 0 6 0 3 8 0 8 8 8 3 0 Triangle: ABC: (0,0) (6,0) (3,8) Triangle: DEF: (0,8) (8,8) (3,0) Corner(s) that touch the other triangle: (3,0) (3,8) Triangles overlap and touch on (3,0) (3,8) 0 8 8 8 3 0 0 0 6 0 3 8 Triangle: ABC: (0,8) (8,8) (3,0) Triangle: DEF: (0,0) (6,0) (3,8) Corner(s) that touch the other triangle: (3,8) (3,0) Triangles overlap and touch on (3,8) (3,0) 0 0 6 0 3 8 0 8 8 8 3 0 Triangle: ABC: (0,0) (6,0) (3,8) Triangle: DEF: (0,8) (8,8) (3,0) Corner(s) that touch the other triangle: (3,0) (3,8) Triangles overlap and touch on (3,0) (3,8) 0 0 0 2 2 0 0 0 4 0 0 6 Triangle: ABC: (0,0) (0,2) (2,0) Triangle: DEF: (0,0) (4,0) (0,6) Corner(s) that touch the other triangle: (0,0) (0,2) (2,0) Triangles overlap and touch on (0,0) (0,2) (2,0) 6 0 0 4 0 0 0 2 2 0 0 0 Triangle: ABC: (6,0) (0,4) (0,0) Triangle: DEF: (0,2) (2,0) (0,0) Corner(s) that touch the other triangle: (0,2) (2,0) (0,0) Triangles overlap and touch on (0,2) (2,0) (0,0) 0 6 4 0 0 0 2 0 0 2 0 0 Triangle: ABC: (0,6) (4,0) (0,0) Triangle: DEF: (2,0) (0,2) (0,0) Corner(s) that touch the other triangle: (2,0) (0,2) (0,0) Triangles overlap and touch on (2,0) (0,2) (0,0) 0 0 2 0 0 2 0 0 0 4 6 0 Triangle: ABC: (0,0) (2,0) (0,2) Triangle: DEF: (0,0) (0,4) (6,0) Corner(s) that touch the other triangle: (0,0) (2,0) (0,2) Triangles overlap and touch on (0,0) (2,0) (0,2) 0 0 0 4 6 0 0 0 2 0 0 2 Triangle: ABC: (0,0) (0,4) (6,0) Triangle: DEF: (0,0) (2,0) (0,2) Corner(s) that touch the other triangle: (0,0) (2,0) (0,2) Triangles overlap and touch on (0,0) (2,0) (0,2) 0 0 2 0 0 2 0 0 0 4 6 0 Triangle: ABC: (0,0) (2,0) (0,2) Triangle: DEF: (0,0) (0,4) (6,0) Corner(s) that touch the other triangle: (0,0) (2,0) (0,2) Triangles overlap and touch on (0,0) (2,0) (0,2) 0 0 5 0 0 5 0 0 5 0 0 6 Triangle: ABC: (0,0) (5,0) (0,5) Triangle: DEF: (0,0) (5,0) (0,6) Corner(s) that touch the other triangle: (0,0) (5,0) (0,5) Triangles have an edge in common: (0,0) (5,0) 6 0 0 5 0 0 5 0 0 5 0 0 Triangle: ABC: (6,0) (0,5) (0,0) Triangle: DEF: (5,0) (0,5) (0,0) Corner(s) that touch the other triangle: (5,0) (0,5) (0,0) Triangles have an edge in common: (0,5) (0,0) 0 6 5 0 0 0 0 5 5 0 0 0 Triangle: ABC: (0,6) (5,0) (0,0) Triangle: DEF: (0,5) (5,0) (0,0) Corner(s) that touch the other triangle: (0,5) (5,0) (0,0) Triangles have an edge in common: (5,0) (0,0) 0 0 0 5 5 0 0 0 0 5 6 0 Triangle: ABC: (0,0) (0,5) (5,0) Triangle: DEF: (0,0) (0,5) (6,0) Corner(s) that touch the other triangle: (0,0) (0,5) (5,0) Triangles have an edge in common: (0,0) (0,5) 0 0 0 5 6 0 0 0 0 5 5 0 Triangle: ABC: (0,0) (0,5) (6,0) Triangle: DEF: (0,0) (0,5) (5,0) Corner(s) that touch the other triangle: (0,0) (0,5) (5,0) Triangles have an edge in common: (0,0) (0,5) 0 0 0 5 5 0 0 0 0 5 6 0 Triangle: ABC: (0,0) (0,5) (5,0) Triangle: DEF: (0,0) (0,5) (6,0) Corner(s) that touch the other triangle: (0,0) (0,5) (5,0) Triangles have an edge in common: (0,0) (0,5) 0 0 0 5 5 0 0 0 0 5 5 0 Triangle: ABC: (0,0) (0,5) (5,0) Triangle: DEF: (0,0) (0,5) (5,0) Corner(s) that touch the other triangle: (0,0) (0,5) (5,0) Triangles are identical 0 5 5 0 0 0 0 5 5 0 0 0 Triangle: ABC: (0,5) (5,0) (0,0) Triangle: DEF: (0,5) (5,0) (0,0) Corner(s) that touch the other triangle: (0,5) (5,0) (0,0) Triangles are identical 5 0 0 5 0 0 5 0 0 5 0 0 Triangle: ABC: (5,0) (0,5) (0,0) Triangle: DEF: (5,0) (0,5) (0,0) Corner(s) that touch the other triangle: (5,0) (0,5) (0,0) Triangles are identical 0 0 5 0 0 5 0 0 5 0 0 5 Triangle: ABC: (0,0) (5,0) (0,5) Triangle: DEF: (0,0) (5,0) (0,5) Corner(s) that touch the other triangle: (0,0) (5,0) (0,5) Triangles are identical 0 0 5 0 0 5 0 0 5 0 0 5 Triangle: ABC: (0,0) (5,0) (0,5) Triangle: DEF: (0,0) (5,0) (0,5) Corner(s) that touch the other triangle: (0,0) (5,0) (0,5) Triangles are identical 0 0 5 0 0 5 0 0 5 0 0 5 Triangle: ABC: (0,0) (5,0) (0,5) Triangle: DEF: (0,0) (5,0) (0,5) Corner(s) that touch the other triangle: (0,0) (5,0) (0,5) Triangles are identical 0 0 5 0 0 5 -10 0 -5 0 -1 6 Triangle: ABC: (0,0) (5,0) (0,5) Triangle: DEF: (-10,0) (-5,0) (-1,6) (0,0) (5,0) (0,5) and (-10,0) (-5,0) (-1,6) don't overlap 6 -1 0 -5 0 -10 5 0 0 5 0 0 Triangle: ABC: (6,-1) (0,-5) (0,-10) Triangle: DEF: (5,0) (0,5) (0,0) (6,-1) (0,-5) (0,-10) and (5,0) (0,5) (0,0) don't overlap -1 6 -5 0 -10 0 0 5 5 0 0 0 Triangle: ABC: (-1,6) (-5,0) (-10,0) Triangle: DEF: (0,5) (5,0) (0,0) (-1,6) (-5,0) (-10,0) and (0,5) (5,0) (0,0) don't overlap 0 0 0 5 5 0 0 -10 0 -5 6 -1 Triangle: ABC: (0,0) (0,5) (5,0) Triangle: DEF: (0,-10) (0,-5) (6,-1) (0,0) (0,5) (5,0) and (0,-10) (0,-5) (6,-1) don't overlap 0 -10 0 -5 6 -1 0 0 0 5 5 0 Triangle: ABC: (0,-10) (0,-5) (6,-1) Triangle: DEF: (0,0) (0,5) (5,0) (0,-10) (0,-5) (6,-1) and (0,0) (0,5) (5,0) don't overlap 0 0 0 5 5 0 0 -10 0 -5 6 -1 Triangle: ABC: (0,0) (0,5) (5,0) Triangle: DEF: (0,-10) (0,-5) (6,-1) (0,0) (0,5) (5,0) and (0,-10) (0,-5) (6,-1) don't overlap 0 0 5 0 2.5 5 0 4 2.5 -1 5 4 Triangle: ABC: (0,0) (5,0) (2.5,5) Triangle: DEF: (0,4) (2.5,-1) (5,4) (0,0) (5,0) (2.5,5) and (0,4) (2.5,-1) (5,4) overlap 4 5 -1 2.5 4 0 5 2.5 0 5 0 0 Triangle: ABC: (4,5) (-1,2.5) (4,0) Triangle: DEF: (5,2.5) (0,5) (0,0) (4,5) (-1,2.5) (4,0) and (5,2.5) (0,5) (0,0) overlap 5 4 2.5 -1 0 4 2.5 5 5 0 0 0 Triangle: ABC: (5,4) (2.5,-1) (0,4) Triangle: DEF: (2.5,5) (5,0) (0,0) (5,4) (2.5,-1) (0,4) and (2.5,5) (5,0) (0,0) overlap 0 0 0 5 5 2.5 4 0 -1 2.5 4 5 Triangle: ABC: (0,0) (0,5) (5,2.5) Triangle: DEF: (4,0) (-1,2.5) (4,5) (0,0) (0,5) (5,2.5) and (4,0) (-1,2.5) (4,5) overlap 4 0 -1 2.5 4 5 0 0 0 5 5 2.5 Triangle: ABC: (4,0) (-1,2.5) (4,5) Triangle: DEF: (0,0) (0,5) (5,2.5) (4,0) (-1,2.5) (4,5) and (0,0) (0,5) (5,2.5) overlap 0 0 0 5 5 2.5 4 0 -1 2.5 4 5 Triangle: ABC: (0,0) (0,5) (5,2.5) Triangle: DEF: (4,0) (-1,2.5) (4,5) (0,0) (0,5) (5,2.5) and (4,0) (-1,2.5) (4,5) overlap 0 0 1 1 0 2 2 1 3 0 3 2 Triangle: ABC: (0,0) (1,1) (0,2) Triangle: DEF: (2,1) (3,0) (3,2) (0,0) (1,1) (0,2) and (2,1) (3,0) (3,2) don't overlap 2 3 0 3 1 2 2 0 1 1 0 0 Triangle: ABC: (2,3) (0,3) (1,2) Triangle: DEF: (2,0) (1,1) (0,0) (2,3) (0,3) (1,2) and (2,0) (1,1) (0,0) don't overlap 3 2 3 0 2 1 0 2 1 1 0 0 Triangle: ABC: (3,2) (3,0) (2,1) Triangle: DEF: (0,2) (1,1) (0,0) (3,2) (3,0) (2,1) and (0,2) (1,1) (0,0) don't overlap 0 0 1 1 2 0 1 2 0 3 2 3 Triangle: ABC: (0,0) (1,1) (2,0) Triangle: DEF: (1,2) (0,3) (2,3) (0,0) (1,1) (2,0) and (1,2) (0,3) (2,3) don't overlap 1 2 0 3 2 3 0 0 1 1 2 0 Triangle: ABC: (1,2) (0,3) (2,3) Triangle: DEF: (0,0) (1,1) (2,0) (1,2) (0,3) (2,3) and (0,0) (1,1) (2,0) don't overlap 0 0 1 1 2 0 1 2 0 3 2 3 Triangle: ABC: (0,0) (1,1) (2,0) Triangle: DEF: (1,2) (0,3) (2,3) (0,0) (1,1) (2,0) and (1,2) (0,3) (2,3) don't overlap 0 0 1 1 0 2 2 1 3 -2 3 4 Triangle: ABC: (0,0) (1,1) (0,2) Triangle: DEF: (2,1) (3,-2) (3,4) (0,0) (1,1) (0,2) and (2,1) (3,-2) (3,4) don't overlap 4 3 -2 3 1 2 2 0 1 1 0 0 Triangle: ABC: (4,3) (-2,3) (1,2) Triangle: DEF: (2,0) (1,1) (0,0) (4,3) (-2,3) (1,2) and (2,0) (1,1) (0,0) don't overlap 3 4 3 -2 2 1 0 2 1 1 0 0 Triangle: ABC: (3,4) (3,-2) (2,1) Triangle: DEF: (0,2) (1,1) (0,0) (3,4) (3,-2) (2,1) and (0,2) (1,1) (0,0) don't overlap 0 0 1 1 2 0 1 2 -2 3 4 3 Triangle: ABC: (0,0) (1,1) (2,0) Triangle: DEF: (1,2) (-2,3) (4,3) (0,0) (1,1) (2,0) and (1,2) (-2,3) (4,3) don't overlap 1 2 -2 3 4 3 0 0 1 1 2 0 Triangle: ABC: (1,2) (-2,3) (4,3) Triangle: DEF: (0,0) (1,1) (2,0) (1,2) (-2,3) (4,3) and (0,0) (1,1) (2,0) don't overlap 0 0 1 1 2 0 1 2 -2 3 4 3 Triangle: ABC: (0,0) (1,1) (2,0) Triangle: DEF: (1,2) (-2,3) (4,3) (0,0) (1,1) (2,0) and (1,2) (-2,3) (4,3) don't overlap 0 0 1 0 0 1 1 0 2 0 1 1 Triangle: ABC: (0,0) (1,0) (0,1) Triangle: DEF: (1,0) (2,0) (1,1) Corner(s) that touch the other triangle: (1,0) Triangles touch on (1,0) we analyze further (0,0) (1,0) (0,1) and (1,0) (2,0) (1,1) don't overlap but touch on (1,0) 1 1 0 2 0 1 1 0 0 1 0 0 Triangle: ABC: (1,1) (0,2) (0,1) Triangle: DEF: (1,0) (0,1) (0,0) Corner(s) that touch the other triangle: (0,1) Triangles touch on (0,1) we analyze further (1,1) (0,2) (0,1) and (1,0) (0,1) (0,0) don't overlap but touch on (0,1) 1 1 2 0 1 0 0 1 1 0 0 0 Triangle: ABC: (1,1) (2,0) (1,0) Triangle: DEF: (0,1) (1,0) (0,0) Corner(s) that touch the other triangle: (1,0) Triangles touch on (1,0) we analyze further (1,1) (2,0) (1,0) and (0,1) (1,0) (0,0) overlap and touch on (1,0) 0 0 0 1 1 0 0 1 0 2 1 1 Triangle: ABC: (0,0) (0,1) (1,0) Triangle: DEF: (0,1) (0,2) (1,1) Corner(s) that touch the other triangle: (0,1) Triangles touch on (0,1) we analyze further (0,0) (0,1) (1,0) and (0,1) (0,2) (1,1) don't overlap but touch on (0,1) 0 1 0 2 1 1 0 0 0 1 1 0 Triangle: ABC: (0,1) (0,2) (1,1) Triangle: DEF: (0,0) (0,1) (1,0) Corner(s) that touch the other triangle: (0,1) Triangles touch on (0,1) we analyze further (0,1) (0,2) (1,1) and (0,0) (0,1) (1,0) don't overlap but touch on (0,1) 0 0 0 1 1 0 0 1 0 2 1 1 Triangle: ABC: (0,0) (0,1) (1,0) Triangle: DEF: (0,1) (0,2) (1,1) Corner(s) that touch the other triangle: (0,1) Triangles touch on (0,1) we analyze further (0,0) (0,1) (1,0) and (0,1) (0,2) (1,1) don't overlap but touch on (0,1)
Pascal
A console application in Free Pascal, created with the Lazarus IDE. It recognizes three possible outcomes: disjoint, positive overlap, and borderline (overlap at a point or line segment). <lang pascal> program TrianglesOverlap; { The program looks for a separating line between the triangles. It's known that only the triangle sides (produced) need to be considered as possible separators (except in the degenerate case when both triangles are reduced to a point). If there's a strong separator, i.e. one that is disjoint from at least one of the triangles, then the triangles are disjoint. If there's only a weak separator, i.e. one that intersects both triangles, then the triangles intersect in a point or a line segment (this program doesn't work out which). If there's no separator, then the triangles have an overlap of positive area. } {$mode objfpc}{$H+}
uses Math, SysUtils;
{$DEFINE USE_FP} {$IFDEF USE_FP} type TCoordinate = double; const TOLERANCE = 1.0E-6; {$ELSE} type TCoordinate = integer; const TOLERANCE = 0; {$ENDIF}
type TVertex = record
x, y : TCoordinate;
end;
function Vertex( x_in, y_in : TCoordinate) : TVertex; begin
result.x := x_in; result.y := y_in;
end;
// Result of testing sides of a triangle for separator. // Values are arbitrary but must be in this numerical order const
SEP_NO_TEST = -1; // triangle is a single point, no sides to be tested SEP_NONE = 0; // didn't find a separator SEP_WEAK = 1; // found a weak separator only SEP_STRONG = 2; // found a strong separator
function EqualVertices( V, W : TVertex) : boolean; begin
result := (Abs(V.x - W.x) <= TOLERANCE)
and (Abs(V.y - W.y) <= TOLERANCE);
end;
// Determinant: twice the signed area of triangle PQR. function Det( P, Q, R : TVertex) : TCoordinate; begin
result := Q.x*R.y - R.x*Q.y + R.x*P.y - P.x*R.y + P.x*Q.y - Q.x*P.y;
end;
// Get result of trying sides of LMN as separators. function TrySides( L, M, N, P, Q, R : TVertex) : integer; var
s, sMin, sMax: TCoordinate; H, K : TVertex;
function TestSide( V, W : TVertex) : integer;
var
detP, detQ, detR, tMin, tMax : TCoordinate;
begin
result := SEP_NONE;
detP := Det( V, W, P);
detQ := Det( V, W, Q);
detR := Det( V, W, R);
tMin := Math.Min( Math.Min( detP, detQ), detR);
tMax := Math.Max( Math.Max( detP, detQ), detR);
if (tMin - sMax > TOLERANCE) or (sMin - tMax > TOLERANCE) then
result := SEP_STRONG
else if (tMin - sMax >= -TOLERANCE) or (sMin - tMax >= -TOLERANCE) then
result := SEP_WEAK;
end;
begin
sMin := 0; sMax := 0; s := Det( L, M, N); if (s <> 0) then begin // L, M, N are not collinear if (s < 0) then sMin := s else sMax := s; // Once we've found a strong separator, there's no need for further testing result := TestSide( M, N); if (result < SEP_STRONG) then result := Math.Max( result, TestSide( N, L)); if (result < SEP_STRONG) then result := Math.Max( result, TestSide( L, M)); end else begin // s = 0 so L, M, N are collinear // Look for distinct vertices from among L, M, N H := L; K := M; if EqualVertices( H, K) then K := N; if EqualVertices( H, K) then result := SEP_NO_TEST // L = M = N else result := TestSide( H, K); end;
end;
function Algo_5( A, B, C, D, E, F : TVertex) : integer; begin
result := TrySides( A, B, C, D, E, F);
if (result < SEP_STRONG) then begin
result := Math.Max( result, TrySides( D, E, F, A, B, C));
if (result = SEP_NO_TEST) then begin // A = B = C and D = E = F
if EqualVertices( A, D) then result := SEP_WEAK
else result := SEP_STRONG;
end;
end;
end;
procedure TestTrianglePair (Ax, Ay, Bx, By, Cx, Cy,
Dx, Dy, Ex, Ey, Fx, Fy : TCoordinate);
var
ovStr : string;
begin
case Algo_5( Vertex(Ax, Ay), Vertex(Bx, By), Vertex(Cx, Cy),
Vertex(Dx, Dy), Vertex(Ex, Ey), Vertex(Fx, Fy)) of
SEP_STRONG : ovStr := 'Disjoint';
SEP_NONE : ovStr := 'Overlap';
else ovStr := 'Borderline';
end;
WriteLn( SysUtils.Format(
'(%g,%g),(%g,%g),(%g,%g) and (%g,%g),(%g,%g),(%g,%g): %s',
[Ax, Ay, Bx, By, Cx, Cy, Dx, Dy, Ex, Ey, Fx, Fy, ovStr]));
end;
// Main routine begin
TestTrianglePair( 0,0,5,0,0,5, 0,0,5,0,0,6); TestTrianglePair( 0,0,0,5,5,0, 0,0,0,5,5,0); TestTrianglePair( 0,0,5,0,0,5, -10,0,-5,0,-1,6); TestTrianglePair( 0,0,5,0,2.5,5, 0,4,2.5,-1,5,4); TestTrianglePair( 0,0,1,1,0,2, 2,1,3,0,3,2); TestTrianglePair( 0,0,1,1,0,2, 2,1,3,-2,3,4); TestTrianglePair( 0,0,1,0,0,1, 1,0,2,0,1,1);
end. </lang>
- Output:
(0,0),(5,0),(0,5) and (0,0),(5,0),(0,6): Overlap (0,0),(0,5),(5,0) and (0,0),(0,5),(5,0): Overlap (0,0),(5,0),(0,5) and (-10,0),(-5,0),(-1,6): Disjoint (0,0),(5,0),(2.5,5) and (0,4),(2.5,-1),(5,4): Overlap (0,0),(1,1),(0,2) and (2,1),(3,0),(3,2): Disjoint (0,0),(1,1),(0,2) and (2,1),(3,-2),(3,4): Disjoint (0,0),(1,0),(0,1) and (1,0),(2,0),(1,1): Borderline
Perl
Port of Lua
<lang perl>use strict; use warnings;
sub det2D {
my $p1 = shift or die "4 Missing first point\n"; my $p2 = shift or die "Missing second point\n"; my $p3 = shift or die "Missing third point\n";
return $p1->{x} * ($p2->{y} - $p3->{y})
+ $p2->{x} * ($p3->{y} - $p1->{y})
+ $p3->{x} * ($p1->{y} - $p2->{y});
}
sub checkTriWinding {
my $p1 = shift or die "14 Missing first point\n"; my $p2 = shift or die "Missing second point\n"; my $p3 = shift or die "Missing third point\n"; my $allowReversed = shift;
my $detTri = det2D($p1, $$p2, $$p3);
if ($detTri < 0.0) {
if ($allowReversed) {
my $t = $$p3;
$$p3 = $$p2;
$$p2 = $t;
} else {
die "triangle has wrong winding direction";
}
}
return undef;
}
sub boundaryCollideChk {
my $p1 = shift or die "33 Missing first point\n"; my $p2 = shift or die "Missing second point\n"; my $p3 = shift or die "Missing third point\n"; my $eps = shift;
return det2D($p1, $p2, $p3) < $eps;
}
sub boundaryDoesntCollideChk {
my $p1 = shift or die "42 Missing first point\n"; my $p2 = shift or die "Missing second point\n"; my $p3 = shift or die "Missing third point\n"; my $eps = shift;
return det2D($p1, $p2, $p3) <= $eps;
}
sub triTri2D {
my $t1 = shift or die "Missing first triangle to calculate with\n"; my $t2 = shift or die "Missing second triangle to calculate with\n"; my $eps = shift; my $allowReversed = shift; my $onBoundary = shift;
# triangles must be expressed anti-clockwise checkTriWinding($t1->[0], \$t1->[1], \$t1->[2], $allowReversed); checkTriWinding($t2->[0], \$t2->[1], \$t2->[2], $allowReversed);
my $chkEdge;
if ($onBoundary) {
# points on the boundary are considered as colliding
$chkEdge = \&boundaryCollideChk;
} else {
# points on the boundary are NOT considered as colliding
$chkEdge = \&boundaryDoesntCollideChk;
}
# for edge E of triangle 1
foreach my $i (0, 1, 2) {
my $j = ($i + 1) % 3;
# check all points of triangle 2 lay on the external side of edge E
# if they do, the triangles do not collide
if ($chkEdge->($t1->[$i], $t1->[$j], $t2->[0], $eps)
and $chkEdge->($t1->[$i], $t1->[$j], $t2->[1], $eps)
and $chkEdge->($t1->[$i], $t1->[$j], $t2->[2], $eps)) {
return 0; # false
}
}
# for edge E of triangle 2
foreach my $i (0, 1, 2) {
my $j = ($i + 1) % 3;
# check all points of triangle 1 lay on the external side of edge E
# if they do, the triangles do not collide
if ($chkEdge->($t2->[$i], $t2->[$j], $t1->[0], $eps)
and $chkEdge->($t2->[$i], $t2->[$j], $t1->[1], $eps)
and $chkEdge->($t2->[$i], $t2->[$j], $t1->[2], $eps)) {
return 0; # false
}
}
return 1; # true
}
sub formatTri {
my $t = shift or die "Missing triangle to format\n";
my $p1 = $t->[0];
my $p2 = $t->[1];
my $p3 = $t->[2];
return "Triangle: ($p1->{x}, $p1->{y}), ($p2->{x}, $p2->{y}), ($p3->{x}, $p3->{y})";
}
sub overlap {
my $t1 = shift or die "Missing first triangle to calculate with\n"; my $t2 = shift or die "Missing second triangle to calculate with\n"; my $eps = shift; my $allowReversed = shift or 0; # false my $onBoundary = shift or 1; # true
unless ($eps) {
$eps = 0.0;
}
if (triTri2D($t1, $t2, $eps, $allowReversed, $onBoundary)) {
return "overlap\n";
} else {
return "do not overlap\n";
}
}
- Main
my @t1 = ({x=>0, y=>0}, {x=>5, y=>0}, {x=>0, y=>5}); my @t2 = ({x=>0, y=>0}, {x=>5, y=>0}, {x=>0, y=>6}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2), "\n";
@t1 = ({x=>0, y=>0}, {x=>0, y=>5}, {x=>5, y=>0}); @t2 = ({x=>0, y=>0}, {x=>0, y=>5}, {x=>5, y=>0}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2, 0.0, 1), "\n";
@t1 = ({x=>0, y=>0}, {x=>5, y=>0}, {x=>0, y=>5}); @t2 = ({x=>-10, y=>0}, {x=>-5, y=>0}, {x=>-1, y=>6}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2), "\n";
@t1 = ({x=>0, y=>0}, {x=>5, y=>0}, {x=>2.5, y=>5}); @t2 = ({x=>0, y=>4}, {x=>2.5, y=>-1}, {x=>5, y=>4}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2), "\n";
@t1 = ({x=>0, y=>0}, {x=>1, y=>1}, {x=>0, y=>2}); @t2 = ({x=>2, y=>1}, {x=>3, y=>0}, {x=>3, y=>2}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2), "\n";
@t1 = ({x=>0, y=>0}, {x=>1, y=>1}, {x=>0, y=>2}); @t2 = ({x=>2, y=>1}, {x=>3, y=>-2}, {x=>3, y=>4}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2), "\n";
- Barely touching
@t1 = ({x=>0, y=>0}, {x=>1, y=>0}, {x=>0, y=>1}); @t2 = ({x=>1, y=>0}, {x=>2, y=>0}, {x=>1, y=>1}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2, 0.0, 0, 1), "\n";
- Barely touching
@t1 = ({x=>0, y=>0}, {x=>1, y=>0}, {x=>0, y=>1}); @t2 = ({x=>1, y=>0}, {x=>2, y=>0}, {x=>1, y=>1}); print formatTri(\@t1), " and\n", formatTri(\@t2), "\n", overlap(\@t1, \@t2, 0.0, 0, 0), "\n";</lang>
- Output:
Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (0, 0), (5, 0), (0, 6) overlap Triangle: (0, 0), (0, 5), (5, 0) and Triangle: (0, 0), (0, 5), (5, 0) overlap Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (-10, 0), (-5, 0), (-1, 6) do not overlap Triangle: (0, 0), (5, 0), (2.5, 5) and Triangle: (0, 4), (2.5, -1), (5, 4) overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, 0), (3, 2) do not overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, -2), (3, 4) do not overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1) overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1) do not overlap
More Idiomatic
<lang perl>use strict; use warnings; use feature 'say';
sub det2D {
my($p1,$p2,$p3) = @_;
return $p1->[0] * ($p2->[1] - $p3->[1])
+ $p2->[0] * ($p3->[1] - $p1->[1])
+ $p3->[0] * ($p1->[1] - $p2->[1]);
}
- triangles must be expressed anti-clockwise
sub checkTriWinding {
my($p1,$p2,$p3,$allowReversed) = @_;
my $detTri = det2D($p1, $$p2, $$p3);
if ($detTri < 0.0) {
if ($allowReversed) { ($$p3,$$p2) = ($$p2,$$p3) }
else { die "triangle has wrong winding direction" }
}
return undef;
}
sub check_edge {
our($t1,$t2,$eps,$onBoundary) = @_;
# points on the boundary may be considered as colliding, or not
my $chkEdge = $onBoundary ? \&boundaryCollideChk : \&boundaryDoesntCollideChk;
sub boundaryCollideChk { return det2D($_[0], $_[1], $_[2]) < $eps }
sub boundaryDoesntCollideChk { return det2D($_[0], $_[1], $_[2]) <= $eps }
# for edge E of triangle 1
foreach my $i (0, 1, 2) {
my $j = ($i + 1) % 3;
# check all points of triangle 2 lay on the external side of edge E
# if they do, the triangles do not collide
if ($chkEdge->($$t1->[$i], $$t1->[$j], $$t2->[0], $eps)
and $chkEdge->($$t1->[$i], $$t1->[$j], $$t2->[1], $eps)
and $chkEdge->($$t1->[$i], $$t1->[$j], $$t2->[2], $eps)) {
return 0; # false
}
}
return 1;
}
sub triTri2D {
my($t1,$t2,$eps,$allowReversed,$onBoundary) = @_; checkTriWinding($$t1->[0], \$$t1->[1], \$$t1->[2], $allowReversed); checkTriWinding($$t2->[0], \$$t2->[1], \$$t2->[2], $allowReversed); return check_edge($t1,$t2,$eps,$onBoundary) && check_edge($t2,$t1,$eps,$onBoundary);
}
sub formatTri {
my $t = shift;
my @pairs;
push @pairs, sprintf "%8s", '(' . $$_[0] . ',' . $$_[1] . ')' for @$$t;
join ', ', @pairs;
}
sub overlap {
my $t1 = shift or die "Missing first triangle to calculate with\n"; my $t2 = shift or die "Missing second triangle to calculate with\n"; my $eps = shift || 0; my $allowReversed = shift || 1; my $onBoundary = shift || 1;
my $triangles = formatTri($t1) . ' and ' . formatTri($t2);
if (triTri2D($t1, $t2, $eps, $allowReversed, $onBoundary)) {
return " overlap:" . $triangles;
} else {
return "do not overlap:" . $triangles;
}
}
my @tests = (
[ [[0,0], [5,0], [0,5]], [ [0,0], [5,0], [0,6]] ], [ [[0,0], [0,5], [5,0]], [ [0,0], [0,5], [5,0]] ], [ [[0,0], [5,0], [0,5]], [ [-10,0], [-5,0], [-1,6]] ], [ [[0,0], [5,0], [2.5,5]], [ [0,4], [2.5,-1], [5,4]] ], [ [[0,0], [1,1], [0,2]], [ [2,1], [3,0], [3,2]] ], [ [[0,0], [1,1], [0,2]], [ [2,1], [3,-2], [3,4]] ], # barely touching [ [[0,0], [1,0], [0,1]], [ [1,0], [2,0], [1,1]], 0.0, 0, 0 ] # barely touching
);
say overlap(\$_->[0], \$_->[1], $_->[2], $_->[3], $_->[4]) for @tests;</lang>
- Output:
overlap: (0,0), (5,0), (0,5) and (0,0), (5,0), (0,6)
overlap: (0,0), (0,5), (5,0) and (0,0), (0,5), (5,0)
do not overlap: (0,0), (5,0), (0,5) and (-10,0), (-5,0), (-1,6)
overlap: (0,0), (5,0), (2.5,5) and (0,4), (2.5,-1), (5,4)
do not overlap: (0,0), (1,1), (0,2) and (2,1), (3,0), (3,2)
do not overlap: (0,0), (1,1), (0,2) and (2,1), (3,-2), (3,4)
overlap: (0,0), (1,0), (0,1) and (1,0), (2,0), (1,1)
Phix
Plus draw all eight pairs of triangles for visual confirmation. <lang Phix>include pGUI.e
Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas
constant triangles = {{{{0,0},{5,0},{0,5}},{{0,0},{5,0},{0,6}}},
{{{0,0},{0,5},{5,0}},{{0,0},{0,5},{5,0}}},
{{{0,0},{5,0},{0,5}},{{-10,0},{-5,0},{-1,6}}},
{{{0,0},{5,0},{2.5,5}},{{0,4},{2.5,-1},{5,4}}},
{{{0,0},{1,1},{0,2}},{{2,1},{3,0},{3,2}}},
{{{0,0},{1,1},{0,2}},{{2,1},{3,-2},{3,4}}},
{{{0,0},{1,0},{0,1}},{{1,0},{2,0},{1,1}}},
{{{0,0},{1,0},{0,1}},{{1,0},{2,0},{1,1}}}}
procedure draw_triangle(sequence t, integer cx,cy, c)
cdCanvasSetForeground(cddbuffer, c)
cdCanvasBegin(cddbuffer,CD_CLOSED_LINES)
for c=1 to 3 do
atom {x,y} = t[c]
cdCanvasVertex(cddbuffer, cx+x*10, cy+y*10)
end for
cdCanvasEnd(cddbuffer)
end procedure
function det2D(sequence triangle)
atom {{p1x,p1y},{p2x,p2y},{p3x,p3y}} := triangle
return p1x*(p2y-p3y) + p2x*(p3y-p1y) + p3x*(p1y-p2y)
end function
bool bReversed function checkWinding(sequence triangle, bool allowReversed)
atom detTri := det2D(triangle);
if detTri<0.0 then
if allowReversed then
bReversed = true
triangle = extract(triangle,{1,3,2})
else
throw("triangle has wrong winding direction")
end if
end if
return triangle
end function
function overlap(sequence t1, t2, atom epsilon=0.0, bool allowReversed=false, onBoundary=true)
-- Trangles must be expressed anti-clockwise
bReversed = false
t1 = checkWinding(t1, allowReversed)
t2 = checkWinding(t2, allowReversed)
for t=1 to 2 do -- check t1 then t2
for edge=1 to 3 do -- check each edge
sequence p1 = t1[edge],
p2 = t1[mod(edge,3)+1]
-- Check all points of trangle 2 lay on the external side
-- of the edge E. If they do, the triangles do not collide.
integer onside = 0
for k=1 to 3 do
integer c = compare(det2D({p1,p2,t2[k]}),epsilon)
if onBoundary then
if not (c<0) then exit end if
else
if not (c<=0) then exit end if
end if
-- -- (the following incomprehensible one-liner is equivalent:) -- if compare(det2D({p1,p2,t2[k]}),epsilon)>-onBoundary then exit end if
onside += 1
end for
if onside=3 then
return iff(onBoundary?"no overlap":"no overlap (no boundary)")
end if
end for
{t2,t1} = {t1,t2} -- flip and re-test
end for
return iff(bReversed?"overlap (reversed)":"overlap")
end function
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
cdCanvasActivate(cddbuffer)
integer cy = 200, cx = 100
for i=1 to length(triangles) do
sequence {t1,t2} = triangles[i]
draw_triangle(t1,cx,cy,CD_RED)
integer s = (i<=2) -- (smudge tests[1..2] by one
-- pixel to show them better)
draw_triangle(t2,cx+s,cy+s,CD_BLUE)
cdCanvasSetForeground(cddbuffer, CD_BLACK)
cdCanvasText(cddbuffer,cx+10,cy-40,overlap(t1,t2,0,i=2,i!=8))
if i=4 then
cy = 100
cx = 100
else
cx += 300
end if
end for
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih) cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas) cdCanvasSetBackground(cddbuffer, CD_WHITE) return IUP_DEFAULT
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "1250x300")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas,"DIALOGFRAME=YES")
IupSetAttribute(dlg, "TITLE", "Triangle overlap")
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupShowXY(dlg,IUP_CENTER,IUP_CENTER) IupSetAttribute(canvas, "RASTERSIZE", NULL) IupMainLoop() IupClose()
end procedure
main()</lang>
Python
Using numpy: <lang python>from __future__ import print_function import numpy as np
def CheckTriWinding(tri, allowReversed): trisq = np.ones((3,3)) trisq[:,0:2] = np.array(tri) detTri = np.linalg.det(trisq) if detTri < 0.0: if allowReversed: a = trisq[2,:].copy() trisq[2,:] = trisq[1,:] trisq[1,:] = a else: raise ValueError("triangle has wrong winding direction") return trisq
def TriTri2D(t1, t2, eps = 0.0, allowReversed = False, onBoundary = True): #Trangles must be expressed anti-clockwise t1s = CheckTriWinding(t1, allowReversed) t2s = CheckTriWinding(t2, allowReversed)
if onBoundary: #Points on the boundary are considered as colliding chkEdge = lambda x: np.linalg.det(x) < eps else: #Points on the boundary are not considered as colliding chkEdge = lambda x: np.linalg.det(x) <= eps
#For edge E of trangle 1, for i in range(3): edge = np.roll(t1s, i, axis=0)[:2,:]
#Check all points of trangle 2 lay on the external side of the edge E. If #they do, the triangles do not collide. if (chkEdge(np.vstack((edge, t2s[0]))) and chkEdge(np.vstack((edge, t2s[1]))) and chkEdge(np.vstack((edge, t2s[2])))): return False
#For edge E of trangle 2, for i in range(3): edge = np.roll(t2s, i, axis=0)[:2,:]
#Check all points of trangle 1 lay on the external side of the edge E. If #they do, the triangles do not collide. if (chkEdge(np.vstack((edge, t1s[0]))) and chkEdge(np.vstack((edge, t1s[1]))) and chkEdge(np.vstack((edge, t1s[2])))): return False
#The triangles collide return True
if __name__=="__main__": t1 = [[0,0],[5,0],[0,5]] t2 = [[0,0],[5,0],[0,6]] print (TriTri2D(t1, t2), True)
t1 = [[0,0],[0,5],[5,0]] t2 = [[0,0],[0,6],[5,0]] print (TriTri2D(t1, t2, allowReversed = True), True)
t1 = [[0,0],[5,0],[0,5]] t2 = [[-10,0],[-5,0],[-1,6]] print (TriTri2D(t1, t2), False)
t1 = [[0,0],[5,0],[2.5,5]] t2 = [[0,4],[2.5,-1],[5,4]] print (TriTri2D(t1, t2), True)
t1 = [[0,0],[1,1],[0,2]] t2 = [[2,1],[3,0],[3,2]] print (TriTri2D(t1, t2), False)
t1 = [[0,0],[1,1],[0,2]] t2 = [[2,1],[3,-2],[3,4]] print (TriTri2D(t1, t2), False)
#Barely touching t1 = [[0,0],[1,0],[0,1]] t2 = [[1,0],[2,0],[1,1]] print (TriTri2D(t1, t2, onBoundary = True), True)
#Barely touching t1 = [[0,0],[1,0],[0,1]] t2 = [[1,0],[2,0],[1,1]] print (TriTri2D(t1, t2, onBoundary = False), False)</lang>
- Output:
True True True True False False True True False False False False True True /False False
Using shapely: <lang python>from __future__ import print_function from shapely.geometry import Polygon
def PolyOverlaps(poly1, poly2): poly1s = Polygon(poly1) poly2s = Polygon(poly2) return poly1s.intersects(poly2s)
if __name__=="__main__": t1 = [[0,0],[5,0],[0,5]] t2 = [[0,0],[5,0],[0,6]] print (PolyOverlaps(t1, t2), True)
t1 = [[0,0],[0,5],[5,0]] t2 = [[0,0],[0,6],[5,0]] print (PolyOverlaps(t1, t2), True)
t1 = [[0,0],[5,0],[0,5]] t2 = [[-10,0],[-5,0],[-1,6]] print (PolyOverlaps(t1, t2), False)
t1 = [[0,0],[5,0],[2.5,5]] t2 = [[0,4],[2.5,-1],[5,4]] print (PolyOverlaps(t1, t2), True)
t1 = [[0,0],[1,1],[0,2]] t2 = [[2,1],[3,0],[3,2]] print (PolyOverlaps(t1, t2), False)
t1 = [[0,0],[1,1],[0,2]] t2 = [[2,1],[3,-2],[3,4]] print (PolyOverlaps(t1, t2), False)
#Barely touching t1 = [[0,0],[1,0],[0,1]] t2 = [[1,0],[2,0],[1,1]] print (PolyOverlaps(t1, t2), "?")</lang>
- Output:
True True True True False False True True False False False False True ?
QB64
<lang QB64> DATA 0,0,5,0,0,5,0,0,5,0,0,6 DATA 0,0,0,5,5,0,0,0,0,5,5,0 DATA 0,0,5,0,0,5,-10,0,-5,0,-1,6 DATA 0,0,5,0,2.5,5,0,4,2.5,-1,5,4 DATA 0,0,1,1,0,2,2,1,3,0,3,2 DATA 0,0,1,1,0,2,2,1,3,-2,3,4
TYPE point
x AS INTEGER y AS INTEGER
END TYPE
DIM coord(12, 3) AS point
workscreen = _NEWIMAGE(800, 800, 32) backscreen = _NEWIMAGE(800, 800, 32)
SCREEN workscreen FOR i = 1 TO 12 '12 triangles
FOR j = 1 TO 3 'with 3 coordinates for each
READ coord(i, j).x 'X coord
READ coord(i, j).y 'Y coord
FixCoord coord(i, j)
NEXT
NEXT _DELAY .5 _SCREENMOVE _MIDDLE
FOR i = 1 TO 12
_DEST workscreen
CLS
_DEST backscreen
_DONTBLEND
CLS , 0
PSET (coord(i, 1).x, coord(i, 1).y), _RGBA32(255, 255, 255, 128)
FOR j = 2 TO 3
LINE -(coord(i, j).x, coord(i, j).y), _RGBA32(255, 255, 255, 128)
NEXT
LINE -(coord(i, 1).x, coord(i, 1).y), _RGBA32(255, 255, 255, 128)
xinside = (coord(i, 1).x + coord(i, 2).x + coord(i, 3).x) / 3
yinside = (coord(i, 1).y + coord(i, 2).y + coord(i, 3).y) / 3
PAINT (xinside, yinside), _RGBA32(255, 255, 255, 128)
_BLEND
_PUTIMAGE , backscreen, 0
CLS , 0
_DONTBLEND
i = i + 1
PSET (coord(i, 1).x, coord(i, 1).y), _RGBA32(255, 0, 0, 128)
FOR j = 2 TO 3
LINE -(coord(i, j).x, coord(i, j).y), _RGBA32(255, 0, 0, 128)
NEXT
LINE -(coord(i, 1).x, coord(i, 1).y), _RGBA32(255, 0, 0, 128)
xinside = (coord(i, 1).x + coord(i, 2).x + coord(i, 3).x) / 3
yinside = (coord(i, 1).y + coord(i, 2).y + coord(i, 3).y) / 3
PAINT (xinside, yinside), _RGBA32(255, 0, 0, 128)
_BLEND
_PUTIMAGE , backscreen, 0
_DEST workscreen
_SOURCE workscreen
overlap = 0
FOR x = 0 TO 999
FOR y = 0 TO 999
IF POINT(x, y) = _RGBA32(190, 63, 63, 255) THEN overlap = -1: GOTO overlap
NEXT
NEXT
overlap:
IF overlap THEN PRINT "OVERLAP" ELSE PRINT "NO OVERLAP"
SLEEP
NEXT SYSTEM
SUB FixCoord (p AS point)
p.x = (10 + p.x) * 30 + 100 p.y = (10 + p.y) * 30
END SUB </lang>
Racket
<lang racket>#lang racket
- A triangle is a list of three pairs of points
- '((x . y) (x . y) (x . y))
(define (to-tri x1 y1 x2 y2 x3 y3) `((,x1 . ,y1) (,x2 . ,y2) (,x3 . ,y3)))
(define det-2D
(match-lambda [`((,x1 . ,y1) (,x2 . ,y2) (,x3 . ,y3)) (+ (* x1 (- y2 y3)) (* x2 (- y3 y1)) (* x3 (- y1 y2)))]))
(define (assert-triangle-winding triangle allow-reversed?)
(cond [(>= (det-2D triangle) 0) triangle] [allow-reversed? (match triangle [(list p1 p2 p3) (list p1 p3 p2)])] [else (error 'assert-triangle-winding "triangle is wound in wrong direction")]))
(define (tri-tri-2d? triangle1 triangle2
#:ϵ (ϵ 0)
#:allow-reversed? (allow-reversed? #f)
#:on-boundary? (on-boundary? #t))
(define check-edge
(if on-boundary? ; Points on the boundary are considered as colliding
(λ (triangle) (< (det-2D triangle) ϵ))
(λ (triangle) (<= (det-2D triangle) ϵ))))
(define (inr t1 t2)
(for*/and ((i (in-range 3)))
;; Check all points of trangle 2 lay on the external side
;; of the edge E. If they do, the triangles do not collide.
(define t1.i (list-ref t1 i))
(define t1.j (list-ref t1 (modulo (add1 i) 3)))
(not (for/and ((k (in-range 3))) (check-edge (list (list-ref t2 k) t1.i t1.j))))))
(let (;; Trangles must be expressed anti-clockwise
(tri1 (assert-triangle-winding triangle1 allow-reversed?))
(tri2 (assert-triangle-winding triangle2 allow-reversed?)))
(and (inr tri1 tri2) (inr tri2 tri1))))
- ---------------------------------------------------------------------------------------------------
(module+ test
(require rackunit)
(define triangleses ; pairs of triangles
(for/list ((a.b (in-list '(((0 0 5 0 0 5) ( 0 0 5 0 0 6))
((0 0 0 5 5 0) ( 0 0 0 5 5 0))
((0 0 5 0 0 5) (-10 0 -5 0 -1 6))
((0 0 5 0 2.5 5) ( 0 4 2.5 -1 5 4))
((0 0 1 1 0 2) ( 2 1 3 0 3 2))
((0 0 1 1 0 2) ( 2 1 3 -2 3 4))))))
(map (curry apply to-tri) a.b)))
(check-equal?
(for/list ((t1.t2 (in-list triangleses)))
(define t1 (first t1.t2))
(define t2 (second t1.t2))
(define-values (r reversed?)
(with-handlers ([exn:fail? (λ (_) (values (tri-tri-2d? t1 t2 #:allow-reversed? #t) #t))])
(values (tri-tri-2d? t1 t2) #f)))
(cons r reversed?))
'((#t . #f) (#t . #t) (#f . #f) (#t . #f) (#f . #f) (#f . #f)))
(let ((c1 (to-tri 0 0 1 0 0 1)) (c2 (to-tri 1 0 2 0 1 1))) (check-true (tri-tri-2d? c1 c2 #:on-boundary? #t)) (check-false (tri-tri-2d? c1 c2 #:on-boundary? #f))))
</lang>
No output → all tests passed
Raku
(formerly Perl 6) First, check if any vertex is inside each other triangle (that should cover most overlapping cases including enclosures). Then see if an edge of triangle A intersects any of two edges of B (for shapes like Star of David [1]) <lang perl6># Reference:
- https://stackoverflow.com/questions/2049582/how-to-determine-if-a-point-is-in-a-2d-triangle
- https://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
use v6;
sub if-overlap ($triangle-pair) {
my (\A,\B) = $triangle-pair; my Bool $result = False;
sub sign (\T) {
return (T.[0][0] - T[2][0]) * (T[1][1] - T[2][1]) -
(T[1][0] - T[2][0]) * (T[0][1] - T[2][1]);
}
sub point-in-triangle (\pt, \Y --> Bool) {
my ($d1, $d2, $d3);
my Bool ($has_neg, $has_pos);
$d1 = sign (pt, Y.[0], Y.[1]);
$d2 = sign (pt, Y.[1], Y.[2]);
$d3 = sign (pt, Y.[2], Y.[0]);
$has_neg = ($d1 < 0) || ($d2 < 0) || ($d3 < 0);
$has_pos = ($d1 > 0) || ($d2 > 0) || ($d3 > 0);
return !($has_neg && $has_pos); }
sub orientation(\P, \Q, \R --> Int) {
my \val = (Q.[1] - P.[1]) * (R.[0] - Q.[0]) -
(Q.[0] - P.[0]) * (R.[1] - Q.[1]);
return 0 if val == 0; # colinear
return (val > 0) ?? 1 !! 2; # clock or counterclock wise }
sub onSegment(\P, \Q, \R --> Bool) {
Q.[0] <= max(P.[0], R.[0]) && Q.[0] >= min(P.[0], R.[0]) &&
Q.[1] <= max(P.[1], R.[1]) && Q.[1] >= min(P.[0], R.[1])
?? True !! False;
}
sub intersect(\A,\B,\C,\D --> Bool) {
my \o1 = orientation A,C,D;
my \o2 = orientation B,C,D;
my \o3 = orientation A,B,C;
my \o4 = orientation A,B,D;
return True if o1 != o2 && o3 != o4;
return True if (o1 == 0 && onSegment(A, C, D)) ;
return True if (o2 == 0 && onSegment(B, C, D)) ;
return True if (o3 == 0 && onSegment(A, B, C)) ;
return True if (o4 == 0 && onSegment(A, B, D)) ;
return False; }
for ^3 {
{$result = True; last } if point-in-triangle A.[$^i] , B or
point-in-triangle B.[$^i] , A ;
}
unless $result {
$result = True if intersect A.[0], A.[1], B.[0], B.[1] or
intersect A.[0], A.[1], B.[0], B.[2]
}
say A, " and ", B, " do", $result ?? "" !! " NOT" , " overlap.";
}
my \DATA = [
[ [(0,0),(5,0),(0,5)] , [(0,0),(5,0),(0,6)] ], [ [(0,0),(0,5),(5,0)] , [(0,0),(0,5),(5,0)] ], [ [(0,0),(5,0),(0,5)] , [(-10,0),(-5,0),(-1,6)] ], [ [(0,0),(5,0),(2.5,5)] , [ (0,4),(2.5,-1),(5,4)] ], [ [(0,0),(1,1),(0,2)] , [(2,1),(3,0),(3,2)] ], [ [(0,0),(1,1),(0,2)] , [(2,1),(3,-2),(3,4)] ], [ [(0,0),(1,0),(0,1)] , [(1,0),(2,0),(1,1)] ]
];
if-overlap $_ for DATA ;</lang>
- Output:
[(0 0) (5 0) (0 5)] and [(0 0) (5 0) (0 6)] do overlap.[(0 0) (0 5) (5 0)] and [(0 0) (0 5) (5 0)] do overlap. [(0 0) (5 0) (0 5)] and [(-10 0) (-5 0) (-1 6)] do NOT overlap. [(0 0) (5 0) (2.5 5)] and [(0 4) (2.5 -1) (5 4)] do overlap. [(0 0) (1 1) (0 2)] and [(2 1) (3 0) (3 2)] do NOT overlap. [(0 0) (1 1) (0 2)] and [(2 1) (3 -2) (3 4)] do NOT overlap. [(0 0) (1 0) (0 1)] and [(1 0) (2 0) (1 1)] do overlap.
REXX
Note: The triangles must be real triangles (no edge of length 0) <lang rexx>/* REXX */ Signal On Halt Signal On Novalue Signal On Syntax
fid='trio.in' oid='trio.txt'; 'erase' oid
Call trio_test '0 0 5 0 0 5 0 0 5 0 0 6'
Call trio_test '0 0 0 5 5 0 0 0 0 5 5 0'
Call trio_test '0 0 5 0 0 5 -10 0 -5 0 -1 6'
Call trio_test '0 0 5 0 2.5 5 0 4 2.5 -1 5 4'
Call trio_test '0 0 1 1 0 2 2 1 3 0 3 2'
Call trio_test '0 0 1 1 0 2 2 1 3 -2 3 4'
Call trio_test '0 0 1 0 0 1 1 0 2 0 1 1'
Call trio_test '1 0 3 0 2 2 1 3 3 3 2 5' Call trio_test '1 0 3 0 2 2 1 3 3 3 2 2' Call trio_test '0 0 2 0 2 2 3 3 5 3 5 5' Call trio_test '2 0 2 6 1 8 0 1 0 5 8 3' Call trio_test '0 0 4 0 0 4 0 2 2 0 2 2' Call trio_test '0 0 4 0 0 4 1 1 2 1 1 2' Exit
trio_test: parse Arg tlist tlist=space(tlist) Parse Arg ax ay bx by cx cy dx dy ex ey fx fy
Say 'ABC:' show_p(ax ay) show_p(bx by) show_p(cx cy) Say 'DEF:' show_p(dx dy) show_p(ex ey) show_p(fx fy)
bordl=bord(tlist) /* corners that are on the other triangle's edges */ If bordl<> Then
Say 'Corners on the other triangles edges:' bordl
wb=words(bordl) /* how many of them? */ Select
When wb=3 Then Do /* all three match */
If ident(ax ay,bx by,cx cy,dx dy,ex ey,fx fy) Then
Say 'Triangles are identical'
Else
Say 'Triangles overlap'
Say
Return
End
When wb=2 Then Do /* two of them match */
Say 'Triangles overlap'
Say ' they have a common edge 'bordl
Say
Return
End
When wb=1 Then Do /* one of them match */
Say 'Triangles touch on' bordl /* other parts may overlap */
Say ' we analyze further'
End
Otherwise /* we know nothing yet */
Nop
End
trio_result=trio(tlist) /* any other overlap? */
Select
When trio_result=0 Then Do /* none whatsoever */
If wb=1 Then
Say 'Triangles touch (border case) at' show_p(bordl)
Else
Say 'Triangles dont overlap'
End
When trio_result>0 Then /* plain overlapping case */
Say 'Triangles overlap'
End
Say Return
trio: /*---------------------------------------------------------------------
- Determine if two triangles overlap
- --------------------------------------------------------------------*/
parse Arg tlist Parse Arg pax pay pbx pby pcx pcy pdx pdy pex pey pfx pfy
abc=subword(tlist,1,6) def=subword(tlist,7,6)
Do i=1 To 3
s.i=subword(abc abc,i*2-1,4) t.i=subword(def def,i*2-1,4) End
abc_= def_=
Do i=1 To 3
abc.i=subword(abc,i*2-1,2) /* corners of ABC */
def.i=subword(def,i*2-1,2) /* corners of DEF */
Parse Var abc.i x y; abc_=abc_ '('||x','y')'
Parse Var def.i x y; def_=def_ '('||x','y')'
End
Call o 'abc_='abc_ Call o 'def_='def_
over=0
Do i=1 To 3 Until over
Do j=1 To 3 Until over
If ssx(s.i t.j) Then Do /* intersection of two edges */
over=1
Leave
End
End
End
If over=0 Then Do /* no edge intersection found */
Do ii=1 To 3 Until over /* look for first possibility */
Call o ' ' 'abc.'ii'='abc.ii 'def='def
Call o 'ii='ii 'def.'ii'='def.ii 'abc='abc
If in_tri(abc.ii,def) Then Do /* a corner of ABC is in DEF */
Say abc.ii 'is within' def
over=1
End
Else If in_tri(def.ii,abc) Then Do /* a corner of DEF is in ABC */
Say def.ii 'is within' abc
over=1
End
End
End
If over=0 Then rw='dont ' Else rw=
Call o 'Triangles' show_p(pax pay) show_p(pbx pby) show_p(pcx pcy),
'and' show_p(pdx pdy) show_p(pex pey) show_p(pfx pfy),
rw'overlap'
Call o Return over
ssx: Procedure Expose oid bordl /*---------------------------------------------------------------------
- Intersection of 2 line segments A-B and C-D
- --------------------------------------------------------------------*/
Parse Arg xa ya xb yb xc yc xd yd
d=ggx(xa ya xb yb xc yc xd yd)
Call o 'ssx:' arg(1) d res=0 Select
When d='-' Then res=0
When d='I' Then Do
If xa<>xb Then Do
xab_min=min(xa,xb)
xcd_min=min(xc,xd)
xab_max=max(xa,xb)
xcd_max=max(xc,xd)
If xab_min>xcd_max |,
xcd_min>xab_max Then
res=0
Else Do
res=1
Select
When xa=xc & isb(xc,xb,xd)=0 Then Do; x=xa; y=ya; End
When xb=xc & isb(xc,xa,xd)=0 Then Do; x=xb; y=yb; End
When xa=xd & isb(xc,xb,xd)=0 Then Do; x=xa; y=ya; End
When xb=xd & isb(xc,xa,xd)=0 Then Do; x=xb; y=yb; End
Otherwise Do
x='*'
y=ya
End
End
Call o 'ssx:' x y
End
End
Else Do
yab_min=min(ya,yb)
ycd_min=min(yc,yd)
yab_max=max(ya,yb)
ycd_max=max(yc,yd)
If yab_min>ycd_max |,
ycd_min>yab_max Then
res=0
Else Do
res=1
x=xa
y='*'
Parse Var bordl x_bord '/' y_bord
If x=x_bord Then Do
Call o xa'/* IGNORED'
res=0
End
End
End
End
Otherwise Do
Parse Var d x y
If is_between(xa,x,xb) &,
is_between(xc,x,xd) &,
is_between(ya,y,yb) &,
is_between(yc,y,yd) Then Do
If x'/'y<>bordl Then
res=1
End
End
End
If res=1 Then Do
Say 'Intersection of line segments: ('||x'/'y')'
Parse Var bordl x_bord '/' y_bord
If x=x_bord Then Do
res=0
Call o x'/'y 'IGNORED'
End
End
Else Call o 'ssx: -'
Return res
ggx: Procedure Expose oid bordl /*---------------------------------------------------------------------
- Intersection of 2 (straight) lines
- --------------------------------------------------------------------*/
Parse Arg xa ya xb yb xc yc xd yd res= If xa=xb Then Do
k1='*' x1=xa If ya=yb Then Do res='Points A and B are identical' rs='*' End End
Else Do
k1=(yb-ya)/(xb-xa) d1=ya-k1*xa End
If xc=xd Then Do
k2='*' x2=xc If yc=yd Then Do res='Points C and D are identical' rs='*' End End
Else Do
k2=(yd-yc)/(xd-xc) d2=yc-k2*xc End
If res= Then Do
If k1='*' Then Do
If k2='*' Then Do
If x1=x2 Then Do
res='Lines AB and CD are identical'
rs='I'
End
Else Do
res='Lines AB and CD are parallel'
rs='-'
End
End
Else Do
x=x1
y=k2*x+d2
End
End
Else Do
If k2='*' Then Do
x=x2
y=k1*x+d1
End
Else Do
If k1=k2 Then Do
If d1=d2 Then Do
res='Lines AB and CD are identical'
rs='I'
End
Else Do
res='Lines AB and CD are parallel'
rs='-'
End
End
Else Do
x=(d2-d1)/(k1-k2)
y=k1*x+d1
End
End
End
End
If res= Then Do
res='Intersection is ('||x'/'y')'
rs=x y
Call o 'line intersection' x y
End
Call o 'A=('xa'/'ya') B=('||xb'/'yb') C=('||xc'/'yc') D=('||xd'/'yd')' '-->' res
Return rs
isb: Procedure
Parse Arg a,b,c Return sign(b-a)<>sign(b-c)
is_between: Procedure Expose oid
Parse Arg a,b,c Return diff_sign(b-a,b-c)
diff_sign: Procedure
Parse Arg diff1,diff2 Return (sign(diff1)<>sign(diff2))|(sign(diff1)=0)
o: /*y 'sigl='sigl */ Return lineout(oid,arg(1))
in_tri: Procedure Expose oid bordl /*---------------------------------------------------------------------
- Determine if the point (px/py) is within the given triangle
- --------------------------------------------------------------------*/
Parse Arg px py,ax ay bx by cx cy abc=ax ay bx by cx cy res=0 maxx=max(ax,bx,cx) minx=min(ax,bx,cx) maxy=max(ay,by,cy) miny=min(ay,by,cy)
If px>maxx|px<minx|py>maxy|py<miny Then
Return 0
Parse Value mk_g(ax ay,bx by) With k.1 d.1 x.1 Parse Value mk_g(bx by,cx cy) With k.2 d.2 x.2 Parse Value mk_g(cx cy,ax ay) With k.3 d.3 x.3 /* say 'g1:' show_g(k.1,d.1,x.1) say 'g2:' show_g(k.2,d.2,x.2) say 'g3:' show_g(k.3,d.3,x.3) Say px py '-' ax ay bx by cx cy
- /
Do i=1 To 3
Select
When k.i='*' Then
Call o 'g.'i':' 'x='||x.i
When k.i=0 Then
Call o 'g.'i':' 'y='d.i
Otherwise
Call o 'g.'i':' 'y=' k.i'*x'dd(d.i)
End
End
If k.1='*' Then Do
y2=k.2*px+d.2 y3=k.3*px+d.3 If is_between(y2,py,y3) Then res=1 End
Else Do
kp1=k.1 dp1=py-kp1*px If k.2='*' Then x12=x.2 Else x12=(d.2-dp1)/(kp1-k.2) If k.3='*' Then x13=x.3 Else x13=(d.3-dp1)/(kp1-k.3) If is_between(x12,px,x13) Then res=1 End
If res=1 Then rr=' '
Else rr=' not '
If pos(px'/'py,bordl)>0 Then Do
ignored=' but is IGNORED' res=0 End
Else
ignored=
Say 'P ('px','py') is'rr'in' abc ignored Return res
bord: /*---------------------------------------------------------------------
- Look for corners of triangles that are situated
- on the edges of the other triangle
- --------------------------------------------------------------------*/
parse Arg tlist Parse Arg pax pay pbx pby pcx pcy pdx pdy pex pey pfx pfy bordl= abc=subword(tlist,1,6) def=subword(tlist,7,6)
Do i=1 To 3
s.i=subword(abc abc,i*2-1,4) t.i=subword(def def,i*2-1,4) End
abc_= def_= Do i=1 To 3
abc.i=subword(abc,i*2-1,2)
def.i=subword(def,i*2-1,2)
Parse Var abc.i x y; abc_=abc_ '('||x','y')'
Parse Var def.i x y; def_=def_ '('||x','y')'
End
Do i=1 To 3
i1=i+1 If i1=4 Then i1=1 Parse Value mk_g(abc.i,abc.i1) With k.1.i d.1.i x.1.i Parse Value mk_g(def.i,def.i1) With k.2.i d.2.i x.2.i End
Do i=1 To 3
Call o show_g(k.1.i,d.1.i,x.1.i) End
Do i=1 To 3
Call o show_g(k.2.i,d.2.i,x.2.i) End
pl= Do i=1 To 3
p=def.i
Do j=1 To 3
j1=j+1
If j1=4 Then j1=1
g='1.'j
If in_segment(p,abc.j,abc.j1) Then Do
pp=Translate(p,'/',' ')
If wordpos(pp,bordl)=0 Then
bordl=bordl pp
End
Call o show_p(p) show_g(k.g,d.g,x.g) '->' bordl
End
End
Call o 'Points on abc:' pl
pl= Do i=1 To 3
p=abc.i
Do j=1 To 3
j1=j+1
If j1=4 Then j1=1
g='2.'j
If in_segment(p,def.j,def.j1)Then Do
pp=Translate(p,'/',' ')
If wordpos(pp,bordl)=0 Then
bordl=bordl pp
End
Call o show_p(p) show_g(k.g,d.g,x.g) '->' bordl
End
End
Call o 'Points on def:' pl
Return bordl
in_segment: Procedure Expose g. sigl /*---------------------------------------------------------------------
- Determine if point x/y is on the line segment ax/ay bx/by
- --------------------------------------------------------------------*/
Parse Arg x y,ax ay,bx by Call show_p(x y) show_p(ax ay) show_p(bx by) Parse Value mk_g(ax ay,bx by) With gk gd gx Select
When gx<> Then res=(x=gx & is_between(ay,y,by)) When gk='*' Then res=(y=gd & is_between(ax,x,bx)) Otherwise Do yy=gk*x+gd res=(y=yy & is_between(ax,x,bx)) End End
Return res
mk_g: Procedure Expose g. /*---------------------------------------------------------------------
- given two points (a and b)
- compute y=k*x+d or, if a vertical line, k='*'; x=c
- --------------------------------------------------------------------*/
Parse Arg a,b /* 2 points */ Parse Var a ax ay Parse Var b bx by If ax=bx Then Do /* vertical line */
gk='*' /* special slope */ gx=ax /* x=ax is the equation */ gd='*' /* not required */ End
Else Do
gk=(by-ay)/(bx-ax) /* compute slope */ gd=ay-gk*ax /* compute y-distance */ gx= /* not required */ End
Return gk gd gx
is_between: Procedure
Parse Arg a,b,c Return diff_sign(b-a,b-c)
diff_sign: Procedure
Parse Arg diff1,diff2 Return (sign(diff1)<>sign(diff2))|(sign(diff1)=0)
show_p: Procedure
Call trace 'O'
Parse Arg x y
If pos('/',x)>0 Then
Parse Var x x '/' y
Return space('('||x'/'y')',0)
isb: Procedure Expose oid
Parse Arg a,b,c Return sign(b-a)<>sign(b-c)
o: Call o arg(1)
Return
show_g: Procedure /*---------------------------------------------------------------------
- given slope, y-distance, and (special) x-value
- compute y=k*x+d or, if a vertical line, k='*'; x=c
- --------------------------------------------------------------------*/
Parse Arg k,d,x Select
When k='*' Then res='x='||x /* vertical line */
When k=0 Then res='y='d /* horizontal line */
Otherwise Do /* ordinary line */
Select
When k=1 Then res='y=x'dd(d)
When k=-1 Then res='y=-x'dd(d)
Otherwise res='y='k'*x'dd(d)
End
End
End
Return res
dd: Procedure /*---------------------------------------------------------------------
- prepare y-distance for display
- --------------------------------------------------------------------*/
Parse Arg dd Select When dd=0 Then dd= /* omit dd if it's zero */ When dd<0 Then dd=dd /* use dd as is (-value) */ Otherwise dd='+'dd /* prepend '+' to positive dd */ End Return dd
ident: Procedure /*---------------------------------------------------------------------
- Determine if the corners ABC match those of DEF (in any order)
- --------------------------------------------------------------------*/
cnt.=0
Do i=1 To 6
Parse Value Arg(i) With x y
cnt.x.y=cnt.x.y+1
End
Do i=1 To 3
Parse Value Arg(i) With x y
If cnt.x.y<>2 Then
Return 0
End
Return 1
Novalue:
Say 'Novalue raised in line' sigl
Say sourceline(sigl)
Say 'Variable' condition('D')
Signal lookaround
Syntax:
Say 'Syntax raised in line' sigl
Say sourceline(sigl)
Say 'rc='rc '('errortext(rc)')'
halt: lookaround:
If fore() Then Do Say 'You can look around now.' Trace ?R Nop End Exit 12</lang>
- Output:
ABC: (0/0) (5/0) (0/5) DEF: (0/0) (5/0) (0/6) Corners on the other triangle's edges: 0/0 5/0 0/5 Triangles overlap ABC: (0/0) (0/5) (5/0) DEF: (0/0) (0/5) (5/0) Corners on the other triangle's edges: 0/0 0/5 5/0 Triangles are identical ABC: (0/0) (5/0) (0/5) DEF: (-10/0) (-5/0) (-1/6) Triangles don't overlap ABC: (0/0) (5/0) (2.5/5) DEF: (0/4) (2.5/-1) (5/4) Intersection of line segments: (2/0) Triangles overlap ABC: (0/0) (1/1) (0/2) DEF: (2/1) (3/0) (3/2) Triangles don't overlap ABC: (0/0) (1/1) (0/2) DEF: (2/1) (3/-2) (3/4) Triangles don't overlap ABC: (0/0) (1/0) (0/1) DEF: (1/0) (2/0) (1/1) Corners on the other triangle's edges: 1/0 Triangles touch on 1/0 we analyze further Intersection of line segments: (1/0) P (1,0) is in 0 0 1 0 0 1 but is IGNORED P (1,0) is in 1 0 2 0 1 1 but is IGNORED P (1,1) is not in 0 0 1 0 0 1 Triangles touch (border case) at (1/0) ABC: (1/0) (3/0) (2/2) DEF: (1/3) (3/3) (2/5) Triangles don't overlap ABC: (1/0) (3/0) (2/2) DEF: (1/3) (3/3) (2/2) Corners on the other triangle's edges: 2/2 Triangles touch on 2/2 we analyze further P (2,2) is in 1 3 3 3 2 2 but is IGNORED P (2,2) is in 1 0 3 0 2 2 but is IGNORED Triangles touch (border case) at (2/2) ABC: (0/0) (2/0) (2/2) DEF: (3/3) (5/3) (5/5) Triangles don't overlap ABC: (2/0) (2/6) (1/8) DEF: (0/1) (0/5) (8/3) Intersection of line segments: (2/4.50) Triangles overlap ABC: (0/0) (4/0) (0/4) DEF: (0/2) (2/0) (2/2) Corners on the other triangle's edges: 0/2 2/0 2/2 Triangles overlap ABC: (0/0) (4/0) (0/4) DEF: (1/1) (2/1) (1/2) P (1,1) is in 0 0 4 0 0 4 1 1 is within 0 0 4 0 0 4 Triangles overlap
Ruby
<lang ruby>require "matrix"
def det2D(p1, p2, p3)
return p1[0] * (p2[1] - p3[1]) + p2[0] * (p3[1] - p1[1]) + p3[0] * (p1[1] - p2[1])
end
def checkTriWinding(p1, p2, p3, allowReversed)
detTri = det2D(p1, p2, p3)
if detTri < 0.0 then
if allowReversed then
p2[0], p3[0] = p3[0], p2[0]
p2[1], p3[1] = p3[1], p2[1]
else
raise "Triangle has incorrect winding"
end
end
end
def boundaryCollideChk(p1, p2, p3, eps)
return det2D(p1, p2, p3) < eps
end
def boundaryDoesntCollideChk(p1, p2, p3, eps)
return det2D(p1, p2, p3) <= eps
end
def triTri2D(t1, t2, eps, allowReversed, onBoundary)
# Triangles must be expressed anti-clockwise checkTriWinding(t1[0], t1[1], t1[2], allowReversed) checkTriWinding(t2[0], t2[1], t2[2], allowReversed)
if onBoundary then
# Points on the boundary are considered as colliding
chkEdge = -> (p1, p2, p3, eps) { boundaryCollideChk(p1, p2, p3, eps) }
else
# Points on the boundary are not considered as colliding
chkEdge = -> (p1, p2, p3, eps) { boundaryDoesntCollideChk(p1, p2, p3, eps) }
end
# For edge E of triangle 1
for i in 0..2 do
j = (i + 1) % 3
# Check all points of trangle 2 lay on the external side of the edge E. If
# they do, the triangles do not collide.
if chkEdge.(t1[i], t1[j], t2[0], eps) and chkEdge.(t1[i], t1[j], t2[1], eps) and chkEdge.(t1[i], t1[j], t2[2], eps) then
return false
end
end
# For edge E of triangle 2
for i in 0..2 do
j = (i + 1) % 3
# Check all points of trangle 1 lay on the external side of the edge E. If
# they do, the triangles do not collide.
if chkEdge.(t2[i], t2[j], t1[0], eps) and chkEdge.(t2[i], t2[j], t1[1], eps) and chkEdge.(t2[i], t2[j], t1[2], eps) then
return false
end
end
# The triangles collide return true
end
def main
t1 = [Vector[0,0], Vector[5,0], Vector[0,5]] t2 = [Vector[0,0], Vector[5,0], Vector[0,6]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, true)]
t1 = [Vector[0,0], Vector[0,5], Vector[5,0]] t2 = [Vector[0,0], Vector[0,5], Vector[5,0]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, true, true)]
t1 = [Vector[ 0,0], Vector[ 5,0], Vector[ 0,5]] t2 = [Vector[-10,0], Vector[-5,0], Vector[-1,6]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, true)]
t1 = [Vector[0,0], Vector[ 5, 0], Vector[2.5,5]] t2 = [Vector[0,4], Vector[2.5,-1], Vector[ 5,4]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, true)]
t1 = [Vector[0,0], Vector[1,1], Vector[0,2]] t2 = [Vector[2,1], Vector[3,0], Vector[3,2]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, true)]
t1 = [Vector[0,0], Vector[1, 1], Vector[0,2]] t2 = [Vector[2,1], Vector[3,-2], Vector[3,4]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, true)]
# Barely touching t1 = [Vector[0,0], Vector[1,0], Vector[0,1]] t2 = [Vector[1,0], Vector[2,0], Vector[1,1]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, true)]
# Barely touching t1 = [Vector[0,0], Vector[1,0], Vector[0,1]] t2 = [Vector[1,0], Vector[2,0], Vector[1,1]] print "Triangle: ", t1, "\n" print "Triangle: ", t2, "\n" print "overlap: %s\n\n" % [triTri2D(t1, t2, 0.0, false, false)]
end
main()</lang>
- Output:
Triangle: [Vector[0, 0], Vector[5, 0], Vector[0, 5]] Triangle: [Vector[0, 0], Vector[5, 0], Vector[0, 6]] overlap: true Triangle: [Vector[0, 0], Vector[0, 5], Vector[5, 0]] Triangle: [Vector[0, 0], Vector[0, 5], Vector[5, 0]] overlap: true Triangle: [Vector[0, 0], Vector[5, 0], Vector[0, 5]] Triangle: [Vector[-10, 0], Vector[-5, 0], Vector[-1, 6]] overlap: false Triangle: [Vector[0, 0], Vector[5, 0], Vector[2.5, 5]] Triangle: [Vector[0, 4], Vector[2.5, -1], Vector[5, 4]] overlap: true Triangle: [Vector[0, 0], Vector[1, 1], Vector[0, 2]] Triangle: [Vector[2, 1], Vector[3, 0], Vector[3, 2]] overlap: false Triangle: [Vector[0, 0], Vector[1, 1], Vector[0, 2]] Triangle: [Vector[2, 1], Vector[3, -2], Vector[3, 4]] overlap: false Triangle: [Vector[0, 0], Vector[1, 0], Vector[0, 1]] Triangle: [Vector[1, 0], Vector[2, 0], Vector[1, 1]] overlap: true Triangle: [Vector[0, 0], Vector[1, 0], Vector[0, 1]] Triangle: [Vector[1, 0], Vector[2, 0], Vector[1, 1]] overlap: false
Scala
<lang scala>object Overlap {
type Point = (Double, Double)
class Triangle(var p1: Point, var p2: Point, var p3: Point) {
override def toString: String = s"Triangle: $p1, $p2, $p3"
}
def det2D(t: Triangle): Double = {
val (p1, p2, p3) = (t.p1, t.p2, t.p3)
p1._1 * (p2._2 - p3._2) +
p2._1 * (p3._2 - p1._2) +
p3._1 * (p1._2 - p2._2)
}
def checkTriWinding(t: Triangle, allowReversed: Boolean): Unit = {
val detTri = det2D(t)
if (detTri < 0.0) {
if (allowReversed) {
val a = t.p3
t.p3 = t.p2
t.p2 = a
} else throw new RuntimeException("Triangle has wrong winding direction")
}
}
def boundaryCollideChk(t: Triangle, eps: Double): Boolean = det2D(t) < eps
def boundaryDoesntCollideChk(t: Triangle, eps: Double): Boolean = det2D(t) <= eps
def triTri2D(t1: Triangle, t2: Triangle, eps: Double = 0.0, allowReversed: Boolean = false, onBoundary: Boolean = true): Boolean = {
//triangles must be expressed anti-clockwise
checkTriWinding(t1, allowReversed)
checkTriWinding(t2, allowReversed)
// 'onBoundary' determines whether points on boundary are considered as colliding or not
val chkEdge = if (onBoundary) Overlap.boundaryCollideChk _ else Overlap.boundaryDoesntCollideChk _
val lp1 = Array(t1.p1, t1.p2, t1.p3)
val lp2 = Array(t2.p1, t2.p2, t2.p3)
// for each edge E of t1
for (i <- 0 until 3) {
val j = (i + 1) % 3
// Check all points of t2 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(new Triangle(lp1(i), lp1(j), lp2(0)), eps)
&& chkEdge(new Triangle(lp1(i), lp1(j), lp2(1)), eps)
&& chkEdge(new Triangle(lp1(i), lp1(j), lp2(2)), eps)) return false
}
// for each edge E of t2
for (i <- 0 until 3) {
val j = (i + 1) % 3
// Check all points of t1 lay on the external side of edge E.
// If they do, the triangles do not overlap.
if (chkEdge(new Triangle(lp2(i), lp2(j), lp1(0)), eps)
&& chkEdge(new Triangle(lp2(i), lp2(j), lp1(1)), eps)
&& chkEdge(new Triangle(lp2(i), lp2(j), lp1(2)), eps)) return false
}
// The triangles overlap true }
def main(args: Array[String]): Unit = {
var t1 = new Triangle((0.0, 0.0), (5.0, 0.0), (0.0, 5.0))
var t2 = new Triangle((0.0, 0.0), (5.0, 0.0), (0.0, 6.0))
println(s"$t1 and\n$t2")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
// need to allow reversed for this pair to avoid exception t1 = new Triangle((0.0, 0.0), (0.0, 5.0), (5.0, 0.0)) t2 = t1 println(s"\n$t1 and\n$t2") println(if (triTri2D(t1, t2, 0.0, allowReversed = true)) "overlap (reversed)" else "do not overlap")
t1 = new Triangle((0.0, 0.0), (5.0, 0.0), (0.0, 5.0)) t2 = new Triangle((-10.0, 0.0), (-5.0, 0.0), (-1.0, 6.0)) println(s"\n$t1 and\n$t2") println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t1.p3 = (2.5, 5.0) t2 = new Triangle((0.0, 4.0), (2.5, -1.0), (5.0, 4.0)) println(s"\n$t1 and\n$t2") println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t1 = new Triangle((0.0, 0.0), (1.0, 1.0), (0.0, 2.0)) t2 = new Triangle((2.0, 1.0), (3.0, 0.0), (3.0, 2.0)) println(s"\n$t1 and\n$t2") println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t2 = new Triangle((2.0, 1.0), (3.0, -2.0), (3.0, 4.0)) println(s"\n$t1 and\n$t2") println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
t1 = new Triangle((0.0, 0.0), (1.0, 0.0), (0.0, 1.0))
t2 = new Triangle((1.0, 0.0), (2.0, 0.0), (1.0, 1.1))
println(s"\n$t1 and\n$t2")
println("which have only a single corner in contact, if boundary points collide")
println(if (triTri2D(t1, t2)) "overlap" else "do not overlap")
println(s"\n$t1 and\n$t2")
println("which have only a single corner in contact, if boundary points do not collide")
println(if (triTri2D(t1, t2, onBoundary = false)) "overlap" else "do not overlap")
}
}</lang>
- Output:
Triangle: (0.0,0.0), (5.0,0.0), (0.0,5.0) and Triangle: (0.0,0.0), (5.0,0.0), (0.0,6.0) overlap Triangle: (0.0,0.0), (0.0,5.0), (5.0,0.0) and Triangle: (0.0,0.0), (0.0,5.0), (5.0,0.0) overlap (reversed) Triangle: (0.0,0.0), (5.0,0.0), (0.0,5.0) and Triangle: (-10.0,0.0), (-5.0,0.0), (-1.0,6.0) do not overlap Triangle: (0.0,0.0), (5.0,0.0), (2.5,5.0) and Triangle: (0.0,4.0), (2.5,-1.0), (5.0,4.0) overlap Triangle: (0.0,0.0), (1.0,1.0), (0.0,2.0) and Triangle: (2.0,1.0), (3.0,0.0), (3.0,2.0) do not overlap Triangle: (0.0,0.0), (1.0,1.0), (0.0,2.0) and Triangle: (2.0,1.0), (3.0,-2.0), (3.0,4.0) do not overlap Triangle: (0.0,0.0), (1.0,0.0), (0.0,1.0) and Triangle: (1.0,0.0), (2.0,0.0), (1.0,1.1) which have only a single corner in contact, if boundary points collide overlap Triangle: (0.0,0.0), (1.0,0.0), (0.0,1.0) and Triangle: (1.0,0.0), (2.0,0.0), (1.0,1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
Visual Basic .NET
<lang vbnet>Module Module1
Class Triangle
Property P1 As Tuple(Of Double, Double)
Property P2 As Tuple(Of Double, Double)
Property P3 As Tuple(Of Double, Double)
Sub New(p1 As Tuple(Of Double, Double), p2 As Tuple(Of Double, Double), p3 As Tuple(Of Double, Double))
Me.P1 = p1
Me.P2 = p2
Me.P3 = p3
End Sub
Function Det2D() As Double
Return P1.Item1 * (P2.Item2 - P3.Item2) +
P2.Item1 * (P3.Item2 - P1.Item2) +
P3.Item1 * (P1.Item2 - P2.Item2)
End Function
Sub CheckTriWinding(allowReversed As Boolean)
Dim detTri = Det2D()
If detTri < 0.0 Then
If allowReversed Then
Dim a = P3
P3 = P2
P2 = a
Else
Throw New Exception("Triangle has wrong winding direction")
End If
End If
End Sub
Function BoundaryCollideChk(eps As Double) As Boolean
Return Det2D() < eps
End Function
Function BoundaryDoesntCollideChk(eps As Double) As Boolean
Return Det2D() <= eps
End Function
Public Overrides Function ToString() As String
Return String.Format("Triangle: {0}, {1}, {2}", P1, P2, P3)
End Function
End Class
Function TriTri2D(t1 As Triangle, t2 As Triangle, Optional eps As Double = 0.0, Optional alloweReversed As Boolean = False, Optional onBoundary As Boolean = True) As Boolean
'Triangles must be expressed anti-clockwise
t1.CheckTriWinding(alloweReversed)
t2.CheckTriWinding(alloweReversed)
'"onboundary" determines whether points on boundary are considered as colliding or not
Dim chkEdge = If(onBoundary, Function(t As Triangle) t.BoundaryCollideChk(eps), Function(t As Triangle) t.BoundaryDoesntCollideChk(eps))
Dim lp1 As New List(Of Tuple(Of Double, Double)) From {t1.P1, t1.P2, t1.P3}
Dim lp2 As New List(Of Tuple(Of Double, Double)) From {t2.P1, t2.P2, t2.P3}
'for each edge E of t1
For i = 0 To 2
Dim j = (i + 1) Mod 3
'Check all points of t2 lay on the external side of edge E.
'If they do, the triangles do not overlap.
If chkEdge(New Triangle(lp1(i), lp1(j), lp2(0))) AndAlso
chkEdge(New Triangle(lp1(i), lp1(j), lp2(1))) AndAlso
chkEdge(New Triangle(lp1(i), lp1(j), lp2(2))) Then
Return False
End If
Next
'for each edge E of t2
For i = 0 To 2
Dim j = (i + 1) Mod 3
'Check all points of t1 lay on the external side of edge E.
'If they do, the triangles do not overlap.
If chkEdge(New Triangle(lp2(i), lp2(j), lp1(0))) AndAlso
chkEdge(New Triangle(lp2(i), lp2(j), lp1(1))) AndAlso
chkEdge(New Triangle(lp2(i), lp2(j), lp1(2))) Then
Return False
End If
Next
'The triangles overlap
Return True
End Function
Sub Overlap(t1 As Triangle, t2 As Triangle, Optional eps As Double = 0.0, Optional allowReversed As Boolean = False, Optional onBoundary As Boolean = True)
If TriTri2D(t1, t2, eps, allowReversed, onBoundary) Then
Console.WriteLine("overlap")
Else
Console.WriteLine("do not overlap")
End If
End Sub
Sub Main()
Dim t1 = New Triangle(Tuple.Create(0.0, 0.0), Tuple.Create(5.0, 0.0), Tuple.Create(0.0, 5.0))
Dim t2 = New Triangle(Tuple.Create(0.0, 0.0), Tuple.Create(5.0, 0.0), Tuple.Create(0.0, 6.0))
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Overlap(t1, t2)
Console.WriteLine()
' need to allow reversed for this pair to avoid exception
t1 = New Triangle(Tuple.Create(0.0, 0.0), Tuple.Create(0.0, 5.0), Tuple.Create(5.0, 0.0))
t2 = t1
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Overlap(t1, t2, 0.0, True)
Console.WriteLine()
t1 = New Triangle(Tuple.Create(0.0, 0.0), Tuple.Create(5.0, 0.0), Tuple.Create(0.0, 5.0))
t2 = New Triangle(Tuple.Create(-10.0, 0.0), Tuple.Create(-5.0, 0.0), Tuple.Create(-1.0, 6.0))
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Overlap(t1, t2)
Console.WriteLine()
t1.P3 = Tuple.Create(2.5, 5.0)
t2 = New Triangle(Tuple.Create(0.0, 4.0), Tuple.Create(2.5, -1.0), Tuple.Create(5.0, 4.0))
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Overlap(t1, t2)
Console.WriteLine()
t1 = New Triangle(Tuple.Create(0.0, 0.0), Tuple.Create(1.0, 1.0), Tuple.Create(0.0, 2.0))
t2 = New Triangle(Tuple.Create(2.0, 1.0), Tuple.Create(3.0, 0.0), Tuple.Create(3.0, 2.0))
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Overlap(t1, t2)
Console.WriteLine()
t2 = New Triangle(Tuple.Create(2.0, 1.0), Tuple.Create(3.0, -2.0), Tuple.Create(3.0, 4.0))
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Overlap(t1, t2)
Console.WriteLine()
t1 = New Triangle(Tuple.Create(0.0, 0.0), Tuple.Create(1.0, 0.0), Tuple.Create(0.0, 1.0))
t2 = New Triangle(Tuple.Create(1.0, 0.0), Tuple.Create(2.0, 0.0), Tuple.Create(1.0, 1.1))
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Console.WriteLine("which have only a single corner in contact, if boundary points collide")
Overlap(t1, t2)
Console.WriteLine()
Console.WriteLine("{0} and", t1)
Console.WriteLine("{0}", t2)
Console.WriteLine("which have only a single corner in contact, if boundary points do not collide")
Overlap(t1, t2, 0.0, False, False)
End Sub
End Module</lang>
- Output:
Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (0, 0), (5, 0), (0, 6) overlap Triangle: (0, 0), (0, 5), (5, 0) and Triangle: (0, 0), (0, 5), (5, 0) overlap Triangle: (0, 0), (5, 0), (0, 5) and Triangle: (-10, 0), (-5, 0), (-1, 6) do not overlap Triangle: (0, 0), (5, 0), (2.5, 5) and Triangle: (0, 4), (2.5, -1), (5, 4) overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, 0), (3, 2) do not overlap Triangle: (0, 0), (1, 1), (0, 2) and Triangle: (2, 1), (3, -2), (3, 4) do not overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1.1) which have only a single corner in contact, if boundary points collide overlap Triangle: (0, 0), (1, 0), (0, 1) and Triangle: (1, 0), (2, 0), (1, 1.1) which have only a single corner in contact, if boundary points do not collide do not overlap
zkl
<lang zkl>// A triangle is three pairs of points: ( (x,y), (x,y), (x,y) )
fcn det2D(triangle){
p1,p2,p3 := triangle; p1[0]*(p2[1] - p3[1]) + p2[0]*(p3[1] - p1[1]) + p3[0]*(p1[1] - p2[1]);
} fcn checkTriWinding(triangle,allowReversed){ //-->triangle, maybe new
detTri:=det2D(triangle);
if(detTri<0.0){
if(allowReversed){ p1,p2,p3 := triangle; return(p1,p3,p2); } // reverse
else throw(Exception.AssertionError(
"triangle has wrong winding direction"));
} triangle // no change
} fcn triTri2D(triangle1,triangle2, eps=0.0, allowReversed=False, onBoundary=True){
// Trangles must be expressed anti-clockwise
triangle1=checkTriWinding(triangle1, allowReversed);
triangle2=checkTriWinding(triangle2, allowReversed);
chkEdge:=
if(onBoundary) // Points on the boundary are considered as colliding
fcn(triangle,eps){ det2D(triangle)<eps }
else // Points on the boundary are not considered as colliding
fcn(triangle,eps){ det2D(triangle)<=eps };; // first ; terminates if
t1,t2 := triangle1,triangle2; // change names to protect the typist
do(2){ // check triangle1 and then triangle2
foreach i in (3){ //For edge E of trangle 1,
j:=(i+1)%3; // 1,2,0 // Check all points of trangle 2 lay on the external side // of the edge E. If they do, the triangles do not collide. if(chkEdge(T(t1[i],t1[j],t2[0]), eps) and chkEdge(T(t1[i],t1[j],t2[1]), eps) and chkEdge(T(t1[i],t1[j],t2[2]), eps)) return(False); // no collision
}
t2,t1 = triangle1,triangle2; // flip and re-test
}
True // The triangles collide
}</lang> <lang zkl>fcn toTri(ax,ay,bx,by,cx,cy){ //-->( (ax,ay),(bx,by),(cx,cy) )
vm.arglist.apply("toFloat").pump(List,Void.Read)
} triangles:=T( // pairs of triangles
T(toTri(0,0, 5,0, 0, 5), toTri( 0,0, 5, 0, 0,6)), T(toTri(0,0, 0,5, 5, 0), toTri( 0,0, 0, 5 , 5,0)), T(toTri(0,0, 5,0, 0, 5), toTri(-10,0, -5, 0, -1,6)), T(toTri(0,0, 5,0, 2.5,5), toTri( 0,4, 2.5,-1, 5,4)), T(toTri(0,0, 1,1, 0, 2), toTri( 2,1, 3, 0, 3,2)), T(toTri(0,0, 1,1, 0, 2), toTri( 2,1, 3, -2, 3,4))
);
// Expect: overlap, overlap (reversed), no overlap, overlap, no overlap, no overlap
foreach t1,t2 in (triangles){
reg r, reversed=False;
try{ r=triTri2D(t1,t2) }
catch(AssertionError){ r=triTri2D(t1,t2,0.0,True); reversed=True; }
print(t1,"\n",t2," ");
println(r and "overlap" or "no overlap", reversed and " (reversed)" or "");
println();
}
c1,c2 := toTri(0,0, 1,0, 0,1), toTri(1,0, 2,0, 1,1); println("Corner case (barely touching): ",triTri2D(c1,c2,0.0,False,True)); // True println("Corner case (barely touching): ",triTri2D(c1,c2,0.0,False,False)); // False</lang>
- Output:
L(L(0,0),L(5,0),L(0,5)) L(L(0,0),L(5,0),L(0,6)) overlap L(L(0,0),L(0,5),L(5,0)) L(L(0,0),L(0,5),L(5,0)) overlap (reversed) L(L(0,0),L(5,0),L(0,5)) L(L(-10,0),L(-5,0),L(-1,6)) no overlap L(L(0,0),L(5,0),L(2.5,5)) L(L(0,4),L(2.5,-1),L(5,4)) overlap L(L(0,0),L(1,1),L(0,2)) L(L(2,1),L(3,0),L(3,2)) no overlap L(L(0,0),L(1,1),L(0,2)) L(L(2,1),L(3,-2),L(3,4)) no overlap Corner case (barely touching): True Corner case (barely touching): False