Sutherland-Hodgman polygon clipping
(Redirected from Sutherland-Hodgson polygon clipping)
You are encouraged to solve this task according to the task description, using any language you may know.
The Sutherland-Hodgman clipping algorithm finds the polygon that is the intersection between an arbitrary polygon (the “subject polygon”) and a convex polygon (the “clip polygon”).
It is used in computer graphics (especially 2D graphics) to reduce the complexity of a scene being displayed by eliminating parts of a polygon that do not need to be displayed.
- Task
Take the closed polygon defined by the points:
![{\displaystyle [(50,150),(200,50),(350,150),(350,300),(250,300),(200,250),(150,350),(100,250),(100,200)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/134194d29d2845dd82bb0f9ec7e98d9f037042ac)
and clip it by the rectangle defined by the points:
![{\displaystyle [(100,100),(300,100),(300,300),(100,300)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/32aa50a15a9624e3635bc936bf67a61bede0c0ac)
Print the sequence of points that define the resulting clipped polygon.
- Extra credit
Display all three polygons on a graphical surface, using a different color for each polygon and filling the resulting polygon.
(When displaying you may use either a north-west or a south-west origin, whichever is more convenient for your display mechanism.)
11l
F clip(subjectPolygon, clipPolygon)
F inside(p, cp1, cp2)
R (cp2.x - cp1.x) * (p.y - cp1.y) > (cp2.y - cp1.y) * (p.x - cp1.x)
F computeIntersection(s, e, cp1, cp2)
V dc = cp1 - cp2
V dp = s - e
V n1 = cp1.x * cp2.y - cp1.y * cp2.x
V n2 = s.x * e.y - s.y * e.x
V n3 = 1.0 / (dc.x * dp.y - dc.y * dp.x)
R ((n1 * dp.x - n2 * dc.x) * n3, (n1 * dp.y - n2 * dc.y) * n3)
V outputList = subjectPolygon
V cp1 = clipPolygon.last
L(clipVertex) clipPolygon
V cp2 = clipVertex
V inputList = outputList
outputList.clear()
V s = inputList.last
L(subjectVertex) inputList
V e = subjectVertex
I inside(e, cp1, cp2)
I !inside(s, cp1, cp2)
outputList.append(computeIntersection(s, e, cp1, cp2))
outputList.append(e)
E I inside(s, cp1, cp2)
outputList.append(computeIntersection(s, e, cp1, cp2))
s = e
cp1 = cp2
R (outputList)
V subjectp = [(50.0, 150.0), (200.0, 50.0), (350.0, 150.0), (350.0, 300.0), (250.0, 300.0), (200.0, 250.0), (150.0, 350.0), (100.0, 250.0), (100.0, 200.0)]
V clipp = [(100.0, 100.0), (300.0, 100.0), (300.0, 300.0), (100.0, 300.0)]
print_elements(clip(subjectp, clipp), sep' "\n")- Output:
(100, 116.667) (125, 100) (275, 100) (300, 116.667) (300, 300) (250, 300) (200, 250) (175, 300) (125, 300) (100, 250)
Ada
with Ada.Containers.Doubly_Linked_Lists;
with Ada.Text_IO;
procedure Main is
package FIO is new Ada.Text_IO.Float_IO (Float);
type Point is record
X, Y : Float;
end record;
function "-" (Left, Right : Point) return Point is
begin
return (Left.X - Right.X, Left.Y - Right.Y);
end "-";
type Edge is array (1 .. 2) of Point;
package Point_Lists is new Ada.Containers.Doubly_Linked_Lists
(Element_Type => Point);
use type Point_Lists.List;
subtype Polygon is Point_Lists.List;
function Inside (P : Point; E : Edge) return Boolean is
begin
return (E (2).X - E (1).X) * (P.Y - E (1).Y) >
(E (2).Y - E (1).Y) * (P.X - E (1).X);
end Inside;
function Intersecton (P1, P2 : Point; E : Edge) return Point is
DE : Point := E (1) - E (2);
DP : Point := P1 - P2;
N1 : Float := E (1).X * E (2).Y - E (1).Y * E (2).X;
N2 : Float := P1.X * P2.Y - P1.Y * P2.X;
N3 : Float := 1.0 / (DE.X * DP.Y - DE.Y * DP.X);
begin
return ((N1 * DP.X - N2 * DE.X) * N3, (N1 * DP.Y - N2 * DE.Y) * N3);
end Intersecton;
function Clip (P, C : Polygon) return Polygon is
use Point_Lists;
A, B, S, E : Cursor;
Inputlist : List;
Outputlist : List := P;
AB : Edge;
begin
A := C.First;
B := C.Last;
while A /= No_Element loop
AB := (Element (B), Element (A));
Inputlist := Outputlist;
Outputlist.Clear;
S := Inputlist.Last;
E := Inputlist.First;
while E /= No_Element loop
if Inside (Element (E), AB) then
if not Inside (Element (S), AB) then
Outputlist.Append
(Intersecton (Element (S), Element (E), AB));
end if;
Outputlist.Append (Element (E));
elsif Inside (Element (S), AB) then
Outputlist.Append
(Intersecton (Element (S), Element (E), AB));
end if;
S := E;
E := Next (E);
end loop;
B := A;
A := Next (A);
end loop;
return Outputlist;
end Clip;
procedure Print (P : Polygon) is
use Point_Lists;
C : Cursor := P.First;
begin
Ada.Text_IO.Put_Line ("{");
while C /= No_Element loop
Ada.Text_IO.Put (" (");
FIO.Put (Element (C).X, Exp => 0);
Ada.Text_IO.Put (',');
FIO.Put (Element (C).Y, Exp => 0);
Ada.Text_IO.Put (')');
C := Next (C);
if C /= No_Element then
Ada.Text_IO.Put (',');
end if;
Ada.Text_IO.New_Line;
end loop;
Ada.Text_IO.Put_Line ("}");
end Print;
Source : Polygon;
Clipper : Polygon;
Result : Polygon;
begin
Source.Append ((50.0, 150.0));
Source.Append ((200.0, 50.0));
Source.Append ((350.0, 150.0));
Source.Append ((350.0, 300.0));
Source.Append ((250.0, 300.0));
Source.Append ((200.0, 250.0));
Source.Append ((150.0, 350.0));
Source.Append ((100.0, 250.0));
Source.Append ((100.0, 200.0));
Clipper.Append ((100.0, 100.0));
Clipper.Append ((300.0, 100.0));
Clipper.Append ((300.0, 300.0));
Clipper.Append ((100.0, 300.0));
Result := Clip (Source, Clipper);
Print (Result);
end Main;
- Output:
{
(100.00000,116.66667),
(125.00000,100.00000),
(275.00000,100.00000),
(300.00000,116.66667),
(300.00000,300.00000),
(250.00000,300.00000),
(200.00000,250.00000),
(175.00000,300.00000),
(125.00000,300.00000),
(100.00000,250.00000)
}
ATS
(*------------------------------------------------------------------*)
(* Sutherland-Hodgman polygon clipping. *)
#include "share/atspre_staload.hats"
#define NIL list_nil ()
#define :: list_cons
(*------------------------------------------------------------------*)
typedef coordinate = double
fn {tk : tkind}
coord_make_g0int (x : g0int tk)
:<> coordinate =
g0i2f x
fn {tk : tkind}
coord_make_g0float (x : g0float tk)
:<> coordinate =
g0f2f x
overload coord with coord_make_g0int
overload coord with coord_make_g0float
(*------------------------------------------------------------------*)
datatype point = point of (coordinate, coordinate)
datatype closedpoly = closedpoly of (arrszref point)
fn
fprint_coordinate (outf : FILEref,
x : coordinate)
: void =
let
val _ = $extfcall (int, "fprintf", outf, "%g", x)
in
end
fn
fprint_point (outf : FILEref,
pt : point) =
let
val+ point (x, y) = pt
in
fprint! (outf, "(");
fprint_coordinate (outf, x);
fprint! (outf, ",");
fprint_coordinate (outf, y);
fprint! (outf, ")")
end
overload fprint with fprint_point
fn
fprint_closedpoly
(outf : FILEref,
poly : closedpoly)
: void =
let
val+ closedpoly points = poly
val n = size points
var i : size_t
in
for (i := i2sz 0; i <> n; i := succ i)
fprint! (outf, points[i], "---");
fprint! (outf, "cycle")
end
fn
print_closedpoly (poly : closedpoly) =
fprint_closedpoly (stdout_ref, poly)
overload fprint with fprint_closedpoly
fn
closedpoly_make_list
(points : List point)
: closedpoly =
closedpoly (arrszref_make_list<point> points)
(*------------------------------------------------------------------*)
fn
evaluate_line (x1 : coordinate,
y1 : coordinate,
x2 : coordinate,
y2 : coordinate,
x : coordinate)
:<> coordinate =
let
val dy = y2 - y1
and dx = x2 - x1
val slope = dy / dx
and intercept = ((dx * y1) - (dy * x1)) / dx
in
(slope * x) + intercept
end
fn
intersection_of_lines
(x1 : coordinate,
y1 : coordinate,
x2 : coordinate,
y2 : coordinate,
x3 : coordinate,
y3 : coordinate,
x4 : coordinate,
y4 : coordinate)
:<> point =
if x1 = x2 then
point (x1, evaluate_line (x3, y3, x4, y4, x1))
else if x3 = x4 then
point (x3, evaluate_line (x1, y1, x2, y2, x3))
else
let
val denominator =
((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4))
and x1y2_y1x2 = (x1 * y2) - (y1 * x2)
and x3y4_y3x4 = (x3 * y4) - (y3 * x4)
val xnumerator = (x1y2_y1x2 * (x3 - x4)) - ((x1 - x2) * x3y4_y3x4)
and ynumerator = (x1y2_y1x2 * (y3 - y4)) - ((y1 - y2) * x3y4_y3x4)
in
point (xnumerator / denominator,
ynumerator / denominator)
end
fn
intersection_of_edges
(e1 : @(point, point),
e2 : @(point, point))
:<> point =
let
val+ @(point (x1, y1), point (x2, y2)) = e1
and @(point (x3, y3), point (x4, y4)) = e2
in
intersection_of_lines (x1, y1, x2, y2, x3, y3, x4, y4)
end
fn
point_is_left_of_edge
(pt : point,
edge : @(point, point))
:<> bool =
let
val+ point (x, y) = pt
and @(point (x1, y1), point (x2, y2)) = edge
in
(* Outer product of the vectors (x1,y1)-->(x,y) and
(x1,y1)-->(x2,y2). *)
((x - x1) * (y2 - y1)) - ((x2 - x1) * (y - y1)) < coord 0
end
fn
clip_subject_edge
(subject_edge : @(point, point),
clip_edge : @(point, point),
accum : List0 point)
: List0 point =
let
macdef left_of = point_is_left_of_edge
macdef intersection =
intersection_of_edges (subject_edge, clip_edge)
val @(s1, s2) = subject_edge
val s2_is_inside = s2 \left_of clip_edge
and s1_is_inside = s1 \left_of clip_edge
in
case+ (s2_is_inside, s1_is_inside) of
| (true, true) => s2 :: accum
| (true, false) => s2 :: intersection :: accum
| (false, true) => intersection :: accum
| (false, false) => accum
end
fun
for_each_subject_edge
(i : size_t,
subject_points : arrszref point,
clip_edge : @(point, point),
accum : List0 point)
: arrszref point =
let
val n = size subject_points
in
if i = n then
arrszref_make_rlist accum
else
let
val s2 = subject_points[i]
and s1 =
begin
if i = 0 then
subject_points[pred n]
else
subject_points[pred i]
end
val accum = clip_subject_edge (@(s1, s2), clip_edge, accum)
in
for_each_subject_edge (succ i, subject_points, clip_edge,
accum)
end
end
fun
for_each_clip_edge
(i : size_t,
subject_points : arrszref point,
clip_points : arrszref point)
: arrszref point =
let
val n = size clip_points
in
if i = n then
subject_points
else
let
val c2 = clip_points[i]
and c1 =
begin
if i = 0 then
clip_points[pred n]
else
clip_points[pred i]
end
val subject_points =
for_each_subject_edge
(i2sz 0, subject_points, @(c1, c2), NIL)
in
for_each_clip_edge (succ i, subject_points, clip_points)
end
end
fn
clip_closedpoly_closedpoly
(subject_poly : closedpoly,
clip_poly : closedpoly)
: closedpoly =
let
val+ closedpoly subject_points = subject_poly
and closedpoly clip_points = clip_poly
val result_points =
for_each_clip_edge (i2sz 0, subject_points, clip_points)
in
closedpoly result_points
end
overload clip with clip_closedpoly_closedpoly
(*------------------------------------------------------------------*)
(* A function to create an EPS file. *)
(* The EPS code is based on that which is generated by the C
implementation of this task. *)
fn
write_eps (outf : FILEref,
subject_poly : closedpoly,
clip_poly : closedpoly,
result_poly : closedpoly)
: void =
let
fn
moveto (pt : point)
: void =
let
val+ point (x, y) = pt
in
fprintln! (outf, x, " ", y, " moveto");
end
fn
lineto (pt : point)
: void =
let
val+ point (x, y) = pt
in
fprintln! (outf, x, " ", y, " lineto");
end
fn
setrgbcolor (rgb : string)
: void =
fprintln! (outf, rgb, " setrgbcolor")
fn closepath () : void = fprintln! (outf, "closepath")
fn fill () : void = fprintln! (outf, "fill")
fn stroke () : void = fprintln! (outf, "stroke")
fn gsave () : void = fprintln! (outf, "gsave")
fn grestore () : void = fprintln! (outf, "grestore")
fn
showpoly (poly : closedpoly,
line_color : string,
fill_color : string)
: void =
let
val+ closedpoly p = poly
val n = size p
var i : size_t
in
moveto p[0];
for (i := i2sz 1; i <> n; i := succ i)
lineto p[i];
closepath ();
setrgbcolor line_color;
gsave ();
setrgbcolor fill_color;
fill ();
grestore ();
stroke ()
end
in
fprintln! (outf, "%!PS-Adobe-3.0 EPSF-3.0");
fprintln! (outf, "%%BoundingBox: 40 40 360 360");
fprintln! (outf, "0 setlinewidth ");
showpoly (clip_poly, ".5 0 0", "1 .7 .7");
showpoly (subject_poly, "0 .2 .5", ".4 .7 1");
fprintln! (outf, "2 setlinewidth");
fprintln! (outf, "[10 8] 0 setdash");
showpoly (result_poly, ".5 0 .5", ".7 .3 .8");
fprintln! (outf, "%%EOF")
end
fn
write_eps_to_file
(outfile : string,
subject_poly : closedpoly,
clip_poly : closedpoly,
result_poly : closedpoly)
: void =
let
val outf = fileref_open_exn (outfile, file_mode_w)
in
write_eps (outf, subject_poly, clip_poly, result_poly);
fileref_close outf
end
(*------------------------------------------------------------------*)
implement
main0 () =
let
val outf = stdout_ref
val subject_poly =
closedpoly_make_list
$list (point (coord 50, coord 150),
point (coord 200, coord 50),
point (coord 350, coord 150),
point (coord 350, coord 300),
point (coord 250, coord 300),
point (coord 200, coord 250),
point (coord 150, coord 350),
point (coord 100, coord 250),
point (coord 100, coord 200))
val clip_poly =
closedpoly_make_list
$list (point (coord 100, coord 100),
point (coord 300, coord 100),
point (coord 300, coord 300),
point (coord 100, coord 300))
val result_poly = clip (subject_poly, clip_poly)
in
fprintln! (outf, result_poly);
write_eps_to_file ("sutherland-hodgman.eps",
subject_poly, clip_poly, result_poly);
fprintln! (outf, "Wrote sutherland-hodgman.eps")
end
(*------------------------------------------------------------------*)- Output:
$ patscc -O3 -DATS_MEMALLOC_GCBDW sutherland-hodgman.dats -lgc && ./a.out (100,116.667)---(125,100)---(275,100)---(300,116.667)---(300,300)---(250,300)---(200,250)---(175,300)---(125,300)---(100,250)---cycle Wrote sutherland-hodgman.eps
Here is a simple fixed-point version of the same program:
(*------------------------------------------------------------------*)
(* Sutherland-Hodgman polygon clipping (fixed-point version). *)
#include "share/atspre_staload.hats"
#define NIL list_nil ()
#define :: list_cons
implement g0int2float<intknd,ldblknd> x = $UNSAFE.cast x
implement g0int2float<llintknd,ldblknd> x = $UNSAFE.cast x
(*------------------------------------------------------------------*)
abst@ype coordinate = llint
extern castfn llint2coordinate : llint -<> coordinate
extern castfn coordinate2llint : coordinate -<> llint
overload lli2coord with llint2coordinate
overload coord2lli with coordinate2llint
#define SCALE 262144 (* 18 fraction bits. *)
fn {tk : tkind}
coordinate_make_g0int (x : g0int tk)
:<> coordinate =
let
val x : llint = g0i2i x
in
llint2coordinate (x * g0i2i SCALE)
end
fn
add_coordinate (x : coordinate, y : coordinate)
:<> coordinate =
lli2coord (coord2lli x + coord2lli y)
fn
sub_coordinate (x : coordinate, y : coordinate)
:<> coordinate =
lli2coord (coord2lli x - coord2lli y)
fn
mul_coordinate (x : coordinate, y : coordinate)
:<> coordinate =
lli2coord ((coord2lli x * coord2lli y) / g0i2i SCALE)
fn
div_coordinate (x : coordinate, y : coordinate)
:<> coordinate =
lli2coord ((coord2lli x * g0i2i SCALE) / coord2lli y)
fn
eq_coordinate (x : coordinate, y : coordinate)
:<> bool =
coord2lli x = coord2lli y
fn
lt_coordinate (x : coordinate, y : coordinate)
:<> bool =
coord2lli x < coord2lli y
overload coord with coordinate_make_g0int
overload + with add_coordinate
overload - with sub_coordinate
overload * with mul_coordinate
overload / with div_coordinate
overload = with eq_coordinate
overload < with lt_coordinate
fn
fprint_coordinate (outf : FILEref,
x : coordinate)
: void =
let
val x : ldouble = g0i2f (coord2lli x)
val x = x / g0i2f SCALE
val _ = $extfcall (int, "fprintf", outf, "%Lg", x)
in
end
(*------------------------------------------------------------------*)
datatype point = point of (coordinate, coordinate)
datatype closedpoly = closedpoly of (arrszref point)
fn
fprint_point (outf : FILEref,
pt : point) =
let
val+ point (x, y) = pt
in
fprint! (outf, "(");
fprint_coordinate (outf, x);
fprint! (outf, ",");
fprint_coordinate (outf, y);
fprint! (outf, ")")
end
overload fprint with fprint_point
fn
fprint_closedpoly
(outf : FILEref,
poly : closedpoly)
: void =
let
val+ closedpoly points = poly
val n = size points
var i : size_t
in
for (i := i2sz 0; i <> n; i := succ i)
fprint! (outf, points[i], "---");
fprint! (outf, "cycle")
end
fn
print_closedpoly (poly : closedpoly) =
fprint_closedpoly (stdout_ref, poly)
overload fprint with fprint_closedpoly
fn
closedpoly_make_list
(points : List point)
: closedpoly =
closedpoly (arrszref_make_list<point> points)
(*------------------------------------------------------------------*)
fn
evaluate_line (x1 : coordinate,
y1 : coordinate,
x2 : coordinate,
y2 : coordinate,
x : coordinate)
:<> coordinate =
let
val dy = y2 - y1
and dx = x2 - x1
val slope = dy / dx
and intercept = ((dx * y1) - (dy * x1)) / dx
in
(slope * x) + intercept
end
fn
intersection_of_lines
(x1 : coordinate,
y1 : coordinate,
x2 : coordinate,
y2 : coordinate,
x3 : coordinate,
y3 : coordinate,
x4 : coordinate,
y4 : coordinate)
:<> point =
if x1 = x2 then
point (x1, evaluate_line (x3, y3, x4, y4, x1))
else if x3 = x4 then
point (x3, evaluate_line (x1, y1, x2, y2, x3))
else
let
val denominator =
((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4))
and x1y2_y1x2 = (x1 * y2) - (y1 * x2)
and x3y4_y3x4 = (x3 * y4) - (y3 * x4)
val xnumerator = (x1y2_y1x2 * (x3 - x4)) - ((x1 - x2) * x3y4_y3x4)
and ynumerator = (x1y2_y1x2 * (y3 - y4)) - ((y1 - y2) * x3y4_y3x4)
in
point (xnumerator / denominator,
ynumerator / denominator)
end
fn
intersection_of_edges
(e1 : @(point, point),
e2 : @(point, point))
:<> point =
let
val+ @(point (x1, y1), point (x2, y2)) = e1
and @(point (x3, y3), point (x4, y4)) = e2
in
intersection_of_lines (x1, y1, x2, y2, x3, y3, x4, y4)
end
fn
point_is_left_of_edge
(pt : point,
edge : @(point, point))
:<> bool =
let
val+ point (x, y) = pt
and @(point (x1, y1), point (x2, y2)) = edge
in
(* Outer product of the vectors (x1,y1)-->(x,y) and
(x1,y1)-->(x2,y2). *)
((x - x1) * (y2 - y1)) - ((x2 - x1) * (y - y1)) < coord 0
end
fn
clip_subject_edge
(subject_edge : @(point, point),
clip_edge : @(point, point),
accum : List0 point)
: List0 point =
let
macdef left_of = point_is_left_of_edge
macdef intersection =
intersection_of_edges (subject_edge, clip_edge)
val @(s1, s2) = subject_edge
val s2_is_inside = s2 \left_of clip_edge
and s1_is_inside = s1 \left_of clip_edge
in
case+ (s2_is_inside, s1_is_inside) of
| (true, true) => s2 :: accum
| (true, false) => s2 :: intersection :: accum
| (false, true) => intersection :: accum
| (false, false) => accum
end
fun
for_each_subject_edge
(i : size_t,
subject_points : arrszref point,
clip_edge : @(point, point),
accum : List0 point)
: arrszref point =
let
val n = size subject_points
in
if i = n then
arrszref_make_rlist accum
else
let
val s2 = subject_points[i]
and s1 =
begin
if i = 0 then
subject_points[pred n]
else
subject_points[pred i]
end
val accum = clip_subject_edge (@(s1, s2), clip_edge, accum)
in
for_each_subject_edge (succ i, subject_points, clip_edge,
accum)
end
end
fun
for_each_clip_edge
(i : size_t,
subject_points : arrszref point,
clip_points : arrszref point)
: arrszref point =
let
val n = size clip_points
in
if i = n then
subject_points
else
let
val c2 = clip_points[i]
and c1 =
begin
if i = 0 then
clip_points[pred n]
else
clip_points[pred i]
end
val subject_points =
for_each_subject_edge
(i2sz 0, subject_points, @(c1, c2), NIL)
in
for_each_clip_edge (succ i, subject_points, clip_points)
end
end
fn
clip_closedpoly_closedpoly
(subject_poly : closedpoly,
clip_poly : closedpoly)
: closedpoly =
let
val+ closedpoly subject_points = subject_poly
and closedpoly clip_points = clip_poly
val result_points =
for_each_clip_edge (i2sz 0, subject_points, clip_points)
in
closedpoly result_points
end
overload clip with clip_closedpoly_closedpoly
(*------------------------------------------------------------------*)
(* A function to create an EPS file. *)
(* The EPS code is based on that which is generated by the C
implementation of this task. *)
fn
write_eps (outf : FILEref,
subject_poly : closedpoly,
clip_poly : closedpoly,
result_poly : closedpoly)
: void =
let
fn
moveto (pt : point)
: void =
let
val+ point (x, y) = pt
in
fprint_coordinate (outf, x);
fprint! (outf, " ");
fprint_coordinate (outf, y);
fprintln! (outf, " moveto")
end
fn
lineto (pt : point)
: void =
let
val+ point (x, y) = pt
in
fprint_coordinate (outf, x);
fprint! (outf, " ");
fprint_coordinate (outf, y);
fprintln! (outf, " lineto")
end
fn
setrgbcolor (rgb : string)
: void =
fprintln! (outf, rgb, " setrgbcolor")
fn closepath () : void = fprintln! (outf, "closepath")
fn fill () : void = fprintln! (outf, "fill")
fn stroke () : void = fprintln! (outf, "stroke")
fn gsave () : void = fprintln! (outf, "gsave")
fn grestore () : void = fprintln! (outf, "grestore")
fn
showpoly (poly : closedpoly,
line_color : string,
fill_color : string)
: void =
let
val+ closedpoly p = poly
val n = size p
var i : size_t
in
moveto p[0];
for (i := i2sz 1; i <> n; i := succ i)
lineto p[i];
closepath ();
setrgbcolor line_color;
gsave ();
setrgbcolor fill_color;
fill ();
grestore ();
stroke ()
end
in
fprintln! (outf, "%!PS-Adobe-3.0 EPSF-3.0");
fprintln! (outf, "%%BoundingBox: 40 40 360 360");
fprintln! (outf, "0 setlinewidth ");
showpoly (clip_poly, ".5 0 0", "1 .7 .7");
showpoly (subject_poly, "0 .2 .5", ".4 .7 1");
fprintln! (outf, "2 setlinewidth");
fprintln! (outf, "[10 8] 0 setdash");
showpoly (result_poly, ".5 0 .5", ".7 .3 .8");
fprintln! (outf, "%%EOF")
end
fn
write_eps_to_file
(outfile : string,
subject_poly : closedpoly,
clip_poly : closedpoly,
result_poly : closedpoly)
: void =
let
val outf = fileref_open_exn (outfile, file_mode_w)
in
write_eps (outf, subject_poly, clip_poly, result_poly);
fileref_close outf
end
(*------------------------------------------------------------------*)
implement
main0 () =
let
val outf = stdout_ref
val subject_poly =
closedpoly_make_list
$list (point (coord 50, coord 150),
point (coord 200, coord 50),
point (coord 350, coord 150),
point (coord 350, coord 300),
point (coord 250, coord 300),
point (coord 200, coord 250),
point (coord 150, coord 350),
point (coord 100, coord 250),
point (coord 100, coord 200))
val clip_poly =
closedpoly_make_list
$list (point (coord 100, coord 100),
point (coord 300, coord 100),
point (coord 300, coord 300),
point (coord 100, coord 300))
val result_poly = clip (subject_poly, clip_poly)
in
fprintln! (outf, result_poly);
write_eps_to_file ("sutherland-hodgman.eps",
subject_poly, clip_poly, result_poly);
fprintln! (outf, "Wrote sutherland-hodgman.eps")
end
(*------------------------------------------------------------------*)- Output:
(100,116.667)---(125,100)---(275,100)---(300,116.666)---(300,300)---(250,300)---(200,250)---(175,300)---(125,300)---(100,250)---cycle Wrote sutherland-hodgman.eps
BBC BASIC
VDU 23,22,200;200;8,16,16,128
VDU 23,23,2;0;0;0;
DIM SubjPoly{(8) x, y}
DIM ClipPoly{(3) x, y}
FOR v% = 0 TO 8 : READ SubjPoly{(v%)}.x, SubjPoly{(v%)}.y : NEXT
DATA 50,150,200,50,350,150,350,300,250,300,200,250,150,350,100,250,100,200
FOR v% = 0 TO 3 : READ ClipPoly{(v%)}.x, ClipPoly{(v%)}.y : NEXT
DATA 100,100, 300,100, 300,300, 100,300
GCOL 4 : PROCplotpoly(SubjPoly{()}, 9)
GCOL 1 : PROCplotpoly(ClipPoly{()}, 4)
nvert% = FNsutherland_hodgman(SubjPoly{()}, ClipPoly{()}, Clipped{()})
GCOL 2 : PROCplotpoly(Clipped{()}, nvert%)
END
DEF FNsutherland_hodgman(subj{()}, clip{()}, RETURN out{()})
LOCAL i%, j%, n%, o%, p1{}, p2{}, s{}, e{}, p{}, inp{()}
DIM p1{x,y}, p2{x,y}, s{x,y}, e{x,y}, p{x,y}
n% = DIM(subj{()},1) + DIM(clip{()},1)
DIM inp{(n%) x, y}, out{(n%) x,y}
FOR o% = 0 TO DIM(subj{()},1) : out{(o%)} = subj{(o%)} : NEXT
p1{} = clip{(DIM(clip{()},1))}
FOR i% = 0 TO DIM(clip{()},1)
p2{} = clip{(i%)}
FOR n% = 0 TO o% - 1 : inp{(n%)} = out{(n%)} : NEXT : o% = 0
IF n% >= 2 THEN
s{} = inp{(n% - 1)}
FOR j% = 0 TO n% - 1
e{} = inp{(j%)}
IF FNside(e{}, p1{}, p2{}) THEN
IF NOT FNside(s{}, p1{}, p2{}) THEN
PROCintersection(p1{}, p2{}, s{}, e{}, p{})
out{(o%)} = p{}
o% += 1
ENDIF
out{(o%)} = e{}
o% += 1
ELSE
IF FNside(s{}, p1{}, p2{}) THEN
PROCintersection(p1{}, p2{}, s{}, e{}, p{})
out{(o%)} = p{}
o% += 1
ENDIF
ENDIF
s{} = e{}
NEXT
ENDIF
p1{} = p2{}
NEXT i%
= o%
REM Which side of the line p1-p2 is the point p?
DEF FNside(p{}, p1{}, p2{})
= (p2.x - p1.x) * (p.y - p1.y) > (p2.y - p1.y) * (p.x - p1.x)
REM Find the intersection of two lines p1-p2 and p3-p4
DEF PROCintersection(p1{}, p2{}, p3{}, p4{}, p{})
LOCAL a{}, b{}, k, l, m : DIM a{x,y}, b{x,y}
a.x = p1.x - p2.x : a.y = p1.y - p2.y
b.x = p3.x - p4.x : b.y = p3.y - p4.y
k = p1.x * p2.y - p1.y * p2.x
l = p3.x * p4.y - p3.y * p4.x
m = 1 / (a.x * b.y - a.y * b.x)
p.x = m * (k * b.x - l * a.x)
p.y = m * (k * b.y - l * a.y)
ENDPROC
REM plot a polygon
DEF PROCplotpoly(poly{()}, n%)
LOCAL i%
MOVE poly{(0)}.x, poly{(0)}.y
FOR i% = 1 TO n%-1
DRAW poly{(i%)}.x, poly{(i%)}.y
NEXT
DRAW poly{(0)}.x, poly{(0)}.y
ENDPROC
C
Most of the code is actually storage util routines, such is C. Prints out nodes, and writes test.eps file in current dir.
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
typedef struct { double x, y; } vec_t, *vec;
inline double dot(vec a, vec b)
{
return a->x * b->x + a->y * b->y;
}
inline double cross(vec a, vec b)
{
return a->x * b->y - a->y * b->x;
}
inline vec vsub(vec a, vec b, vec res)
{
res->x = a->x - b->x;
res->y = a->y - b->y;
return res;
}
/* tells if vec c lies on the left side of directed edge a->b
* 1 if left, -1 if right, 0 if colinear
*/
int left_of(vec a, vec b, vec c)
{
vec_t tmp1, tmp2;
double x;
vsub(b, a, &tmp1);
vsub(c, b, &tmp2);
x = cross(&tmp1, &tmp2);
return x < 0 ? -1 : x > 0;
}
int line_sect(vec x0, vec x1, vec y0, vec y1, vec res)
{
vec_t dx, dy, d;
vsub(x1, x0, &dx);
vsub(y1, y0, &dy);
vsub(x0, y0, &d);
/* x0 + a dx = y0 + b dy ->
x0 X dx = y0 X dx + b dy X dx ->
b = (x0 - y0) X dx / (dy X dx) */
double dyx = cross(&dy, &dx);
if (!dyx) return 0;
dyx = cross(&d, &dx) / dyx;
if (dyx <= 0 || dyx >= 1) return 0;
res->x = y0->x + dyx * dy.x;
res->y = y0->y + dyx * dy.y;
return 1;
}
/* === polygon stuff === */
typedef struct { int len, alloc; vec v; } poly_t, *poly;
poly poly_new()
{
return (poly)calloc(1, sizeof(poly_t));
}
void poly_free(poly p)
{
free(p->v);
free(p);
}
void poly_append(poly p, vec v)
{
if (p->len >= p->alloc) {
p->alloc *= 2;
if (!p->alloc) p->alloc = 4;
p->v = (vec)realloc(p->v, sizeof(vec_t) * p->alloc);
}
p->v[p->len++] = *v;
}
/* this works only if all of the following are true:
* 1. poly has no colinear edges;
* 2. poly has no duplicate vertices;
* 3. poly has at least three vertices;
* 4. poly is convex (implying 3).
*/
int poly_winding(poly p)
{
return left_of(p->v, p->v + 1, p->v + 2);
}
void poly_edge_clip(poly sub, vec x0, vec x1, int left, poly res)
{
int i, side0, side1;
vec_t tmp;
vec v0 = sub->v + sub->len - 1, v1;
res->len = 0;
side0 = left_of(x0, x1, v0);
if (side0 != -left) poly_append(res, v0);
for (i = 0; i < sub->len; i++) {
v1 = sub->v + i;
side1 = left_of(x0, x1, v1);
if (side0 + side1 == 0 && side0)
/* last point and current straddle the edge */
if (line_sect(x0, x1, v0, v1, &tmp))
poly_append(res, &tmp);
if (i == sub->len - 1) break;
if (side1 != -left) poly_append(res, v1);
v0 = v1;
side0 = side1;
}
}
poly poly_clip(poly sub, poly clip)
{
int i;
poly p1 = poly_new(), p2 = poly_new(), tmp;
int dir = poly_winding(clip);
poly_edge_clip(sub, clip->v + clip->len - 1, clip->v, dir, p2);
for (i = 0; i < clip->len - 1; i++) {
tmp = p2; p2 = p1; p1 = tmp;
if(p1->len == 0) {
p2->len = 0;
break;
}
poly_edge_clip(p1, clip->v + i, clip->v + i + 1, dir, p2);
}
poly_free(p1);
return p2;
}
int main()
{
int i;
vec_t c[] = {{100,100}, {300,100}, {300,300}, {100,300}};
//vec_t c[] = {{100,300}, {300,300}, {300,100}, {100,100}};
vec_t s[] = { {50,150}, {200,50}, {350,150},
{350,300},{250,300},{200,250},
{150,350},{100,250},{100,200}};
#define clen (sizeof(c)/sizeof(vec_t))
#define slen (sizeof(s)/sizeof(vec_t))
poly_t clipper = {clen, 0, c};
poly_t subject = {slen, 0, s};
poly res = poly_clip(&subject, &clipper);
for (i = 0; i < res->len; i++)
printf("%g %g\n", res->v[i].x, res->v[i].y);
/* long and arduous EPS printout */
FILE * eps = fopen("test.eps", "w");
fprintf(eps, "%%!PS-Adobe-3.0\n%%%%BoundingBox: 40 40 360 360\n"
"/l {lineto} def /m{moveto} def /s{setrgbcolor} def"
"/c {closepath} def /gs {fill grestore stroke} def\n");
fprintf(eps, "0 setlinewidth %g %g m ", c[0].x, c[0].y);
for (i = 1; i < clen; i++)
fprintf(eps, "%g %g l ", c[i].x, c[i].y);
fprintf(eps, "c .5 0 0 s gsave 1 .7 .7 s gs\n");
fprintf(eps, "%g %g m ", s[0].x, s[0].y);
for (i = 1; i < slen; i++)
fprintf(eps, "%g %g l ", s[i].x, s[i].y);
fprintf(eps, "c 0 .2 .5 s gsave .4 .7 1 s gs\n");
fprintf(eps, "2 setlinewidth [10 8] 0 setdash %g %g m ",
res->v[0].x, res->v[0].y);
for (i = 1; i < res->len; i++)
fprintf(eps, "%g %g l ", res->v[i].x, res->v[i].y);
fprintf(eps, "c .5 0 .5 s gsave .7 .3 .8 s gs\n");
fprintf(eps, "%%%%EOF");
fclose(eps);
printf("test.eps written\n");
return 0;
}
- Output:
200 250175 300 125 300 100 250 100 200 100 116.667 125 100 275 100 300 116.667 300 300 250 300
test.eps written
C#
This was written in .net 4.0 using wpf
Worker class:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
namespace Sutherland
{
public static class SutherlandHodgman
{
#region Class: Edge
/// <summary>
/// This represents a line segment
/// </summary>
private class Edge
{
public Edge(Point from, Point to)
{
this.From = from;
this.To = to;
}
public readonly Point From;
public readonly Point To;
}
#endregion
/// <summary>
/// This clips the subject polygon against the clip polygon (gets the intersection of the two polygons)
/// </summary>
/// <remarks>
/// Based on the psuedocode from:
/// http://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman
/// </remarks>
/// <param name="subjectPoly">Can be concave or convex</param>
/// <param name="clipPoly">Must be convex</param>
/// <returns>The intersection of the two polygons (or null)</returns>
public static Point[] GetIntersectedPolygon(Point[] subjectPoly, Point[] clipPoly)
{
if (subjectPoly.Length < 3 || clipPoly.Length < 3)
{
throw new ArgumentException(string.Format("The polygons passed in must have at least 3 points: subject={0}, clip={1}", subjectPoly.Length.ToString(), clipPoly.Length.ToString()));
}
List<Point> outputList = subjectPoly.ToList();
// Make sure it's clockwise
if (!IsClockwise(subjectPoly))
{
outputList.Reverse();
}
// Walk around the clip polygon clockwise
foreach (Edge clipEdge in IterateEdgesClockwise(clipPoly))
{
List<Point> inputList = outputList.ToList(); // clone it
outputList.Clear();
if (inputList.Count == 0)
{
// Sometimes when the polygons don't intersect, this list goes to zero. Jump out to avoid an index out of range exception
break;
}
Point S = inputList[inputList.Count - 1];
foreach (Point E in inputList)
{
if (IsInside(clipEdge, E))
{
if (!IsInside(clipEdge, S))
{
Point? point = GetIntersect(S, E, clipEdge.From, clipEdge.To);
if (point == null)
{
throw new ApplicationException("Line segments don't intersect"); // may be colinear, or may be a bug
}
else
{
outputList.Add(point.Value);
}
}
outputList.Add(E);
}
else if (IsInside(clipEdge, S))
{
Point? point = GetIntersect(S, E, clipEdge.From, clipEdge.To);
if (point == null)
{
throw new ApplicationException("Line segments don't intersect"); // may be colinear, or may be a bug
}
else
{
outputList.Add(point.Value);
}
}
S = E;
}
}
// Exit Function
return outputList.ToArray();
}
#region Private Methods
/// <summary>
/// This iterates through the edges of the polygon, always clockwise
/// </summary>
private static IEnumerable<Edge> IterateEdgesClockwise(Point[] polygon)
{
if (IsClockwise(polygon))
{
#region Already clockwise
for (int cntr = 0; cntr < polygon.Length - 1; cntr++)
{
yield return new Edge(polygon[cntr], polygon[cntr + 1]);
}
yield return new Edge(polygon[polygon.Length - 1], polygon[0]);
#endregion
}
else
{
#region Reverse
for (int cntr = polygon.Length - 1; cntr > 0; cntr--)
{
yield return new Edge(polygon[cntr], polygon[cntr - 1]);
}
yield return new Edge(polygon[0], polygon[polygon.Length - 1]);
#endregion
}
}
/// <summary>
/// Returns the intersection of the two lines (line segments are passed in, but they are treated like infinite lines)
/// </summary>
/// <remarks>
/// Got this here:
/// http://stackoverflow.com/questions/14480124/how-do-i-detect-triangle-and-rectangle-intersection
/// </remarks>
private static Point? GetIntersect(Point line1From, Point line1To, Point line2From, Point line2To)
{
Vector direction1 = line1To - line1From;
Vector direction2 = line2To - line2From;
double dotPerp = (direction1.X * direction2.Y) - (direction1.Y * direction2.X);
// If it's 0, it means the lines are parallel so have infinite intersection points
if (IsNearZero(dotPerp))
{
return null;
}
Vector c = line2From - line1From;
double t = (c.X * direction2.Y - c.Y * direction2.X) / dotPerp;
//if (t < 0 || t > 1)
//{
// return null; // lies outside the line segment
//}
//double u = (c.X * direction1.Y - c.Y * direction1.X) / dotPerp;
//if (u < 0 || u > 1)
//{
// return null; // lies outside the line segment
//}
// Return the intersection point
return line1From + (t * direction1);
}
private static bool IsInside(Edge edge, Point test)
{
bool? isLeft = IsLeftOf(edge, test);
if (isLeft == null)
{
// Colinear points should be considered inside
return true;
}
return !isLeft.Value;
}
private static bool IsClockwise(Point[] polygon)
{
for (int cntr = 2; cntr < polygon.Length; cntr++)
{
bool? isLeft = IsLeftOf(new Edge(polygon[0], polygon[1]), polygon[cntr]);
if (isLeft != null) // some of the points may be colinear. That's ok as long as the overall is a polygon
{
return !isLeft.Value;
}
}
throw new ArgumentException("All the points in the polygon are colinear");
}
/// <summary>
/// Tells if the test point lies on the left side of the edge line
/// </summary>
private static bool? IsLeftOf(Edge edge, Point test)
{
Vector tmp1 = edge.To - edge.From;
Vector tmp2 = test - edge.To;
double x = (tmp1.X * tmp2.Y) - (tmp1.Y * tmp2.X); // dot product of perpendicular?
if (x < 0)
{
return false;
}
else if (x > 0)
{
return true;
}
else
{
// Colinear points;
return null;
}
}
private static bool IsNearZero(double testValue)
{
return Math.Abs(testValue) <= .000000001d;
}
#endregion
}
}Window code:
<Window x:Class="Sutherland.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Sutherland Hodgman" Background="#B0B0B0" ResizeMode="CanResizeWithGrip" Width="525" Height="450">
<Grid Margin="4">
<Grid.RowDefinitions>
<RowDefinition Height="1*"/>
<RowDefinition Height="auto"/>
</Grid.RowDefinitions>
<Border Grid.Row="0" CornerRadius="4" BorderBrush="#707070" Background="#FFFFFF" BorderThickness="2">
<Canvas Name="canvas"/>
</Border>
<UniformGrid Grid.Row="1" Rows="1" Margin="0,4,0,0">
<Button Name="btnTriRect" Content="Triangle - Rectangle" Margin="4,0" Click="btnTriRect_Click"/>
<Button Name="btnConvex" Content="Concave - Convex" Click="btnConvex_Click"/>
</UniformGrid>
</Grid>
</Window>
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
namespace Sutherland
{
public partial class MainWindow : Window
{
#region Declaration Section
private Random _rand = new Random();
private Brush _subjectBack = new SolidColorBrush(ColorFromHex("30427FCF"));
private Brush _subjectBorder = new SolidColorBrush(ColorFromHex("427FCF"));
private Brush _clipBack = new SolidColorBrush(ColorFromHex("30D65151"));
private Brush _clipBorder = new SolidColorBrush(ColorFromHex("D65151"));
private Brush _intersectBack = new SolidColorBrush(ColorFromHex("609F18CC"));
private Brush _intersectBorder = new SolidColorBrush(ColorFromHex("9F18CC"));
#endregion
#region Constructor
public MainWindow()
{
InitializeComponent();
}
#endregion
#region Event Listeners
private void btnTriRect_Click(object sender, RoutedEventArgs e)
{
try
{
double width = canvas.ActualWidth;
double height = canvas.ActualHeight;
Point[] poly1 = new Point[] {
new Point(_rand.NextDouble() * width, _rand.NextDouble() * height),
new Point(_rand.NextDouble() * width, _rand.NextDouble() * height),
new Point(_rand.NextDouble() * width, _rand.NextDouble() * height) };
Point rectPoint = new Point(_rand.NextDouble() * (width * .75d), _rand.NextDouble() * (height * .75d)); // don't let it start all the way at the bottom right
Rect rect = new Rect(
rectPoint,
new Size(_rand.NextDouble() * (width - rectPoint.X), _rand.NextDouble() * (height - rectPoint.Y)));
Point[] poly2 = new Point[] { rect.TopLeft, rect.TopRight, rect.BottomRight, rect.BottomLeft };
Point[] intersect = SutherlandHodgman.GetIntersectedPolygon(poly1, poly2);
canvas.Children.Clear();
ShowPolygon(poly1, _subjectBack, _subjectBorder, 1d);
ShowPolygon(poly2, _clipBack, _clipBorder, 1d);
ShowPolygon(intersect, _intersectBack, _intersectBorder, 3d);
}
catch (Exception ex)
{
MessageBox.Show(ex.ToString(), this.Title, MessageBoxButton.OK, MessageBoxImage.Error);
}
}
private void btnConvex_Click(object sender, RoutedEventArgs e)
{
try
{
Point[] poly1 = new Point[] { new Point(50, 150), new Point(200, 50), new Point(350, 150), new Point(350, 300), new Point(250, 300), new Point(200, 250), new Point(150, 350), new Point(100, 250), new Point(100, 200) };
Point[] poly2 = new Point[] { new Point(100, 100), new Point(300, 100), new Point(300, 300), new Point(100, 300) };
Point[] intersect = SutherlandHodgman.GetIntersectedPolygon(poly1, poly2);
canvas.Children.Clear();
ShowPolygon(poly1, _subjectBack, _subjectBorder, 1d);
ShowPolygon(poly2, _clipBack, _clipBorder, 1d);
ShowPolygon(intersect, _intersectBack, _intersectBorder, 3d);
}
catch (Exception ex)
{
MessageBox.Show(ex.ToString(), this.Title, MessageBoxButton.OK, MessageBoxImage.Error);
}
}
#endregion
#region Private Methods
private void ShowPolygon(Point[] points, Brush background, Brush border, double thickness)
{
if (points == null || points.Length == 0)
{
return;
}
Polygon polygon = new Polygon();
polygon.Fill = background;
polygon.Stroke = border;
polygon.StrokeThickness = thickness;
foreach (Point point in points)
{
polygon.Points.Add(point);
}
canvas.Children.Add(polygon);
}
/// <summary>
/// This is just a wrapper to the color converter (why can't they have a method off the color class with all
/// the others?)
/// </summary>
private static Color ColorFromHex(string hexValue)
{
if (hexValue.StartsWith("#"))
{
return (Color)ColorConverter.ConvertFromString(hexValue);
}
else
{
return (Color)ColorConverter.ConvertFromString("#" + hexValue);
}
}
#endregion
}
}
C++
#include <iostream>
#include <span>
#include <vector>
struct vec2 {
float x = 0.0f, y = 0.0f;
constexpr vec2 operator+(vec2 other) const {
return vec2{x + other.x, y + other.y};
}
constexpr vec2 operator-(vec2 other) const {
return vec2{x - other.x, y - other.y};
}
};
constexpr vec2 operator*(vec2 a, float b) { return vec2{a.x * b, a.y * b}; }
constexpr float dot(vec2 a, vec2 b) { return a.x * b.x + a.y * b.y; }
constexpr float cross(vec2 a, vec2 b) { return a.x * b.y - b.x * a.y; }
// check if a point is on the LEFT side of an edge
constexpr bool is_inside(vec2 point, vec2 a, vec2 b) {
return (cross(a - b, point) + cross(b, a)) < 0.0f;
}
// calculate intersection point
constexpr vec2 intersection(vec2 a1, vec2 a2, vec2 b1, vec2 b2) {
return ((b1 - b2) * cross(a1, a2) - (a1 - a2) * cross(b1, b2)) *
(1.0f / cross(a1 - a2, b1 - b2));
}
// Sutherland-Hodgman clipping
std::vector<vec2> suther_land_hodgman(
std::span<vec2 const> subject_polygon, std::span<vec2 const> clip_polygon) {
if (clip_polygon.empty() || subject_polygon.empty()) {
return {};
}
std::vector<vec2> ring{subject_polygon.begin(), subject_polygon.end()};
vec2 p1 = clip_polygon[clip_polygon.size() - 1];
std::vector<vec2> input;
for (vec2 p2 : clip_polygon) {
input.clear();
input.insert(input.end(), ring.begin(), ring.end());
vec2 s = input[input.size() - 1];
ring.clear();
for (vec2 e : input) {
if (is_inside(e, p1, p2)) {
if (!is_inside(s, p1, p2)) {
ring.push_back(intersection(p1, p2, s, e));
}
ring.push_back(e);
} else if (is_inside(s, p1, p2)) {
ring.push_back(intersection(p1, p2, s, e));
}
s = e;
}
p1 = p2;
}
return ring;
}
int main(int argc, char **argv) {
// subject polygon
vec2 subject_polygon[] = {{50, 150}, {200, 50}, {350, 150},
{350, 300}, {250, 300}, {200, 250},
{150, 350}, {100, 250}, {100, 200}};
// clipping polygon
vec2 clip_polygon[] = {{100, 100}, {300, 100}, {300, 300}, {100, 300}};
// apply clipping
std::vector<vec2> clipped_polygon =
suther_land_hodgman(subject_polygon, clip_polygon);
// print clipped polygon points
std::cout << "Clipped polygon points:" << std::endl;
for (vec2 p : clipped_polygon) {
std::cout << "(" << p.x << ", " << p.y << ")" << std::endl;
}
return EXIT_SUCCESS;
}
- Output:
Clipped polygon points: (100, 116.667) (125, 100) (275, 100) (300, 116.667) (300, 300) (250, 300) (200, 250) (175, 300) (125, 300) (100, 250)
Common Lisp
;;; Sutherland-Hodgman polygon clipping.
(defun evaluate-line (x1 y1 x2 y2 x)
;; Given the straight line between (x1,y1) and (x2,y2), evaluate it
;; at x.
(let ((dy (- y2 y1))
(dx (- x2 x1)))
(let ((slope (/ dy dx))
(intercept (/ (- (* dx y1) (* dy x1)) dx)))
(+ (* slope x) intercept))))
(defun intersection-of-lines (x1 y1 x2 y2 x3 y3 x4 y4)
;; Given the line between (x1,y1) and (x2,y2), and the line between
;; (x3,y3) and (x4,y4), find their intersection.
(cond ((= x1 x2) (list x1 (evaluate-line x3 y3 x4 y4 x1)))
((= x3 x4) (list x3 (evaluate-line x1 y1 x2 y2 x3)))
(t (let ((denominator (- (* (- x1 x2) (- y3 y4))
(* (- y1 y2) (- x3 x4))))
(x1*y2-y1*x2 (- (* x1 y2) (* y1 x2)))
(x3*y4-y3*x4 (- (* x3 y4) (* y3 x4))))
(let ((xnumerator (- (* x1*y2-y1*x2 (- x3 x4))
(* (- x1 x2) x3*y4-y3*x4)))
(ynumerator (- (* x1*y2-y1*x2 (- y3 y4))
(* (- y1 y2) x3*y4-y3*x4))))
(list (/ xnumerator denominator)
(/ ynumerator denominator)))))))
(defun intersection-of-edges (e1 e2)
;;
;; A point is a list of two coordinates, and an edge is a list of
;; two points.
;;
(let ((point1 (car e1))
(point2 (cadr e1))
(point3 (car e2))
(point4 (cadr e2)))
(let ((x1 (car point1))
(y1 (cadr point1))
(x2 (car point2))
(y2 (cadr point2))
(x3 (car point3))
(y3 (cadr point3))
(x4 (car point4))
(y4 (cadr point4)))
(intersection-of-lines x1 y1 x2 y2 x3 y3 x4 y4))))
(defun point-is-left-of-edge-p (pt edge)
(let ((x (car pt))
(y (cadr pt))
(x1 (caar edge))
(y1 (cadar edge))
(x2 (caadr edge))
(y2 (cadadr edge)))
;; Outer product of the vectors (x1,y1)-->(x,y) and
;; (x1,y1)-->(x2,y2)
(< (- (* (- x x1) (- y2 y1))
(* (- x2 x1) (- y y1)))
0)))
(defun clip-subject-edge (subject-edge clip-edge accum)
(flet ((intersect ()
(intersection-of-edges subject-edge clip-edge)))
(let ((s1 (car subject-edge))
(s2 (cadr subject-edge)))
(let ((s2-is-inside (point-is-left-of-edge-p s2 clip-edge))
(s1-is-inside (point-is-left-of-edge-p s1 clip-edge)))
(if s2-is-inside
(if s1-is-inside
(cons s2 accum)
(cons s2 (cons (intersect) accum)))
(if s1-is-inside
(cons (intersect) accum)
accum))))))
(defun for-each-subject-edge (i subject-points clip-edge accum)
(let ((n (length subject-points))
(accum '()))
(loop for i from 0 to (1- n)
do (let ((s2 (aref subject-points i))
(s1 (aref subject-points
(- (if (zerop i) n i) 1))))
(setf accum (clip-subject-edge (list s1 s2)
clip-edge accum))))
(coerce (reverse accum) 'vector)))
(defun for-each-clip-edge (i subject-points clip-points)
(let ((n (length clip-points)))
(loop for i from 0 to (1- n)
do (let ((c2 (aref clip-points i))
(c1 (aref clip-points (- (if (zerop i) n i) 1))))
(setf subject-points
(for-each-subject-edge 0 subject-points
(list c1 c2) '()))))
subject-points))
(defun clip (subject-points clip-points)
(for-each-clip-edge 0 subject-points clip-points))
(defun write-eps (outf subject-points clip-points result-points)
(flet ((x (pt) (coerce (car pt) 'float))
(y (pt) (coerce (cadr pt) 'float))
(code (s)
(princ s outf)
(terpri outf)))
(flet ((moveto (pt)
(princ (x pt) outf)
(princ " " outf)
(princ (y pt) outf)
(princ " moveto" outf)
(terpri outf))
(lineto (pt)
(princ (x pt) outf)
(princ " " outf)
(princ (y pt) outf)
(princ " lineto" outf)
(terpri outf))
(setrgbcolor (rgb)
(princ rgb outf)
(princ " setrgbcolor" outf)
(terpri outf))
(closepath () (code "closepath"))
(fill-it () (code "fill"))
(stroke () (code "stroke"))
(gsave () (code "gsave"))
(grestore () (code "grestore")))
(flet ((showpoly (poly line-color fill-color)
(let ((n (length poly)))
(moveto (aref poly 0))
(loop for i from 1 to (1- n)
do (lineto (aref poly i)))
(closepath)
(setrgbcolor line-color)
(gsave)
(setrgbcolor fill-color)
(fill-it)
(grestore)
(stroke))))
(code "%!PS-Adobe-3.0 EPSF-3.0")
(code "%%BoundingBox: 40 40 360 360")
(code "0 setlinewidth")
(showpoly clip-points ".5 0 0" "1 .7 .7")
(showpoly subject-points "0 .2 .5" ".4 .7 1")
(code "2 setlinewidth")
(code "[10 8] 0 setdash")
(showpoly result-points ".5 0 .5" ".7 .3 .8")
(code "%%EOF")))))
(defun write-eps-to-file (outfile subject-points clip-points
result-points)
(with-open-file (outf outfile :direction :output
:if-exists :supersede
:if-does-not-exist :create)
(write-eps outf subject-points clip-points result-points)))
(defvar subject-points
#((50 150)
(200 50)
(350 150)
(350 300)
(250 300)
(200 250)
(150 350)
(100 250)
(100 200)))
(defvar clip-points
#((100 100)
(300 100)
(300 300)
(100 300)))
(defvar result-points (clip subject-points clip-points))
(princ result-points)
(terpri)
(write-eps-to-file "sutherland-hodgman.eps"
subject-points clip-points result-points)
(princ "Wrote sutherland-hodgman.eps")
(terpri)
- Output:
$ clisp sutherland-hodgman.lisp #((100 350/3) (125 100) (275 100) (300 350/3) (300 300) (250 300) (200 250) (175 300) (125 300) (100 250)) Wrote sutherland-hodgman.eps
D
import std.stdio, std.array, std.range, std.typecons, std.algorithm;
struct Vec2 { // To be replaced with Phobos code.
double x, y;
Vec2 opBinary(string op="-")(in Vec2 other)
const pure nothrow @safe @nogc {
return Vec2(this.x - other.x, this.y - other.y);
}
typeof(x) cross(in Vec2 other) const pure nothrow @safe @nogc {
return this.x * other.y - this.y * other.x;
}
}
immutable(Vec2)[] clip(in Vec2[] subjectPolygon, in Vec2[] clipPolygon)
pure /*nothrow*/ @safe in {
assert(subjectPolygon.length > 1);
assert(clipPolygon.length > 1);
// Probably clipPolygon needs to be convex and probably
// its vertices need to be listed in a direction.
} out(result) {
assert(result.length > 1);
} body {
alias Edge = Tuple!(Vec2,"p", Vec2,"q");
static enum isInside = (in Vec2 p, in Edge cle)
pure nothrow @safe @nogc =>
(cle.q.x - cle.p.x) * (p.y - cle.p.y) >
(cle.q.y - cle.p.y) * (p.x - cle.p.x);
static Vec2 intersection(in Edge se, in Edge cle)
pure nothrow @safe @nogc {
immutable dc = cle.p - cle.q;
immutable dp = se.p - se.q;
immutable n1 = cle.p.cross(cle.q);
immutable n2 = se.p.cross(se.q);
immutable n3 = 1.0 / dc.cross(dp);
return Vec2((n1 * dp.x - n2 * dc.x) * n3,
(n1 * dp.y - n2 * dc.y) * n3);
}
// How much slower is this compared to lower-level code?
static enum edges = (in Vec2[] poly) pure nothrow @safe @nogc =>
// poly[$ - 1 .. $].chain(poly).zip!Edge(poly);
poly[$ - 1 .. $].chain(poly).zip(poly).map!Edge;
immutable(Vec2)[] result = subjectPolygon.idup; // Not nothrow.
foreach (immutable clipEdge; edges(clipPolygon)) {
immutable inputList = result;
result.destroy;
foreach (immutable inEdge; edges(inputList)) {
if (isInside(inEdge.q, clipEdge)) {
if (!isInside(inEdge.p, clipEdge))
result ~= intersection(inEdge, clipEdge);
result ~= inEdge.q;
} else if (isInside(inEdge.p, clipEdge))
result ~= intersection(inEdge, clipEdge);
}
}
return result;
}
// Code adapted from the C version.
void saveEPSImage(in string fileName, in Vec2[] subjPoly,
in Vec2[] clipPoly, in Vec2[] clipped)
in {
assert(!fileName.empty);
assert(subjPoly.length > 1);
assert(clipPoly.length > 1);
assert(clipped.length > 1);
} body {
auto eps = File(fileName, "w");
// The image bounding box is hard-coded, not computed.
eps.writeln(
"%%!PS-Adobe-3.0
%%%%BoundingBox: 40 40 360 360
/l {lineto} def
/m {moveto} def
/s {setrgbcolor} def
/c {closepath} def
/gs {fill grestore stroke} def
");
eps.writef("0 setlinewidth %g %g m ", clipPoly[0].tupleof);
foreach (immutable cl; clipPoly[1 .. $])
eps.writef("%g %g l ", cl.tupleof);
eps.writefln("c 0.5 0 0 s gsave 1 0.7 0.7 s gs");
eps.writef("%g %g m ", subjPoly[0].tupleof);
foreach (immutable s; subjPoly[1 .. $])
eps.writef("%g %g l ", s.tupleof);
eps.writefln("c 0 0.2 0.5 s gsave 0.4 0.7 1 s gs");
eps.writef("2 setlinewidth [10 8] 0 setdash %g %g m ",
clipped[0].tupleof);
foreach (immutable c; clipped[1 .. $])
eps.writef("%g %g l ", c.tupleof);
eps.writefln("c 0.5 0 0.5 s gsave 0.7 0.3 0.8 s gs");
eps.writefln("%%%%EOF");
eps.close;
writeln(fileName, " written.");
}
void main() {
alias V = Vec2;
immutable subjectPolygon = [V(50, 150), V(200, 50), V(350, 150),
V(350, 300), V(250, 300), V(200, 250),
V(150, 350), V(100, 250), V(100, 200)];
immutable clippingPolygon = [V(100, 100), V(300, 100),
V(300, 300), V(100, 300)];
immutable clipped = subjectPolygon.clip(clippingPolygon);
writefln("%(%s\n%)", clipped);
saveEPSImage("sutherland_hodgman_clipping_out.eps",
subjectPolygon, clippingPolygon, clipped);
}
- Output:
immutable(Vec2)(100, 116.667) immutable(Vec2)(125, 100) immutable(Vec2)(275, 100) immutable(Vec2)(300, 116.667) immutable(Vec2)(300, 300) immutable(Vec2)(250, 300) immutable(Vec2)(200, 250) immutable(Vec2)(175, 300) immutable(Vec2)(125, 300) immutable(Vec2)(100, 250) sutherland_hodgman_clipping_out.eps written.
It also outputs an EPS file, the same as the C entry.
Elixir
defmodule SutherlandHodgman do
defp inside(cp1, cp2, p), do: (cp2.x-cp1.x)*(p.y-cp1.y) > (cp2.y-cp1.y)*(p.x-cp1.x)
defp intersection(cp1, cp2, s, e) do
{dcx, dcy} = {cp1.x-cp2.x, cp1.y-cp2.y}
{dpx, dpy} = {s.x-e.x, s.y-e.y}
n1 = cp1.x*cp2.y - cp1.y*cp2.x
n2 = s.x*e.y - s.y*e.x
n3 = 1.0 / (dcx*dpy - dcy*dpx)
%{x: (n1*dpx - n2*dcx) * n3, y: (n1*dpy - n2*dcy) * n3}
end
def polygon_clipping(subjectPolygon, clipPolygon) do
Enum.chunk([List.last(clipPolygon) | clipPolygon], 2, 1)
|> Enum.reduce(subjectPolygon, fn [cp1,cp2],acc ->
Enum.chunk([List.last(acc) | acc], 2, 1)
|> Enum.reduce([], fn [s,e],outputList ->
case {inside(cp1, cp2, e), inside(cp1, cp2, s)} do
{true, true} -> [e | outputList]
{true, false} -> [e, intersection(cp1,cp2,s,e) | outputList]
{false, true} -> [intersection(cp1,cp2,s,e) | outputList]
_ -> outputList
end
end)
|> Enum.reverse
end)
end
end
subjectPolygon = [[50, 150], [200, 50], [350, 150], [350, 300], [250, 300],
[200, 250], [150, 350], [100, 250], [100, 200]]
|> Enum.map(fn [x,y] -> %{x: x, y: y} end)
clipPolygon = [[100, 100], [300, 100], [300, 300], [100, 300]]
|> Enum.map(fn [x,y] -> %{x: x, y: y} end)
SutherlandHodgman.polygon_clipping(subjectPolygon, clipPolygon)
|> Enum.each(&IO.inspect/1)
- Output:
%{x: 100.0, y: 116.66666666666667}
%{x: 125.00000000000001, y: 100.0}
%{x: 275.0, y: 100.0}
%{x: 300.0, y: 116.66666666666667}
%{x: 300.0, y: 299.99999999999994}
%{x: 250.0, y: 300.0}
%{x: 200, y: 250}
%{x: 175.0, y: 300.0}
%{x: 125.0, y: 300.0}
%{x: 100.0, y: 250.0}
Evaldraw
This is losely based on the C version. Since Evaldraw doesnt have dynamic memory, all sizes must be declared up front. We limit ourselves to polygons of up to 32 vertices. This is fine, as the input polygon with its 9 vertices, when clipped against the clipper rectangle only produces a 11 vertex polygon. If we run out of vertices at runtime, the errno function is called and displays an error number.
struct vec{ x, y; };
enum{MAX_POLY_VERTS=32};
enum{NUM_RECT_VERTS=4, NUM_SUBJECT_VERTS=9}
struct poly_t{
len; // number of vertices
vec v[MAX_POLY_VERTS]; // wrap array of vertices inside struct
};
()
{
vec subject_verts[NUM_SUBJECT_VERTS] = { 50,150, 200,50, 350,150, 350,300,250,300,200,250, 150,350,100,250,100,200 };
vec rectangle_vertices[NUM_RECT_VERTS] = {100,100, 300,100, 300,300, 100,300};
poly_t clipper; // This polygon will define the valid area
clipper.len = 0;
for(i=0; i<NUM_RECT_VERTS; i++) {
poly_append( clipper, rectangle_vertices[i] );
}
poly_t subject; // This polygon will be clipped so its contained within the valid area.
subject.len = 0;
for(i=0; i<NUM_SUBJECT_VERTS; i++) {
poly_append( subject, subject_verts[i] );
}
poly_t clipped_result; poly_clip(subject, clipper, clipped_result);
cls(0);
setcol(255,255,255); drawpoly(clipper, 0);
setcol(255,0,255); drawpoly(subject, 0);
setcol(255,255,0); drawpoly(clipped_result, 1);
moveto(0,0); printf("%g in\n%2.0f out", subject.len, clipped_result.len);
}
poly_clip(poly_t subject, poly_t clip, poly_t pout) {
dir = poly_winding(clip);
// Clip all subject edges against first edge in clipper
poly_t p0; // current set of clipped edges
poly_t p1; // next set of clipped edges
p1.len = 0; // Clear p1
poly_edge_clip(subject, clip.v[clip.len - 1], clip.v[0], dir, p1);
for (i = 0; i < clip.len - 1; i++) { // Visit each edge in the clip polygon
poly_copy(p1,p0); // Copy p1 into p0. We could also have done p0=p1.
p1.len = 0; // Clear p1
poly_edge_clip(p0, clip.v[i], clip.v[i+1], dir, p1);
if(p1.len == 0) break; // no vertices in output, finished.
}
pout = p1;
}
poly_winding(poly_t p) {
return left_of(p.v[0], p.v[1], p.v[2]);
}
poly_edge_clip(poly_t subject, vec clip0, vec clip1, left, poly_t res) {
vec v0; v0 = subject.v[subject.len - 1];
if (res.len != 0) errno(200); // Expect empty result so far
side0 = left_of(clip0, clip1, v0);
if (side0 != -left) { poly_append(res, v0); }
// Intersect subject edge v0-v1 against clipper edge clip0-clip1
for (i = 0; i < subject.len; i++) {
vec v1; v1 = subject.v[i];
side1 = left_of(clip0, clip1, v1);
// side0+side1==0 means v0 and v1 cross the edge. v0 is inside.
if ( (side0 + side1 == 0) && side0) {
vec isect; if (line_sect(clip0, clip1, v0, v1, isect)) poly_append(res, isect);
}
if (i == subject.len - 1) break; // Back to last, finished
if (side1 != -left) { poly_append(res, v1); } // add v1 to poly
v0 = v1;
side0 = side1;
}
}
poly_append(poly_t p, vec v) {
p.v[p.len++] = v;
if(p.len>MAX_POLY_VERTS) errno(100);
}
poly_copy(poly_t src, poly_t dst) { // This improves on assigning dst to src as
for(i=0; i<src.len; i++) { // only necessary amount of vertices are copied.
dst.v[i] = src.v[i];
}
dst.len = src.len;
}
left_of(vec a, vec b, vec c) {
vec ab; vsub(ab, b, a);
vec bc; vsub(bc, c, b);
return sgn( cross2D(ab, bc) ); // return 1 if ab is left side of c. -1 if right. 0 if colinear.
}
line_sect(vec a0, vec a1, vec b0, vec b1, vec isect) {
vec da; vsub(da,a1,a0);
vec db; vsub(db,b1,b0);
vec d; vsub(d,a0, b0);
/* a0+t da = b0+s db -> a0 X da = b0 X da + s db X da -> s = (a0 - b0) X da / (db X da) */
double dbXda = cross2D(db, da);
if (!dbXda) return 0;
s = cross2D(&d, &da) / dbXda;
if (s <= 0 || s >= 1) return 0;
isect.x = b0.x + s * db.x;
isect.y = b0.y + s * db.y;
return 1;
}
errno(code) { // Since we dont have asserts, halt and print an error code
while(1) {
cls(32,32,32); setcol(200,0,0); moveto(0,0);
printf("errno(%g)", code); refresh(); sleep(1);
}
}
drawpoly(poly_t p, show_verts) {
for(i=0; i<p.len+1; i++) {
vec v = p.v[i%p.len];
if (show_verts) for(j=0; j<32; j++) { setpix( v.x+nrnd, v.y+nrnd); }
if(i==0) moveto(v.x,v.y); else lineto(v.x,v.y);
}
}
// 2D cross product - also known as directed area product.
cross2D(vec a, vec b) { return a.x * b.y - a.y * b.x; }
vsub(vec c, vec a, vec b) { c.x = a.x - b.x; c.y = a.y - b.y; }
Fortran
Infos: The polygons are fortran type with an allocatable array "vertex" that contains the vertices and an integer n that is the size of the polygon. For any polygon, the first vertex and the last vertex have to be the same. As you will see, in the main function, we allocate the vertex array of the result polygon with its maximal size.
module SutherlandHodgmanUtil
! functions and type needed for Sutherland-Hodgman algorithm
! -------------------------------------------------------- !
type polygon
!type for polygons
! when you define a polygon, the first and the last vertices have to be the same
integer :: n
double precision, dimension(:,:), allocatable :: vertex
end type polygon
contains
! -------------------------------------------------------- !
subroutine sutherlandHodgman( ref, clip, outputPolygon )
! Sutherland Hodgman algorithm for 2d polygons
! -- parameters of the subroutine --
type(polygon) :: ref, clip, outputPolygon
! -- variables used is the subroutine
type(polygon) :: workPolygon ! polygon clipped step by step
double precision, dimension(2) :: y1,y2 ! vertices of edge to clip workPolygon
integer :: i
! allocate workPolygon with the maximal possible size
! the sum of the size of polygon ref and clip
allocate(workPolygon%vertex( ref%n+clip%n , 2 ))
! initialise the work polygon with clip
workPolygon%n = clip%n
workPolygon%vertex(1:workPolygon%n,:) = clip%vertex(1:workPolygon%n,:)
do i=1,ref%n-1 ! for each edge i of the polygon ref
y1(:) = ref%vertex(i,:) ! vertex 1 of edge i
y2(:) = ref%vertex(i+1,:) ! vertex 2 of edge i
! clip the work polygon by edge i
call edgeClipping( workPolygon, y1, y2, outputPolygon)
! workPolygon <= outputPolygon
workPolygon%n = outputPolygon%n
workPolygon%vertex(1:workPolygon%n,:) = outputPolygon%vertex(1:workPolygon%n,:)
end do
deallocate(workPolygon%vertex)
end subroutine sutherlandHodgman
! -------------------------------------------------------- !
subroutine edgeClipping( poly, y1, y2, outputPoly )
! make the clipping of the polygon by the line (x1x2)
type(polygon) :: poly, outputPoly
double precision, dimension(2) :: y1, y2, x1, x2, intersecPoint
integer :: i, c
c = 0 ! counter for the output polygon
do i=1,poly%n-1 ! for each edge i of poly
x1(:) = poly%vertex(i,:) ! vertex 1 of edge i
x2(:) = poly%vertex(i+1,:) ! vertex 2 of edge i
if ( inside(x1, y1, y2) ) then ! if vertex 1 in inside clipping region
if ( inside(x2, y1, y2) ) then ! if vertex 2 in inside clipping region
! add the vertex 2 to the output polygon
c = c+1
outputPoly%vertex(c,:) = x2(:)
else ! vertex i+1 is outside
intersecPoint = intersection(x1, x2, y1,y2)
c = c+1
outputPoly%vertex(c,:) = intersecPoint(:)
end if
else ! vertex i is outside
if ( inside(x2, y1, y2) ) then
intersecPoint = intersection(x1, x2, y1,y2)
c = c+1
outputPoly%vertex(c,:) = intersecPoint(:)
c = c+1
outputPoly%vertex(c,:) = x2(:)
end if
end if
end do
if (c .gt. 0) then
! if the last vertice is not equal to the first one
if ( (outputPoly%vertex(1,1) .ne. outputPoly%vertex(c,1)) .or. &
(outputPoly%vertex(1,2) .ne. outputPoly%vertex(c,2))) then
c=c+1
outputPoly%vertex(c,:) = outputPoly%vertex(1,:)
end if
end if
! set the size of the outputPolygon
outputPoly%n = c
end subroutine edgeClipping
! -------------------------------------------------------- !
function intersection( x1, x2, y1, y2)
! computes the intersection between segment [x1x2]
! and line the line (y1y2)
! -- parameters of the function --
double precision, dimension(2) :: x1, x2, & ! points of the segment
y1, y2 ! points of the line
double precision, dimension(2) :: intersection, vx, vy, x1y1
double precision :: a
vx(:) = x2(:) - x1(:)
vy(:) = y2(:) - y1(:)
! if the vectors are colinear
if ( crossProduct(vx,vy) .eq. 0.d0) then
x1y1(:) = y1(:) - x1(:)
! if the the segment [x1x2] is included in the line (y1y2)
if ( crossProduct(x1y1,vx) .eq. 0.d0) then
! the intersection is the last point of the segment
intersection(:) = x2(:)
end if
else ! the vectors are not colinear
! we want to find the inersection between [x1x2]
! and (y1,y2).
! mathematically, we want to find a in [0;1] such
! that :
! x1 + a vx = y1 + b vy
! <=> a vx = x1y1 + b vy
! <=> a vx^vy = x1y1^vy , ^ is cross product
! <=> a = x1y1^vy / vx^vy
x1y1(:) = y1(:) - x1(:)
! we compute a
a = crossProduct(x1y1,vy)/crossProduct(vx,vy)
! if a is not in [0;1]
if ( (a .gt. 1.d0) .or. (a .lt. 0)) then
! no intersection
else
intersection(:) = x1(:) + a*vx(:)
end if
end if
end function intersection
! -------------------------------------------------------- !
function inside( p, y1, y2)
! function that tells is the point p is at left of the line (y1y2)
double precision, dimension(2) :: p, y1, y2, v1, v2
logical :: inside
v1(:) = y2(:) - y1(:)
v2(:) = p(:) - y1(:)
if ( crossProduct(v1,v2) .ge. 0.d0) then
inside = .true.
else
inside = .false.
end if
contains
end function inside
! -------------------------------------------------------- !
function dotProduct( v1, v2)
! compute the dot product of vectors v1 and v2
double precision, dimension(2) :: v1
double precision, dimension(2) :: v2
double precision :: dotProduct
dotProduct = v1(1)*v2(1) + v1(2)*v2(2)
end function dotProduct
! -------------------------------------------------------- !
function crossProduct( v1, v2)
! compute the crossproduct of vectors v1 and v2
double precision, dimension(2) :: v1
double precision, dimension(2) :: v2
double precision :: crossProduct
crossProduct = v1(1)*v2(2) - v1(2)*v2(1)
end function crossProduct
end module SutherlandHodgmanUtil
program main
! load the module for S-H algorithm
use SutherlandHodgmanUtil, only : polygon, &
sutherlandHodgman, &
edgeClipping
type(polygon) :: p1, p2, res
integer :: c, n
double precision, dimension(2) :: y1, y2
! when you define a polygon, the first and the last vertices have to be the same
! first polygon
p1%n = 10
allocate(p1%vertex(p1%n,2))
p1%vertex(1,1)=50.d0
p1%vertex(1,2)=150.d0
p1%vertex(2,1)=200.d0
p1%vertex(2,2)=50.d0
p1%vertex(3,1)= 350.d0
p1%vertex(3,2)= 150.d0
p1%vertex(4,1)= 350.d0
p1%vertex(4,2)= 300.d0
p1%vertex(5,1)= 250.d0
p1%vertex(5,2)= 300.d0
p1%vertex(6,1)= 200.d0
p1%vertex(6,2)= 250.d0
p1%vertex(7,1)= 150.d0
p1%vertex(7,2)= 350.d0
p1%vertex(8,1)= 100.d0
p1%vertex(8,2)= 250.d0
p1%vertex(9,1)= 100.d0
p1%vertex(9,2)= 200.d0
p1%vertex(10,1)= 50.d0
p1%vertex(10,2)= 150.d0
y1 = (/ 100.d0, 300.d0 /)
y2 = (/ 300.d0, 300.d0 /)
! second polygon
p2%n = 5
allocate(p2%vertex(p2%n,2))
p2%vertex(1,1)= 100.d0
p2%vertex(1,2)= 100.d0
p2%vertex(2,1)= 300.d0
p2%vertex(2,2)= 100.d0
p2%vertex(3,1)= 300.d0
p2%vertex(3,2)= 300.d0
p2%vertex(4,1)= 100.d0
p2%vertex(4,2)= 300.d0
p2%vertex(5,1)= 100.d0
p2%vertex(5,2)= 100.d0
allocate(res%vertex(p1%n+p2%n,2))
call sutherlandHodgman( p2, p1, res)
write(*,*) "Suterland-Hodgman"
do c=1, res%n
write(*,*) res%vertex(c,1), res%vertex(c,2)
end do
deallocate(res%vertex)
end program main
Output:
Suterland-Hodgman 300.00000000000000 300.00000000000000 250.00000000000000 300.00000000000000 200.00000000000000 250.00000000000000 175.00000000000000 300.00000000000000 125.00000000000000 300.00000000000000 100.00000000000000 250.00000000000000 100.00000000000000 200.00000000000000 100.00000000000000 200.00000000000000 100.00000000000000 116.66666666666667 125.00000000000000 100.00000000000000 275.00000000000000 100.00000000000000 300.00000000000000 116.66666666666666 300.00000000000000 300.00000000000000
FreeBASIC
FreeBASIC has inbuilt gfx graphics (a main feature), but I have no access to graphics uploads. So no extra credits.
Type Point
As Double x,y
End Type
Type Line
As Point s,f'start/finish
End Type
Function isleft(L As Line,p As Point) As Long
Return -Sgn((L.s.x-L.f.x)*(p.y-L.f.y)-(p.x-L.f.x)*(L.s.y-L.f.y))
End Function
Function segmentintersections(L1 As Line,L2 As Line) As Long
If isleft(L2,L1.s) = isleft(L2,L1.f) Then Return 0
If isleft(L1,L2.s) = isleft(L1,L2.f) Then Return 0
Return 1
End Function
Function allintersections(l1 As Line,l2 As Line,_out As Point) As Long
Const tolerance=.01
Var p1=l1.s, p2=l1.f, p3=l2.s, p4=l2.f
Var x12=p1.x-p2.x, x34=p3.x-p4.x, y12=p1.y-p2.y, y34=p3.y-p4.y
Var c=x12*y34-y12*x34
If Abs(c)<tolerance Then Return 0
Var a=p1.x*p2.y-p1.y*p2.x, b=p3.x*p4.y-p3.y*p4.x
_out.x = (a*x34-b*x12)/c
_out.y = (a*y34-b*y12)/c
Return 1
End Function
Dim As Point p1(...)={(50,150),(200,50),(350,150),(350,300),(250,300),(200,250), _
(150,350),(100,250),(100,200)}
Dim As Point p2(...)={(100,100),(300,100),(300,300),(100,300)}
'get the line segments around the polygons
Dim As Line L1(...)={(p1(0),p1(1)),(p1(1),p1(2)),(p1(2),p1(3)),(p1(3),p1(4)),(p1(4),p1(5)),_
(p1(5),p1(6)),(p1(6),p1(7)),(p1(7),p1(8)),(p1(8),p1(0))}
Dim As Line L2(...)={(p2(0),p2(1)),(p2(1),p2(2)),(p2(2),p2(3)),(p2(3),p2(0))}
'would normally draw these lines now, but not here.
Dim As Point x
For n1 As Long=Lbound(L1) To Ubound(L1)
For n2 As Long=Lbound(L2) To Ubound(L2)
If allintersections(L1(n1),L2(n2),x) And segmentintersections(L1(n1),L2(n2)) Then
Print x.x,x.y
End If
Next
Next
Sleep
- Output:
125 100 100 116.6666666666667 275 100 300 116.6666666666667 300 300 250 300 175 300 125 300 100 250 100 200
Go
No extra credit today.
package main
import "fmt"
type point struct {
x, y float32
}
var subjectPolygon = []point{{50, 150}, {200, 50}, {350, 150}, {350, 300},
{250, 300}, {200, 250}, {150, 350}, {100, 250}, {100, 200}}
var clipPolygon = []point{{100, 100}, {300, 100}, {300, 300}, {100, 300}}
func main() {
var cp1, cp2, s, e point
inside := func(p point) bool {
return (cp2.x-cp1.x)*(p.y-cp1.y) > (cp2.y-cp1.y)*(p.x-cp1.x)
}
intersection := func() (p point) {
dcx, dcy := cp1.x-cp2.x, cp1.y-cp2.y
dpx, dpy := s.x-e.x, s.y-e.y
n1 := cp1.x*cp2.y - cp1.y*cp2.x
n2 := s.x*e.y - s.y*e.x
n3 := 1 / (dcx*dpy - dcy*dpx)
p.x = (n1*dpx - n2*dcx) * n3
p.y = (n1*dpy - n2*dcy) * n3
return
}
outputList := subjectPolygon
cp1 = clipPolygon[len(clipPolygon)-1]
for _, cp2 = range clipPolygon { // WP clipEdge is cp1,cp2 here
inputList := outputList
outputList = nil
s = inputList[len(inputList)-1]
for _, e = range inputList {
if inside(e) {
if !inside(s) {
outputList = append(outputList, intersection())
}
outputList = append(outputList, e)
} else if inside(s) {
outputList = append(outputList, intersection())
}
s = e
}
cp1 = cp2
}
fmt.Println(outputList)
}
- Output:
[{100 116.66667} {125 100} {275 100} {300 116.66667} {300 300} {250 300} {200 250} {175 300} {125 300} {100 250}]
(You can try it online)
Haskell
module SuthHodgClip (clipTo) where
import Data.List
type Pt a = (a, a)
type Ln a = (Pt a, Pt a)
type Poly a = [Pt a]
-- Return a polygon from a list of points.
polyFrom ps = last ps : ps
-- Return a list of lines from a list of points.
linesFrom pps@(_:ps) = zip pps ps
-- Return true if the point (x,y) is on or to the left of the oriented line
-- defined by (px,py) and (qx,qy).
(.|) :: (Num a, Ord a) => Pt a -> Ln a -> Bool
(x,y) .| ((px,py),(qx,qy)) = (qx-px)*(y-py) >= (qy-py)*(x-px)
-- Return the intersection of two lines.
(><) :: Fractional a => Ln a -> Ln a -> Pt a
((x1,y1),(x2,y2)) >< ((x3,y3),(x4,y4)) =
let (r,s) = (x1*y2-y1*x2, x3*y4-y3*x4)
(t,u,v,w) = (x1-x2, y3-y4, y1-y2, x3-x4)
d = t*u-v*w
in ((r*w-t*s)/d, (r*u-v*s)/d)
-- Intersect the line segment (p0,p1) with the clipping line's left halfspace,
-- returning the point closest to p1. In the special case where p0 lies outside
-- the halfspace and p1 lies inside we return both the intersection point and
-- p1. This ensures we will have the necessary segment along the clipping line.
(-|) :: (Fractional a, Ord a) => Ln a -> Ln a -> [Pt a]
ln@(p0, p1) -| clipLn =
case (p0 .| clipLn, p1 .| clipLn) of
(False, False) -> []
(False, True) -> [isect, p1]
(True, False) -> [isect]
(True, True) -> [p1]
where isect = ln >< clipLn
-- Intersect the polygon with the clipping line's left halfspace.
(<|) :: (Fractional a, Ord a) => Poly a -> Ln a -> Poly a
poly <| clipLn = polyFrom $ concatMap (-| clipLn) (linesFrom poly)
-- Intersect a target polygon with a clipping polygon. The latter is assumed to
-- be convex.
clipTo :: (Fractional a, Ord a) => [Pt a] -> [Pt a] -> [Pt a]
targPts `clipTo` clipPts =
let targPoly = polyFrom targPts
clipLines = linesFrom (polyFrom clipPts)
in foldl' (<|) targPoly clipLines
Print the resulting list of points and display the polygons in a window.
import Graphics.HGL
import SuthHodgClip
targPts = [( 50,150), (200, 50), (350,150), (350,300), (250,300),
(200,250), (150,350), (100,250), (100,200)] :: [(Float,Float)]
clipPts = [(100,100), (300,100), (300,300), (100,300)] :: [(Float,Float)]
toInts = map (\(a,b) -> (round a, round b))
complete xs = last xs : xs
drawSolid w c = drawInWindow w . withRGB c . polygon
drawLines w p = drawInWindow w . withPen p . polyline . toInts . complete
blue = RGB 0x99 0x99 0xff
green = RGB 0x99 0xff 0x99
pink = RGB 0xff 0x99 0x99
white = RGB 0xff 0xff 0xff
main = do
let resPts = targPts `clipTo` clipPts
sz = 400
win = [(0,0), (sz,0), (sz,sz), (0,sz)]
runWindow "Sutherland-Hodgman Polygon Clipping" (sz,sz) $ \w -> do
print $ toInts resPts
penB <- createPen Solid 3 blue
penP <- createPen Solid 5 pink
drawSolid w white win
drawLines w penB targPts
drawLines w penP clipPts
drawSolid w green $ toInts resPts
getKey w
- Output:
[(100,200),(100,200),(100,117),(125,100),(275,100),(300,117),(300,300),(250,300),(200,250),(175,300),(125,300),(100,250),(100,200)]
J
Solution:
NB. assumes counterclockwise orientation.
NB. determine whether point y is inside edge x.
isinside=:0< [:-/ .* {.@[ -~"1 {:@[,:]
NB. (p0,:p1) intersection (p2,:p3)
intersection=:|:@[ (+/ .* (,-.)) [:{. ,.&(-~/) %.~ -&{:
SutherlandHodgman=:4 :0 NB. clip S-H subject
clip=.2 ]\ (,{.) x
subject=.y
for_edge. clip do.
S=.{:input=.subject
subject=.0 2$0
for_E. input do.
if. edge isinside E do.
if. -.edge isinside S do.
subject=.subject,edge intersection S,:E end.
subject=.subject,E
elseif. edge isinside S do.
subject=.subject,edge intersection S,:E end.
S=.E
end.
end.
subject
)
- Example use:
subject=: 50 150,200 50,350 150,350 300,250 300,200 250,150 350,100 250,:100 200
clip=: 100 100,300 100,300 300,:100 300
clip SutherlandHodgman subject
100 116.667
125 100
275 100
300 116.667
300 300
250 300
200 250
175 300
125 300
100 250
Java
import java.awt.*;
import java.awt.geom.Line2D;
import java.util.*;
import java.util.List;
import javax.swing.*;
public class SutherlandHodgman extends JFrame {
SutherlandHodgmanPanel panel;
public static void main(String[] args) {
JFrame f = new SutherlandHodgman();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setVisible(true);
}
public SutherlandHodgman() {
Container content = getContentPane();
content.setLayout(new BorderLayout());
panel = new SutherlandHodgmanPanel();
content.add(panel, BorderLayout.CENTER);
setTitle("SutherlandHodgman");
pack();
setLocationRelativeTo(null);
}
}
class SutherlandHodgmanPanel extends JPanel {
List<double[]> subject, clipper, result;
public SutherlandHodgmanPanel() {
setPreferredSize(new Dimension(600, 500));
// these subject and clip points are assumed to be valid
double[][] subjPoints = {{50, 150}, {200, 50}, {350, 150}, {350, 300},
{250, 300}, {200, 250}, {150, 350}, {100, 250}, {100, 200}};
double[][] clipPoints = {{100, 100}, {300, 100}, {300, 300}, {100, 300}};
subject = new ArrayList<>(Arrays.asList(subjPoints));
result = new ArrayList<>(subject);
clipper = new ArrayList<>(Arrays.asList(clipPoints));
clipPolygon();
}
private void clipPolygon() {
int len = clipper.size();
for (int i = 0; i < len; i++) {
int len2 = result.size();
List<double[]> input = result;
result = new ArrayList<>(len2);
double[] A = clipper.get((i + len - 1) % len);
double[] B = clipper.get(i);
for (int j = 0; j < len2; j++) {
double[] P = input.get((j + len2 - 1) % len2);
double[] Q = input.get(j);
if (isInside(A, B, Q)) {
if (!isInside(A, B, P))
result.add(intersection(A, B, P, Q));
result.add(Q);
} else if (isInside(A, B, P))
result.add(intersection(A, B, P, Q));
}
}
}
private boolean isInside(double[] a, double[] b, double[] c) {
return (a[0] - c[0]) * (b[1] - c[1]) > (a[1] - c[1]) * (b[0] - c[0]);
}
private double[] intersection(double[] a, double[] b, double[] p, double[] q) {
double A1 = b[1] - a[1];
double B1 = a[0] - b[0];
double C1 = A1 * a[0] + B1 * a[1];
double A2 = q[1] - p[1];
double B2 = p[0] - q[0];
double C2 = A2 * p[0] + B2 * p[1];
double det = A1 * B2 - A2 * B1;
double x = (B2 * C1 - B1 * C2) / det;
double y = (A1 * C2 - A2 * C1) / det;
return new double[]{x, y};
}
@Override
public void paintComponent(Graphics g) {
super.paintComponent(g);
Graphics2D g2 = (Graphics2D) g;
g2.translate(80, 60);
g2.setStroke(new BasicStroke(3));
g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
drawPolygon(g2, subject, Color.blue);
drawPolygon(g2, clipper, Color.red);
drawPolygon(g2, result, Color.green);
}
private void drawPolygon(Graphics2D g2, List<double[]> points, Color color) {
g2.setColor(color);
int len = points.size();
Line2D line = new Line2D.Double();
for (int i = 0; i < len; i++) {
double[] p1 = points.get(i);
double[] p2 = points.get((i + 1) % len);
line.setLine(p1[0], p1[1], p2[0], p2[1]);
g2.draw(line);
}
}
}
JavaScript
Solution:
<html>
<head>
<script>
function clip (subjectPolygon, clipPolygon) {
var cp1, cp2, s, e;
var inside = function (p) {
return (cp2[0]-cp1[0])*(p[1]-cp1[1]) > (cp2[1]-cp1[1])*(p[0]-cp1[0]);
};
var intersection = function () {
var dc = [ cp1[0] - cp2[0], cp1[1] - cp2[1] ],
dp = [ s[0] - e[0], s[1] - e[1] ],
n1 = cp1[0] * cp2[1] - cp1[1] * cp2[0],
n2 = s[0] * e[1] - s[1] * e[0],
n3 = 1.0 / (dc[0] * dp[1] - dc[1] * dp[0]);
return [(n1*dp[0] - n2*dc[0]) * n3, (n1*dp[1] - n2*dc[1]) * n3];
};
var outputList = subjectPolygon;
cp1 = clipPolygon[clipPolygon.length-1];
for (var j in clipPolygon) {
cp2 = clipPolygon[j];
var inputList = outputList;
outputList = [];
s = inputList[inputList.length - 1]; //last on the input list
for (var i in inputList) {
e = inputList[i];
if (inside(e)) {
if (!inside(s)) {
outputList.push(intersection());
}
outputList.push(e);
}
else if (inside(s)) {
outputList.push(intersection());
}
s = e;
}
cp1 = cp2;
}
return outputList
}
function drawPolygon(context, polygon, strokeStyle, fillStyle) {
context.strokeStyle = strokeStyle;
context.fillStyle = fillStyle;
context.beginPath();
context.moveTo(polygon[0][0],polygon[0][1]); //first vertex
for (var i = 1; i < polygon.length ; i++)
context.lineTo(polygon[i][0],polygon[i][1]);
context.lineTo(polygon[0][0],polygon[0][1]); //back to start
context.fill();
context.stroke();
context.closePath();
}
window.onload = function () {
var context = document.getElementById('canvas').getContext('2d');
var subjectPolygon = [[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]],
clipPolygon = [[100, 100], [300, 100], [300, 300], [100, 300]];
var clippedPolygon = clip(subjectPolygon, clipPolygon);
drawPolygon(context, clipPolygon, '#888','#88f');
drawPolygon(context, subjectPolygon, '#888','#8f8');
drawPolygon(context, clippedPolygon, '#000','#0ff');
}
</script>
<body>
<canvas id='canvas' width='400' height='400'></canvas>
</body>
</html>
You can see it running here
Julia
using Luxor
isinside(p, a, b) = (b.x - a.x) * (p.y - a.y) > (b.y - a.y) * (p.x - a.x)
function intersection(a, b, s, f)
dc = [a.x - b.x, a.y - b.y]
dp = [s.x - f.x, s.y - f.y]
n1 = a.x * b.y - a.y * b.x
n2 = s.x * f.y - s.y * f.x
n3 = 1.0 / (dc[1] * dp[2] - dc[2] * dp[1])
Point((n1 * dp[1] - n2 * dc[1]) * n3, (n1 * dp[2] - n2 * dc[2]) * n3)
end
function clipSH(spoly, cpoly)
outarr = spoly
q = cpoly[end]
for p in cpoly
inarr = outarr
outarr = Point[]
s = inarr[end]
for vtx in inarr
if isinside(vtx, q, p)
if !isinside(s, q, p)
push!(outarr, intersection(q, p, s, vtx))
end
push!(outarr, vtx)
elseif isinside(s, q, p)
push!(outarr, intersection(q, p, s, vtx))
end
s = vtx
end
q = p
end
outarr
end
subjectp = [Point(50, 150), Point(200, 50), Point(350, 150), Point(350, 300),
Point(250, 300), Point(200, 250), Point(150, 350), Point(100, 250), Point(100, 200)]
clipp = [Point(100, 100), Point(300, 100), Point(300, 300), Point(100, 300)]
Drawing(400, 400, "intersecting-polygons.png")
background("white")
sethue("red")
poly(subjectp, :stroke, close=true)
sethue("blue")
poly(clipp, :stroke, close=true)
clipped = clipSH(subjectp, clipp)
sethue("gold")
poly(clipped, :fill, close=true)
finish()
preview()
println(clipped)
- Output:
Point[Point(100.0, 116.667), Point(125.0, 100.0), Point(275.0, 100.0), Point(300.0, 116.667),
Point(300.0, 300.0), Point(250.0, 300.0), Point(200.0, 250.0), Point(175.0, 300.0),
Point(125.0, 300.0), Point(100.0, 250.0)]
Kotlin
// version 1.1.2
import java.awt.*
import java.awt.geom.Line2D
import javax.swing.*
class SutherlandHodgman : JPanel() {
private val subject = listOf(
doubleArrayOf( 50.0, 150.0), doubleArrayOf(200.0, 50.0), doubleArrayOf(350.0, 150.0),
doubleArrayOf(350.0, 300.0), doubleArrayOf(250.0, 300.0), doubleArrayOf(200.0, 250.0),
doubleArrayOf(150.0, 350.0), doubleArrayOf(100.0, 250.0), doubleArrayOf(100.0, 200.0)
)
private val clipper = listOf(
doubleArrayOf(100.0, 100.0), doubleArrayOf(300.0, 100.0),
doubleArrayOf(300.0, 300.0), doubleArrayOf(100.0, 300.0)
)
private var result = subject.toMutableList()
init {
preferredSize = Dimension(600, 500)
clipPolygon()
}
private fun clipPolygon() {
val len = clipper.size
for (i in 0 until len) {
val len2 = result.size
val input = result
result = mutableListOf<DoubleArray>()
val a = clipper[(i + len - 1) % len]
val b = clipper[i]
for (j in 0 until len2) {
val p = input[(j + len2 - 1) % len2]
val q = input[j]
if (isInside(a, b, q)) {
if (!isInside(a, b, p)) result.add(intersection(a, b, p, q))
result.add(q)
}
else if (isInside(a, b, p)) result.add(intersection(a, b, p, q))
}
}
}
private fun isInside(a: DoubleArray, b: DoubleArray, c: DoubleArray) =
(a[0] - c[0]) * (b[1] - c[1]) > (a[1] - c[1]) * (b[0] - c[0])
private fun intersection(a: DoubleArray, b: DoubleArray,
p: DoubleArray, q: DoubleArray): DoubleArray {
val a1 = b[1] - a[1]
val b1 = a[0] - b[0]
val c1 = a1 * a[0] + b1 * a[1]
val a2 = q[1] - p[1]
val b2 = p[0] - q[0]
val c2 = a2 * p[0] + b2 * p[1]
val d = a1 * b2 - a2 * b1
val x = (b2 * c1 - b1 * c2) / d
val y = (a1 * c2 - a2 * c1) / d
return doubleArrayOf(x, y)
}
override fun paintComponent(g: Graphics) {
super.paintComponent(g)
val g2 = g as Graphics2D
g2.translate(80, 60)
g2.stroke = BasicStroke(3.0f)
g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON)
drawPolygon(g2, subject, Color.blue)
drawPolygon(g2, clipper, Color.red)
drawPolygon(g2, result, Color.green)
}
private fun drawPolygon(g2: Graphics2D, points: List<DoubleArray>, color: Color) {
g2.color = color
val len = points.size
val line = Line2D.Double()
for (i in 0 until len) {
val p1 = points[i]
val p2 = points[(i + 1) % len]
line.setLine(p1[0], p1[1], p2[0], p2[1])
g2.draw(line)
}
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
with(f) {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
add(SutherlandHodgman(), BorderLayout.CENTER)
title = "Sutherland-Hodgman"
pack()
setLocationRelativeTo(null)
isVisible = true
}
}
}
Lua
No extra credit.
subjectPolygon = {
{50, 150}, {200, 50}, {350, 150}, {350, 300},
{250, 300}, {200, 250}, {150, 350}, {100, 250}, {100, 200}
}
clipPolygon = {{100, 100}, {300, 100}, {300, 300}, {100, 300}}
function inside(p, cp1, cp2)
return (cp2.x-cp1.x)*(p.y-cp1.y) > (cp2.y-cp1.y)*(p.x-cp1.x)
end
function intersection(cp1, cp2, s, e)
local dcx, dcy = cp1.x-cp2.x, cp1.y-cp2.y
local dpx, dpy = s.x-e.x, s.y-e.y
local n1 = cp1.x*cp2.y - cp1.y*cp2.x
local n2 = s.x*e.y - s.y*e.x
local n3 = 1 / (dcx*dpy - dcy*dpx)
local x = (n1*dpx - n2*dcx) * n3
local y = (n1*dpy - n2*dcy) * n3
return {x=x, y=y}
end
function clip(subjectPolygon, clipPolygon)
local outputList = subjectPolygon
local cp1 = clipPolygon[#clipPolygon]
for _, cp2 in ipairs(clipPolygon) do -- WP clipEdge is cp1,cp2 here
local inputList = outputList
outputList = {}
local s = inputList[#inputList]
for _, e in ipairs(inputList) do
if inside(e, cp1, cp2) then
if not inside(s, cp1, cp2) then
outputList[#outputList+1] = intersection(cp1, cp2, s, e)
end
outputList[#outputList+1] = e
elseif inside(s, cp1, cp2) then
outputList[#outputList+1] = intersection(cp1, cp2, s, e)
end
s = e
end
cp1 = cp2
end
return outputList
end
function main()
local function mkpoints(t)
for i, p in ipairs(t) do
p.x, p.y = p[1], p[2]
end
end
mkpoints(subjectPolygon)
mkpoints(clipPolygon)
local outputList = clip(subjectPolygon, clipPolygon)
for _, p in ipairs(outputList) do
print(('{%f, %f},'):format(p.x, p.y))
end
end
main()
- Output:
{100.000000, 116.666667},
{125.000000, 100.000000},
{275.000000, 100.000000},
{300.000000, 116.666667},
{300.000000, 300.000000},
{250.000000, 300.000000},
{200.000000, 250.000000},
{175.000000, 300.000000},
{125.000000, 300.000000},
{100.000000, 250.000000},
(You can also see it live)
Mathematica /Wolfram Language
Geometry is built in to the Wolfram Language.
p1 = Polygon[{{50, 150}, {200, 50}, {350, 150}, {350, 300}, {250, 300}, {200, 250}, {150, 350}, {100, 250}, {100, 200}}];
p2 = Polygon[{{100, 100}, {300, 100}, {300, 300}, {100, 300}}];
RegionIntersection[p1, p2]
Graphics[{Red, p1, Blue, p2, Green, RegionIntersection[p1, p2]}]
- Output:
Polygon[{{125, 100}, {100, 350/3}, {100, 200}, {100, 250}, {125, 300}, {175, 300}, {200, 250}, {250, 300}, {300, 300}, {300, 350/3}, {275, 100}}]
MATLAB / Octave
%The inputs are a table of x-y pairs for the verticies of the subject
%polygon and boundary polygon. (x values in column 1 and y values in column
%2) The output is a table of x-y pairs for the clipped version of the
%subject polygon.
function clippedPolygon = sutherlandHodgman(subjectPolygon,clipPolygon)
%% Helper Functions
%computerIntersection() assumes the two lines intersect
function intersection = computeIntersection(line1,line2)
%this is an implementation of
%http://en.wikipedia.org/wiki/Line-line_intersection
intersection = zeros(1,2);
detL1 = det(line1);
detL2 = det(line2);
detL1x = det([line1(:,1),[1;1]]);
detL1y = det([line1(:,2),[1;1]]);
detL2x = det([line2(:,1),[1;1]]);
detL2y = det([line2(:,2),[1;1]]);
denominator = det([detL1x detL1y;detL2x detL2y]);
intersection(1) = det([detL1 detL1x;detL2 detL2x]) / denominator;
intersection(2) = det([detL1 detL1y;detL2 detL2y]) / denominator;
end %computeIntersection
%inside() assumes the boundary is oriented counter-clockwise
function in = inside(point,boundary)
pointPositionVector = [diff([point;boundary(1,:)]) 0];
boundaryVector = [diff(boundary) 0];
crossVector = cross(pointPositionVector,boundaryVector);
if ( crossVector(3) <= 0 )
in = true;
else
in = false;
end
end %inside
%% Sutherland-Hodgman Algorithm
clippedPolygon = subjectPolygon;
numVerticies = size(clipPolygon,1);
clipVertexPrevious = clipPolygon(end,:);
for clipVertex = (1:numVerticies)
clipBoundary = [clipPolygon(clipVertex,:) ; clipVertexPrevious];
inputList = clippedPolygon;
clippedPolygon = [];
if ~isempty(inputList),
previousVertex = inputList(end,:);
end
for subjectVertex = (1:size(inputList,1))
if ( inside(inputList(subjectVertex,:),clipBoundary) )
if( not(inside(previousVertex,clipBoundary)) )
subjectLineSegment = [previousVertex;inputList(subjectVertex,:)];
clippedPolygon(end+1,1:2) = computeIntersection(clipBoundary,subjectLineSegment);
end
clippedPolygon(end+1,1:2) = inputList(subjectVertex,:);
elseif( inside(previousVertex,clipBoundary) )
subjectLineSegment = [previousVertex;inputList(subjectVertex,:)];
clippedPolygon(end+1,1:2) = computeIntersection(clipBoundary,subjectLineSegment);
end
previousVertex = inputList(subjectVertex,:);
clipVertexPrevious = clipPolygon(clipVertex,:);
end %for subject verticies
end %for boundary verticies
end %sutherlandHodgman
- Output:
>> subject = [[50;200;350;350;250;200;150;100;100],[150;50;150;300;300;250;350;250;200]];
>> clipPolygon = [[100;300;300;100],[100;100;300;300]];
>> clippedSubject = sutherlandHodgman(subject,clipPolygon);
>> plot([subject(:,1);subject(1,1)],[subject(:,2);subject(1,2)],[0,0,1])
>> hold on
>> plot([clipPolygon(:,1);clipPolygon(1,1)],[clipPolygon(:,2);clipPolygon(1,2)],'r')
>> patch(clippedSubject(:,1),clippedSubject(:,2),0);
>> axis square
Mercury
:- module sutherland_hodgman_task.
:- interface.
:- import_module io.
:- pred main(io::di, io::uo) is det.
:- implementation.
:- import_module exception.
:- import_module float.
:- import_module list.
:- import_module pair.
:- import_module string.
:- type plane_point == pair(float).
:- func xcoord(plane_point) = float.
:- func ycoord(plane_point) = float.
:- func plane_point(float, float) = plane_point.
:- pred write_plane_point(plane_point::in, io::di, io::uo) is det.
:- pred write_plane_point_list(list(plane_point)::in, string::in,
io::di, io::uo) is det.
xcoord(Pt) = fst(Pt).
ycoord(Pt) = snd(Pt).
plane_point(X, Y) = pair(X, Y).
write_plane_point(Pt, !IO) :-
write_string("(", !IO),
write_float(xcoord(Pt), !IO),
write_string(", ", !IO),
write_float(ycoord(Pt), !IO),
write_string(")", !IO).
write_plane_point_list(Pts, Separator, !IO) :-
write_list(Pts, Separator, write_plane_point, !IO).
:- type plane_edge == pair(plane_point).
:- func point0(plane_edge) = plane_point.
:- func point1(plane_edge) = plane_point.
:- func plane_edge(plane_point, plane_point) = plane_edge.
point0(Edge) = fst(Edge).
point1(Edge) = snd(Edge).
plane_edge(Pt0, Pt1) = pair(Pt0, Pt1).
:- func evaluate_line(float, float, float, float, float) = float.
evaluate_line(X1, Y1, X2, Y2, X) = Y :-
%% Given the line (X1,Y1)--(X2,Y2), evaluate it at X.
Dy = Y2 - Y1,
Dx = X2 - X1,
Slope = Dy / Dx,
Intercept = ((Dx * Y1) - (Dy * X1)) / Dx,
Y = (Slope * X) + Intercept.
:- func intersection_of_lines(float, float, float, float,
float, float, float, float)
= plane_point.
intersection_of_lines(X1, Y1, X2, Y2, X3, Y3, X4, Y4) = Pt :-
%% Given the lines (X1,Y1)--(X2,Y2) and (X3,Y3)--(X3,Y4), find their
%% point of intersection.
(if (X1 = X2)
then (Pt = plane_point(X1, evaluate_line(X3, Y3, X4, Y4, X1)))
else if (X3 = X4)
then (Pt = plane_point(X3, evaluate_line(X1, Y1, X2, Y2, X3)))
else (Pt = plane_point(X, Y),
X = Xnumerator / Denominator,
Y = Ynumerator / Denominator,
Denominator =
((X1 - X2) * (Y3 - Y4)) - ((Y1 - Y2) * (X3 - X4)),
Xnumerator =
(X1Y2_Y1X2 * (X3 - X4)) - ((X1 - X2) * X3Y4_Y3X4),
Ynumerator =
(X1Y2_Y1X2 * (Y3 - Y4)) - ((Y1 - Y2) * X3Y4_Y3X4),
X1Y2_Y1X2 = (X1 * Y2) - (Y1 * X2),
X3Y4_Y3X4 = (X3 * Y4) - (Y3 * X4))).
:- func intersection_of_edges(plane_edge, plane_edge) = plane_point.
intersection_of_edges(E1, E2) = Pt :-
%% Given two edges, find their point of intersection (on the
%% assumption that there is such an intersection).
Pt = intersection_of_lines(X1, Y1, X2, Y2, X3, Y3, X4, Y4),
Pt1 = point0(E1), Pt2 = point1(E1),
Pt3 = point0(E2), Pt4 = point1(E2),
X1 = xcoord(Pt1), Y1 = ycoord(Pt1),
X2 = xcoord(Pt2), Y2 = ycoord(Pt2),
X3 = xcoord(Pt3), Y3 = ycoord(Pt3),
X4 = xcoord(Pt4), Y4 = ycoord(Pt4).
:- pred point_is_left_of_edge(plane_point::in, plane_edge::in)
is semidet.
point_is_left_of_edge(Pt, Edge) :-
%% Is Pt left of Edge?
(OP < 0.0),
%% OP = outer product of the vectors (x1,y1)-->(x,y) and
%% (x1,y1)-->(x2,y2). *)
OP = ((X - X1) * (Y2 - Y1)) - ((X2 - X1) * (Y - Y1)),
Pt1 = point0(Edge), Pt2 = point1(Edge),
X1 = xcoord(Pt1), Y1 = ycoord(Pt1),
X2 = xcoord(Pt2), Y2 = ycoord(Pt2),
X = xcoord(Pt), Y = ycoord(Pt).
:- func clip_subject_edge(plane_edge, plane_edge,
list(plane_point)) = list(plane_point).
clip_subject_edge(Subject_edge, Clip_edge, Accum0) = Accum :-
S1 = point0(Subject_edge), S2 = point1(Subject_edge),
(if (point_is_left_of_edge(S2, Clip_edge))
then (if (point_is_left_of_edge(S1, Clip_edge))
then (Accum = [S2 | Accum0])
else (Accum = [S2, Intersection | Accum0],
Intersection =
intersection_of_edges(Subject_edge, Clip_edge)))
else (if (point_is_left_of_edge(S1, Clip_edge))
then (Accum = [Intersection | Accum0],
Intersection =
intersection_of_edges(Subject_edge, Clip_edge))
else (Accum = Accum0))).
:- func plane_points_to_plane_edges(list(plane_point))
= list(plane_edge).
plane_points_to_plane_edges(Pts) = Edges :-
plane_points_to_plane_edges_(Pt_first, Pts, [], Edges),
Pt_first = det_head(Pts).
:- pred plane_points_to_plane_edges_(plane_point::in,
list(plane_point)::in,
list(plane_edge)::in,
list(plane_edge)::out) is det.
%% Convert a list of points to a list of edges.
plane_points_to_plane_edges_(Pt_first, [Pt0, Pt1 | Rest],
Edges0, Edges) :-
plane_points_to_plane_edges_(Pt_first, [Pt1 | Rest],
[plane_edge(Pt0, Pt1) | Edges0],
Edges).
plane_points_to_plane_edges_(Pt_first, [Pt_last], Edges0, Edges) :-
Edges = [plane_edge(Pt_last, Pt_first) | reverse(Edges0)].
plane_points_to_plane_edges_(_, [], _, _) :-
throw("list(plane_point) was expected to have length >= 2").
:- pred for_each_subject_edge(list(plane_edge)::in, plane_edge::in,
list(plane_point)::in,
list(plane_point)::out) is det.
for_each_subject_edge([], _, Accum0, Accum) :-
(Accum = reverse(Accum0)).
for_each_subject_edge([Subject_edge | Rest], Clip_edge,
Accum0, Accum) :-
Accum1 = clip_subject_edge(Subject_edge, Clip_edge, Accum0),
for_each_subject_edge(Rest, Clip_edge, Accum1, Accum).
:- func clip_subject_with_clip_edge(list(plane_point), plane_edge)
= list(plane_point).
clip_subject_with_clip_edge(Subject_pts, Clip_edge) = Pts :-
for_each_subject_edge(Subject_edges, Clip_edge, [], Pts),
Subject_edges = plane_points_to_plane_edges(Subject_pts).
:- pred for_each_clip_edge(list(plane_point)::in,
list(plane_point)::out,
list(plane_edge)::in) is det.
for_each_clip_edge(Subject_pts0, Subject_pts, []) :-
(Subject_pts = Subject_pts0).
for_each_clip_edge(Subject_pts0, Subject_pts,
[Clip_edge | Rest]) :-
Subject_pts1 = clip_subject_with_clip_edge(Subject_pts0, Clip_edge),
for_each_clip_edge(Subject_pts1, Subject_pts, Rest).
:- func clip(list(plane_point), list(plane_point))
= list(plane_point).
clip(Subject_pts, Clip_pts) = Result_pts :-
for_each_clip_edge(Subject_pts, Result_pts, Clip_edges),
Clip_edges = plane_points_to_plane_edges(Clip_pts).
:- pred moveto(text_output_stream::in, plane_point::in,
io::di, io::uo) is det.
moveto(Stream, Pt, !IO) :-
write_float(Stream, xcoord(Pt), !IO),
write_string(Stream, " ", !IO),
write_float(Stream, ycoord(Pt), !IO),
write_string(Stream, " moveto\n", !IO).
:- pred lineto(plane_point::in, io::di, io::uo) is det.
lineto(Pt, !IO) :-
write_float(xcoord(Pt), !IO),
write_string(" ", !IO),
write_float(ycoord(Pt), !IO),
write_string(" lineto\n", !IO).
:- pred setrgbcolor(text_output_stream::in,
string::in, io::di, io::uo) is det.
setrgbcolor(Stream, Color, !IO) :-
write_string(Stream, Color, !IO),
write_string(Stream, " setrgbcolor\n", !IO).
:- pred write_polygon(text_output_stream::in,
list(plane_point)::in,
string::in, string::in,
io::di, io::uo) is det.
write_polygon(Stream, Pts, Line_color, Fill_color, !IO) :-
if ([First_pt | Rest] = Pts)
then (moveto(Stream, First_pt, !IO),
write_list(Stream, Rest, "", lineto, !IO),
write_string(Stream, "closepath\n", !IO),
setrgbcolor(Stream, Line_color, !IO),
write_string(Stream, "gsave\n", !IO),
setrgbcolor(Stream, Fill_color, !IO),
write_string(Stream, "fill\n", !IO),
write_string(Stream, "grestore\n", !IO),
write_string(Stream, "stroke\n", !IO))
else true.
:- pred write_eps(text_output_stream::in,
list(plane_point)::in,
list(plane_point)::in,
list(plane_point)::in,
io::di, io::uo) is det.
write_eps(Stream, Subject_pts, Clip_pts, Result_pts, !IO) :-
write_string(Stream, "%!PS-Adobe-3.0 EPSF-3.0\n", !IO),
write_string(Stream, "%%BoundingBox: 40 40 360 360\n", !IO),
write_string(Stream, "0 setlinewidth\n", !IO),
write_polygon(Stream, Clip_pts, ".5 0 0", "1 .7 .7", !IO),
write_polygon(Stream, Subject_pts, "0 .2 .5", ".4 .7 1", !IO),
write_string(Stream, "2 setlinewidth\n", !IO),
write_string(Stream, "[10 8] 0 setdash\n", !IO),
write_polygon(Stream, Result_pts, ".5 0 .5", ".7 .3 .8", !IO),
write_string(Stream, "%%EOF\n", !IO).
:- pred write_eps_to_file(string::in,
list(plane_point)::in,
list(plane_point)::in,
list(plane_point)::in,
io::di, io::uo) is det.
write_eps_to_file(Filename, Subject_pts, Clip_pts, Result_pts, !IO) :-
open_output(Filename, Open_result, !IO),
(if (Open_result = ok(Outp))
then write_eps(Outp, Subject_pts, Clip_pts, Result_pts, !IO)
else throw("Failed to open " ++ Filename ++ " for output.")).
main(!IO) :-
Subject_pts = [plane_point(50.0, 150.0),
plane_point(200.0, 50.0),
plane_point(350.0, 150.0),
plane_point(350.0, 300.0),
plane_point(250.0, 300.0),
plane_point(200.0, 250.0),
plane_point(150.0, 350.0),
plane_point(100.0, 250.0),
plane_point(100.0, 200.0)],
Clip_pts = [plane_point(100.0, 100.0),
plane_point(300.0, 100.0),
plane_point(300.0, 300.0),
plane_point(100.0, 300.0)],
Result_pts = clip(Subject_pts, Clip_pts),
write_plane_point_list(Result_pts, "\n", !IO), nl(!IO),
EPSF = "sutherland-hodgman.eps",
write_eps_to_file(EPSF, Subject_pts, Clip_pts, Result_pts, !IO),
write_string("Wrote " ++ EPSF, !IO), nl(!IO).
%%% local variables:
%%% mode: mercury
%%% prolog-indent-width: 2
%%% end:- Output:
$ mmc sutherland_hodgman_task.m && ./sutherland_hodgman_task (100.0, 116.66666666666669) (124.99999999999999, 100.0) (275.0, 100.0) (300.0, 116.66666666666667) (300.0, 300.0) (250.0, 300.0) (200.0, 250.0) (175.0, 300.0) (125.0, 300.0) (100.0, 250.0) Wrote sutherland-hodgman.eps
Modula-2
(* Sutherland-Hodgman polygon clipping, for ISO Modula-2. *)
MODULE Sutherland_Hodgman_Task;
IMPORT STextIO, SRealIO;
IMPORT TextIO, RealIO;
IMPORT IOChan, StreamFile;
TYPE PlanePoint =
RECORD
x : REAL;
y : REAL;
END;
PlaneEdge =
RECORD
pt0 : PlanePoint; (* The start point. *)
pt1 : PlanePoint; (* The end point. *)
END;
PROCEDURE evaluate_line (x1, y1, x2, y2, x : REAL) : REAL;
VAR dy, dx, slope, intercept : REAL;
BEGIN
dy := y2 - y1;
dx := x2 - x1;
slope := dy / dx;
intercept := ((dx * y1) - (dy * x1)) / dx;
RETURN (slope * x) + intercept
END evaluate_line;
PROCEDURE intersection_of_lines
(x1, y1, x2, y2, x3, y3, x4, y4 : REAL) : PlanePoint;
VAR intersection : PlanePoint;
denominator, xnumerator, ynumerator : REAL;
x1y2_y1x2, x3y4_y3x4 : REAL;
BEGIN
IF x1 = x2 THEN
intersection.x := x1;
intersection.y := evaluate_line (x3, y3, x4, y4, x1);
ELSIF x3 = x4 THEN
intersection.x := x3;
intersection.y := evaluate_line (x1, y1, x2, y2, x3);
ELSE
denominator := ((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4));
x1y2_y1x2 := (x1 * y2) - (y1 * x2);
x3y4_y3x4 := (x3 * y4) - (y3 * x4);
xnumerator := (x1y2_y1x2 * (x3 - x4)) - ((x1 - x2) * x3y4_y3x4);
ynumerator := (x1y2_y1x2 * (y3 - y4)) - ((y1 - y2) * x3y4_y3x4);
intersection.x := xnumerator / denominator;
intersection.y := ynumerator / denominator;
END;
RETURN intersection;
END intersection_of_lines;
PROCEDURE intersection_of_edges
(e1, e2 : PlaneEdge) : PlanePoint;
BEGIN
RETURN intersection_of_lines (e1.pt0.x, e1.pt0.y,
e1.pt1.x, e1.pt1.y,
e2.pt0.x, e2.pt0.y,
e2.pt1.x, e2.pt1.y);
END intersection_of_edges;
PROCEDURE point_is_left_of_edge
(pt : PlanePoint;
edge : PlaneEdge) : BOOLEAN;
VAR x, y, x1, y1, x2, y2, op : REAL;
BEGIN
x := pt.x;
y := pt.y;
x1 := edge.pt0.x;
y1 := edge.pt0.y;
x2 := edge.pt1.x;
y2 := edge.pt1.y;
(* Outer product of the vectors (x1,y1)-->(x,y) and
(x1,y1)-->(x2,y2). *)
op := ((x - x1) * (y2 - y1)) - ((x2 - x1) * (y - y1));
RETURN (op < 0.0);
END point_is_left_of_edge;
PROCEDURE clip_subject_edge
(subject_edge : PlaneEdge;
clip_edge : PlaneEdge;
VAR n : CARDINAL;
VAR points : ARRAY OF PlanePoint);
VAR s1, s2 : PlanePoint;
s2_is_inside, s1_is_inside : BOOLEAN;
BEGIN
s1 := subject_edge.pt0;
s2 := subject_edge.pt1;
s2_is_inside := point_is_left_of_edge (s2, clip_edge);
s1_is_inside := point_is_left_of_edge (s1, clip_edge);
IF s2_is_inside THEN
IF s1_is_inside THEN
points[n] := s2;
n := n + 1;
ELSE
points[n] := intersection_of_edges (subject_edge, clip_edge);
n := n + 1;
points[n] := s2;
n := n + 1;
END;
ELSIF s1_is_inside THEN
points[n] := intersection_of_edges (subject_edge, clip_edge);
n := n + 1;
END;
END clip_subject_edge;
PROCEDURE for_each_subject_edge
(nsubject : CARDINAL;
subject_points : ARRAY OF PlanePoint;
clip_edge : PlaneEdge;
VAR n : CARDINAL;
VAR points : ARRAY OF PlanePoint);
VAR subject_edge : PlaneEdge;
i, j : CARDINAL;
BEGIN
n := 0;
FOR i := 0 TO nsubject - 1 DO
IF i = 0 THEN
j := nsubject - 1;
ELSE
j := i - 1;
END;
subject_edge.pt1 := subject_points[i];
subject_edge.pt0 := subject_points[j];
clip_subject_edge (subject_edge, clip_edge, n, points);
END;
END for_each_subject_edge;
PROCEDURE clip (VAR nsubject : CARDINAL;
VAR subject_points : ARRAY OF PlanePoint;
nclip : CARDINAL;
clip_points : ARRAY OF PlanePoint;
VAR workspace : ARRAY OF PlanePoint);
VAR clip_edge : PlaneEdge;
i, j, nwork : CARDINAL;
BEGIN
FOR i := 0 TO nclip - 1 DO
IF i = 0 THEN
j := nclip - 1;
ELSE
j := i - 1;
END;
clip_edge.pt1 := clip_points[i];
clip_edge.pt0 := clip_points[j];
for_each_subject_edge (nsubject, subject_points, clip_edge,
nwork, workspace);
FOR j := 0 TO nwork - 1 DO
subject_points[j] := workspace[j];
END;
nsubject := nwork;
END;
END clip;
PROCEDURE set_point
(VAR points : ARRAY OF PlanePoint;
i : CARDINAL;
x, y : REAL);
BEGIN
points[i].x := x;
points[i].y := y;
END set_point;
PROCEDURE write_polygon
(cid : IOChan.ChanId;
npoly : CARDINAL;
polygon : ARRAY OF PlanePoint;
line_color : ARRAY OF CHAR;
fill_color : ARRAY OF CHAR);
VAR i : CARDINAL;
BEGIN
RealIO.WriteReal (cid, polygon[0].x, 10);
TextIO.WriteString (cid, ' ');
RealIO.WriteReal (cid, polygon[0].y, 10);
TextIO.WriteString (cid, ' moveto');
TextIO.WriteLn (cid);
FOR i := 1 TO npoly - 1 DO
RealIO.WriteReal (cid, polygon[i].x, 10);
TextIO.WriteString (cid, ' ');
RealIO.WriteReal (cid, polygon[i].y, 10);
TextIO.WriteString (cid, ' lineto');
TextIO.WriteLn (cid);
END;
TextIO.WriteString (cid, 'closepath');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, line_color);
TextIO.WriteString (cid, ' setrgbcolor');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, 'gsave');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, fill_color);
TextIO.WriteString (cid, ' setrgbcolor');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, 'fill');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, 'grestore');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, 'stroke');
TextIO.WriteLn (cid);
END write_polygon;
PROCEDURE write_eps
(cid : IOChan.ChanId;
nsubject : CARDINAL;
subject_polygon : ARRAY OF PlanePoint;
nclip : CARDINAL;
clip_polygon : ARRAY OF PlanePoint;
nresult : CARDINAL;
result_polygon : ARRAY OF PlanePoint);
BEGIN
TextIO.WriteString (cid, '%!PS-Adobe-3.0 EPSF-3.0');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, '%%BoundingBox: 40 40 360 360');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, '0 setlinewidth');
TextIO.WriteLn (cid);
write_polygon (cid, nclip, clip_polygon,
'.5 0 0', '1 .7 .7');
write_polygon (cid, nsubject, subject_polygon,
'0 .2 .5', '.4 .7 1');
TextIO.WriteString (cid, '2 setlinewidth');
TextIO.WriteLn (cid);
TextIO.WriteString (cid, '[10 8] 0 setdash');
TextIO.WriteLn (cid);
write_polygon (cid, nresult, result_polygon,
'.5 0 .5', '.7 .3 .8');
TextIO.WriteString (cid, '%%EOF');
TextIO.WriteLn (cid);
END write_eps;
PROCEDURE write_eps_to_file
(filename : ARRAY OF CHAR;
nsubject : CARDINAL;
subject_polygon : ARRAY OF PlanePoint;
nclip : CARDINAL;
clip_polygon : ARRAY OF PlanePoint;
nresult : CARDINAL;
result_polygon : ARRAY OF PlanePoint);
VAR cid : IOChan.ChanId;
open_results : StreamFile.OpenResults;
BEGIN
StreamFile.Open (cid, filename,
StreamFile.write,
open_results);
write_eps (cid,
nsubject, subject_polygon,
nclip, clip_polygon,
nresult, result_polygon);
StreamFile.Close (cid);
END write_eps_to_file;
CONST NMax = 100;
VAR subject_polygon : ARRAY [0 .. NMax - 1] OF PlanePoint;
clip_polygon : ARRAY [0 .. NMax - 1] OF PlanePoint;
workspace : ARRAY [0 .. NMax - 1] OF PlanePoint;
result_polygon : ARRAY [0 .. NMax - 1] OF PlanePoint;
nsubject, nclip, nresult, i : CARDINAL;
BEGIN
nsubject := 9;
set_point (subject_polygon, 0, 50.0, 150.0);
set_point (subject_polygon, 1, 200.0, 50.0);
set_point (subject_polygon, 2, 350.0, 150.0);
set_point (subject_polygon, 3, 350.0, 300.0);
set_point (subject_polygon, 4, 250.0, 300.0);
set_point (subject_polygon, 5, 200.0, 250.0);
set_point (subject_polygon, 6, 150.0, 350.0);
set_point (subject_polygon, 7, 100.0, 250.0);
set_point (subject_polygon, 8, 100.0, 200.0);
nclip := 4;
set_point (clip_polygon, 0, 100.0, 100.0);
set_point (clip_polygon, 1, 300.0, 100.0);
set_point (clip_polygon, 2, 300.0, 300.0);
set_point (clip_polygon, 3, 100.0, 300.0);
FOR i := 0 TO nsubject - 1 DO
result_polygon[i] := subject_polygon[i];
END;
nresult := nsubject;
clip (nresult, result_polygon, nclip, clip_polygon,
workspace);
FOR i := 0 TO nsubject - 1 DO
STextIO.WriteString ('(');
SRealIO.WriteReal (result_polygon[i].x, 8);
STextIO.WriteString (', ');
SRealIO.WriteReal (result_polygon[i].y, 8);
STextIO.WriteString (')');
STextIO.WriteLn;
END;
write_eps_to_file ('sutherland-hodgman.eps',
nsubject, subject_polygon,
nclip, clip_polygon,
nresult, result_polygon);
STextIO.WriteString ('Wrote sutherland-hodgman.eps');
STextIO.WriteLn;
END Sutherland_Hodgman_Task.
- Output:
gm2 sutherland_hodgman_task.mod && ./a.out (100.0000, 116.6667) (125.0000, 100.0000) (275.0000, 100.0000) (300.0000, 116.6667) (300.0000, 300.0000) (250.0000, 300.0000) (200.0000, 250.0000) (175.0000, 300.0000) (125.0000, 300.0000) Wrote sutherland-hodgman.eps
Nim
import sequtils, strformat
type
Vec2 = tuple[x, y: float]
Edge = tuple[p, q: Vec2]
Polygon = seq[Vec2]
func `-`(a, b: Vec2): Vec2 = (a.x - b.x, a.y - b.y)
func cross(a, b: Vec2): float = a.x * b.y - a.y * b.x
func isInside(p: Vec2; edge: Edge): bool =
(edge.q.x - edge.p.x) * (p.y - edge.p.y) > (edge.q.y - edge.p.y) * (p.x - edge.p.x)
func intersection(sEdge, cEdge: Edge): Vec2 =
let
dc = cEdge.p - cEdge.q
dp = sEdge.p - sEdge.q
n1 = cEdge.p.cross(cEdge.q)
n2 = sEdge.p.cross(sEdge.q)
n3 = 1 / dc.cross(dp)
result = ((n1 * dp.x - n2 * dc.x) * n3, (n1 * dp.y - n2 * dc.y) * n3)
func edges(poly: Polygon): seq[Edge] =
(poly[^1] & poly).zip(poly)
func clip(subjectPolygon, clipPolygon: Polygon): Polygon =
assert subjectPolygon.len > 1
assert clipPolygon.len > 1
result = subjectPolygon
for clipEdge in clipPolygon.edges:
let inputList = move(result)
result.reset()
for inEdge in inputList.edges:
if inEdge.q.isInside(clipEdge):
if not inEdge.p.isInside(clipEdge):
result.add intersection(inEdge, clipEdge)
result.add inEdge.q
elif inEdge.p.isInside(clipEdge):
result.add intersection(inEdge, clipEdge)
proc saveEpsImage(filename: string; subject, clip, clipped: Polygon) =
let eps = open(filename, fmWrite)
eps.write "%%!PS-Adobe-3.0\n%%%%BoundingBox: 40 40 360 360\n/l {lineto} def\n/m {moveto} def\n",
"/s {setrgbcolor} def\n/c {closepath} def\n/gs {fill grestore stroke} def\n"
eps.write &"0 setlinewidth {clip[0].x} {clip[0].y} m "
for i in 1..clip.high:
eps.write &"{clip[i].x} {clip[i].y} l "
eps.writeLine "c 0.5 0 0 s gsave 1 0.7 0.7 s gs"
eps.write &"{subject[0].x} {subject[0].y} m "
for i in 1..subject.high:
eps.write &"{subject[i].x} {subject[i].y} l "
eps.writeLine "c 0 0.2 0.5 s gsave 0.4 0.7 1 s gs"
eps.write &"2 setlinewidth [10 8] 0 setdash {clipped[0].x} {clipped[0].y} m "
for i in 1..clipped.high:
eps.write &"{clipped[i].x} {clipped[i].y} l "
eps.writeLine &"c 0.5 0 0.5 s gsave 0.7 0.3 0.8 s gs"
eps.writeLine "%%%%EOF"
eps.close()
echo &"File “{filename}” written."
when isMainModule:
let
subjectPolygon = @[(50.0, 150.0), (200.0, 50.0), (350.0, 150.0),
(350.0, 300.0), (250.0, 300.0), (200.0, 250.0),
(150.0, 350.0), (100.0, 250.0), (100.0, 200.0)]
clippingPolygon = @[(100.0, 100.0), (300.0, 100.0), (300.0, 300.0), (100.0, 300.0)]
clipped = subjectPolygon.clip(clippingPolygon)
for point in clipped:
echo &"({point.x:.3f}, {point.y:.3f})"
saveEpsImage("sutherland_hodgman_clipping_out.eps", subjectPolygon, clippingPolygon, clipped)
- Output:
(100.000, 116.667) (125.000, 100.000) (275.000, 100.000) (300.000, 116.667) (300.000, 300.000) (250.000, 300.000) (200.000, 250.000) (175.000, 300.000) (125.000, 300.000) (100.000, 250.000) File “sutherland_hodgman_clipping_out.eps” written.
OCaml
let is_inside (x,y) ((ax,ay), (bx,by)) =
(bx -. ax) *. (y -. ay) > (by -. ay) *. (x -. ax)
let intersection (sx,sy) (ex,ey) ((ax,ay), (bx,by)) =
let dc_x, dc_y = (ax -. bx, ay -. by) in
let dp_x, dp_y = (sx -. ex, sy -. ey) in
let n1 = ax *. by -. ay *. bx in
let n2 = sx *. ey -. sy *. ex in
let n3 = 1.0 /. (dc_x *. dp_y -. dc_y *. dp_x) in
((n1 *. dp_x -. n2 *. dc_x) *. n3,
(n1 *. dp_y -. n2 *. dc_y) *. n3)
let last lst = List.hd (List.rev lst)
let polygon_iter_edges poly f init =
if poly = [] then init else
let p0 = List.hd poly in
let rec aux acc = function
| p1 :: p2 :: tl -> aux (f (p1, p2) acc) (p2 :: tl)
| p :: [] -> f (p, p0) acc
| [] -> acc
in
aux init poly
let poly_clip subject_polygon clip_polygon =
polygon_iter_edges clip_polygon (fun clip_edge input_list ->
fst (
List.fold_left (fun (out, s) e ->
match (is_inside e clip_edge), (is_inside s clip_edge) with
| true, false -> (e :: (intersection s e clip_edge) :: out), e
| true, true -> (e :: out), e
| false, true -> ((intersection s e clip_edge) :: out), e
| false, false -> (out, e)
) ([], last input_list) input_list)
) subject_polygon
let () =
let subject_polygon =
[ ( 50.0, 150.0); (200.0, 50.0); (350.0, 150.0);
(350.0, 300.0); (250.0, 300.0); (200.0, 250.0);
(150.0, 350.0); (100.0, 250.0); (100.0, 200.0); ] in
let clip_polygon =
[ (100.0, 100.0); (300.0, 100.0); (300.0, 300.0); (100.0, 300.0) ] in
List.iter (fun (x,y) ->
Printf.printf " (%g, %g)\n" x y;
) (poly_clip subject_polygon clip_polygon)
- Output:
(100, 116.667) (125, 100) (275, 100) (300, 116.667) (300, 300) (250, 300) (200, 250) (175, 300) (125, 300) (100, 250)
We can display the result in a window using the Graphics module:
let subject_polygon =
[ ( 50.0, 150.0); (200.0, 50.0); (350.0, 150.0);
(350.0, 300.0); (250.0, 300.0); (200.0, 250.0);
(150.0, 350.0); (100.0, 250.0); (100.0, 200.0); ]
let clip_polygon =
[ (100.0, 100.0); (300.0, 100.0); (300.0, 300.0); (100.0, 300.0) ]
let () =
Graphics.open_graph " 400x400";
let to_grid poly =
let round x = int_of_float (floor (x +. 0.5)) in
Array.map
(fun (x, y) -> (round x, round y))
(Array.of_list poly)
in
let draw_poly fill stroke poly =
let p = to_grid poly in
Graphics.set_color fill;
Graphics.fill_poly p;
Graphics.set_color stroke;
Graphics.draw_poly p;
in
draw_poly Graphics.red Graphics.blue subject_polygon;
draw_poly Graphics.cyan Graphics.blue clip_polygon;
draw_poly Graphics.magenta Graphics.blue (poly_clip subject_polygon clip_polygon);
let _ = Graphics.wait_next_event [Graphics.Button_down; Graphics.Key_pressed] in
Graphics.close_graph ()
Perl
use strict;
use warnings;
sub intersection {
my($L11, $L12, $L21, $L22) = @_;
my ($d1x, $d1y) = ($$L11[0] - $$L12[0], $$L11[1] - $$L12[1]);
my ($d2x, $d2y) = ($$L21[0] - $$L22[0], $$L21[1] - $$L22[1]);
my $n1 = $$L11[0] * $$L12[1] - $$L11[1] * $$L12[0];
my $n2 = $$L21[0] * $$L22[1] - $$L21[1] * $$L22[0];
my $n3 = 1 / ($d1x * $d2y - $d2x * $d1y);
[($n1 * $d2x - $n2 * $d1x) * $n3, ($n1 * $d2y - $n2 * $d1y) * $n3]
}
sub is_inside {
my($p1, $p2, $p3) = @_;
($$p2[0] - $$p1[0]) * ($$p3[1] - $$p1[1]) > ($$p2[1] - $$p1[1]) * ($$p3[0] - $$p1[0])
}
sub sutherland_hodgman {
my($polygon, $clip) = @_;
my @output = @$polygon;
my $clip_point1 = $$clip[-1];
for my $clip_point2 (@$clip) {
my @input = @output;
@output = ();
my $start = $input[-1];
for my $end (@input) {
if (is_inside($clip_point1, $clip_point2, $end)) {
push @output, intersection($clip_point1, $clip_point2, $start, $end)
unless is_inside($clip_point1, $clip_point2, $start);
push @output, $end;
} elsif (is_inside($clip_point1, $clip_point2, $start)) {
push @output, intersection($clip_point1, $clip_point2, $start, $end);
}
$start = $end;
}
$clip_point1 = $clip_point2;
}
@output
}
my @polygon = ([50, 150], [200, 50], [350, 150], [350, 300], [250, 300],
[200, 250], [150, 350], [100, 250], [100, 200]);
my @clip = ([100, 100], [300, 100], [300, 300], [100, 300]);
my @clipped = sutherland_hodgman(\@polygon, \@clip);
print "Clipped polygon:\n";
print '(' . join(' ', @$_) . ') ' for @clipped;
- Output:
Clipped polygon: (100 116.666666666667) (125 100) (275 100) (300 116.666666666667) (300 300) (250 300) (200 250) (175 300) (125 300) (100 250)
Phix
You can run this online here.
-- -- demo\rosetta\Sutherland_Hodgman_polygon_clipping.exw -- ==================================================== -- with javascript_semantics enum X,Y function inside(sequence cp1, cp2, p) return (cp2[X]-cp1[X])*(p[Y]-cp1[Y])>(cp2[Y]-cp1[Y])*(p[X]-cp1[X]) end function function intersect(sequence cp1, cp2, s, e) atom {dcx,dcy} = {cp1[X]-cp2[X],cp1[Y]-cp2[Y]}, {dpx,dpy} = {s[X]-e[X],s[Y]-e[Y]}, n1 = cp1[X]*cp2[Y]-cp1[Y]*cp2[X], n2 = s[X]*e[Y]-s[Y]*e[X], n3 = 1/(dcx*dpy-dcy*dpx) return {(n1*dpx-n2*dcx)*n3,(n1*dpy-n2*dcy)*n3} end function function sutherland_hodgman(sequence subjectPolygon, clipPolygon) sequence cp1 = clipPolygon[$], outputList = subjectPolygon for i=1 to length(clipPolygon) do sequence cp2 = clipPolygon[i], inputList = outputList, s = inputList[$] outputList = {} for j=1 to length(inputList) do sequence e = inputList[j] if inside(cp1,cp2,e) then if not inside(cp1,cp2,s) then outputList = append(outputList,intersect(cp1,cp2,s,e)) end if outputList = append(outputList,e) elsif inside(cp1,cp2,s) then outputList = append(outputList,intersect(cp1,cp2,s,e)) end if s = e end for cp1 = cp2 end for return outputList end function constant subjectPolygon = {{50, 150}, {200, 50}, {350, 150}, {350, 300}, {250, 300}, {200, 250}, {150, 350}, {100, 250}, {100, 200}}, clipPolygon = {{100, 100}, {300, 100}, {300, 300}, {100, 300}} sequence clippedPolygon = sutherland_hodgman(subjectPolygon,clipPolygon) include pGUI.e Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas procedure draw_poly(sequence poly) cdCanvasBegin(cddbuffer,CD_FILL) for i=1 to length(poly) do atom {x,y} = poly[i] cdCanvasVertex(cddbuffer,x,y) end for cdCanvasEnd(cddbuffer) end procedure function redraw_cb(Ihandle /*ih*/) cdCanvasActivate(cddbuffer) cdCanvasClear(cddbuffer) cdCanvasSetForeground(cddbuffer, CD_CYAN) draw_poly(subjectPolygon) cdCanvasSetForeground(cddbuffer, CD_MAGENTA) draw_poly(clipPolygon) cdCanvasSetForeground(cddbuffer, CD_ORANGE) draw_poly(clippedPolygon) 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) cdCanvasSetForeground(cddbuffer, CD_GRAY) return IUP_DEFAULT end function procedure main() IupOpen() canvas = IupCanvas("RASTERSIZE=400x400") IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"), "ACTION", Icallback("redraw_cb")}) dlg = IupDialog(canvas, "RESIZE=NO") IupSetAttribute(dlg, "TITLE", "Sutherland-Hodgman polygon clipping") IupShow(dlg) if platform()!=JS then IupMainLoop() IupClose() end if end procedure main()
PHP
<?php
function clip ($subjectPolygon, $clipPolygon) {
function inside ($p, $cp1, $cp2) {
return ($cp2[0]-$cp1[0])*($p[1]-$cp1[1]) > ($cp2[1]-$cp1[1])*($p[0]-$cp1[0]);
}
function intersection ($cp1, $cp2, $e, $s) {
$dc = [ $cp1[0] - $cp2[0], $cp1[1] - $cp2[1] ];
$dp = [ $s[0] - $e[0], $s[1] - $e[1] ];
$n1 = $cp1[0] * $cp2[1] - $cp1[1] * $cp2[0];
$n2 = $s[0] * $e[1] - $s[1] * $e[0];
$n3 = 1.0 / ($dc[0] * $dp[1] - $dc[1] * $dp[0]);
return [($n1*$dp[0] - $n2*$dc[0]) * $n3, ($n1*$dp[1] - $n2*$dc[1]) * $n3];
}
$outputList = $subjectPolygon;
$cp1 = end($clipPolygon);
foreach ($clipPolygon as $cp2) {
$inputList = $outputList;
$outputList = [];
$s = end($inputList);
foreach ($inputList as $e) {
if (inside($e, $cp1, $cp2)) {
if (!inside($s, $cp1, $cp2)) {
$outputList[] = intersection($cp1, $cp2, $e, $s);
}
$outputList[] = $e;
}
else if (inside($s, $cp1, $cp2)) {
$outputList[] = intersection($cp1, $cp2, $e, $s);
}
$s = $e;
}
$cp1 = $cp2;
}
return $outputList;
}
$subjectPolygon = [[50, 150], [200, 50], [350, 150], [350, 300], [250, 300], [200, 250], [150, 350], [100, 250], [100, 200]];
$clipPolygon = [[100, 100], [300, 100], [300, 300], [100, 300]];
$clippedPolygon = clip($subjectPolygon, $clipPolygon);
echo json_encode($clippedPolygon);
echo "\n";
?>
PureBasic
Structure point_f
x.f
y.f
EndStructure
Procedure isInside(*p.point_f, *cp1.point_f, *cp2.point_f)
If (*cp2\x - *cp1\x) * (*p\y - *cp1\y) > (*cp2\y - *cp1\y) * (*p\x - *cp1\x)
ProcedureReturn 1
EndIf
EndProcedure
Procedure intersection(*cp1.point_f, *cp2.point_f, *s.point_f, *e.point_f, *newPoint.point_f)
Protected.point_f dc, dp
Protected.f n1, n2, n3
dc\x = *cp1\x - *cp2\x: dc\y = *cp1\y - *cp2\y
dp\x = *s\x - *e\x: dp\y = *s\y - *e\y
n1 = *cp1\x * *cp2\y - *cp1\y * *cp2\x
n2 = *s\x * *e\y - *s\y * *e\x
n3 = 1 / (dc\x * dp\y - dc\y * dp\x)
*newPoint\x = (n1 * dp\x - n2 * dc\x) * n3: *newPoint\y = (n1 * dp\y - n2 * dc\y) * n3
EndProcedure
Procedure clip(List vPolygon.point_f(), List vClippedBy.point_f(), List vClippedPolygon.point_f())
Protected.point_f cp1, cp2, s, e, newPoint
CopyList(vPolygon(), vClippedPolygon())
If LastElement(vClippedBy())
cp1 = vClippedBy()
NewList vPreClipped.point_f()
ForEach vClippedBy()
cp2 = vClippedBy()
CopyList(vClippedPolygon(), vPreClipped())
ClearList(vClippedPolygon())
If LastElement(vPreClipped())
s = vPreClipped()
ForEach vPreClipped()
e = vPreClipped()
If isInside(e, cp1, cp2)
If Not isInside(s, cp1, cp2)
intersection(cp1, cp2, s, e, newPoint)
AddElement(vClippedPolygon()): vClippedPolygon() = newPoint
EndIf
AddElement(vClippedPolygon()): vClippedPolygon() = e
ElseIf isInside(s, cp1, cp2)
intersection(cp1, cp2, s, e, newPoint)
AddElement(vClippedPolygon()): vClippedPolygon() = newPoint
EndIf
s = e
Next
EndIf
cp1 = cp2
Next
EndIf
EndProcedure
DataSection
Data.f 50,150, 200,50, 350,150, 350,300, 250,300, 200,250, 150,350, 100,250, 100,200 ;subjectPolygon's vertices (x,y)
Data.f 100,100, 300,100, 300,300, 100,300 ;clipPolygon's vertices (x,y)
EndDataSection
NewList subjectPolygon.point_f()
For i = 1 To 9
AddElement(subjectPolygon())
Read.f subjectPolygon()\x
Read.f subjectPolygon()\y
Next
NewList clipPolygon.point_f()
For i = 1 To 4
AddElement(clipPolygon())
Read.f clipPolygon()\x
Read.f clipPolygon()\y
Next
NewList newPolygon.point_f()
clip(subjectPolygon(), clipPolygon(), newPolygon())
If OpenConsole()
ForEach newPolygon()
PrintN("(" + StrF(newPolygon()\x, 2) + ", " + StrF(newPolygon()\y, 2) + ")")
Next
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
- Output:
(100.00, 116.67) (125.00, 100.00) (275.00, 100.00) (300.00, 116.67) (300.00, 300.00) (250.00, 300.00) (200.00, 250.00) (175.00, 300.00) (125.00, 300.00) (100.00, 250.00)
Python
def clip(subjectPolygon, clipPolygon):
def inside(p):
return(cp2[0]-cp1[0])*(p[1]-cp1[1]) > (cp2[1]-cp1[1])*(p[0]-cp1[0])
def computeIntersection():
dc = [ cp1[0] - cp2[0], cp1[1] - cp2[1] ]
dp = [ s[0] - e[0], s[1] - e[1] ]
n1 = cp1[0] * cp2[1] - cp1[1] * cp2[0]
n2 = s[0] * e[1] - s[1] * e[0]
n3 = 1.0 / (dc[0] * dp[1] - dc[1] * dp[0])
return [(n1*dp[0] - n2*dc[0]) * n3, (n1*dp[1] - n2*dc[1]) * n3]
outputList = subjectPolygon
cp1 = clipPolygon[-1]
for clipVertex in clipPolygon:
cp2 = clipVertex
inputList = outputList
outputList = []
s = inputList[-1]
for subjectVertex in inputList:
e = subjectVertex
if inside(e):
if not inside(s):
outputList.append(computeIntersection())
outputList.append(e)
elif inside(s):
outputList.append(computeIntersection())
s = e
cp1 = cp2
return(outputList)
Racket
Shameless rewrite of haskell version.
#lang racket
(module sutherland-hodgman racket
(provide clip-to)
(provide make-edges)
(provide (struct-out point))
(struct point (x y) #:transparent)
(struct edge (p1 p2) #:transparent)
(struct polygon (points edges) #:transparent)
(define (make-edges points)
(let ([points-shifted
(match points
[(list a b ...) (append b (list a))])])
(map edge points points-shifted)))
(define (is-point-left? pt ln)
(match-let ([(point x y) pt]
[(edge (point px py) (point qx qy)) ln])
(>= (* (- qx px) (- y py))
(* (- qy py) (- x px)))))
;; Return the intersection of two lines
(define (isect-lines l1 l2)
(match-let ([(edge (point x1 y1) (point x2 y2)) l1]
[(edge (point x3 y3) (point x4 y4)) l2])
(let* ([r (- (* x1 y2) (* y1 x2))] [s (- (* x3 y4) (* y3 x4))]
[t (- x1 x2)] [u (- y3 y4)] [v (- y1 y2)] [w (- x3 x4)]
[d (- (* t u) (* v w))])
(point (/ (- (* r w) (* t s)) d)
(/ (- (* r u) (* v s)) d)))))
;; Intersect the line segment (p0,p1) with the clipping line's left halfspace,
;; returning the point closest to p1. In the special case where p0 lies outside
;; the halfspace and p1 lies inside we return both the intersection point and p1.
;; This ensures we will have the necessary segment along the clipping line.
(define (intersect segment clip-line)
(define (isect) (isect-lines segment clip-line))
(match-let ([(edge p0 p1) segment])
(match/values (values (is-point-left? p0 clip-line) (is-point-left? p1 clip-line))
[(#f #f) '()]
[(#f #t) (list (isect) p1)]
[(#t #f) (list (isect))]
[(#t #t) (list p1)])))
;; Intersect the polygon with the clipping line's left halfspace
(define (isect-polygon poly-edges clip-line)
(for/fold ([p '()]) ([e poly-edges])
(append p (intersect e clip-line))))
;; Intersect a subject polygon with a clipping polygon. The latter is assumed to be convex.
(define (clip-to sp-pts cp-edges)
(for/fold ([out-poly sp-pts]) ([clip-line cp-edges])
(isect-polygon (make-edges out-poly) clip-line))))
Testing code (Couldn't find a way to attach image with polygons)
(require racket/gui)
(require 'sutherland-hodgman)
(define (make-points pt-list)
(for/list ([p pt-list])
(make-object point% (point-x p) (point-y p))))
(define subject-poly-points
(list (point 50 150) (point 200 50) (point 350 150)
(point 350 300) (point 250 300) (point 200 250)
(point 150 350) (point 100 250) (point 100 200)))
(define clip-poly-points
(list (point 100 100)
(point 300 100)
(point 300 300)
(point 100 300)))
(define clip-poly-edges
(make-edges clip-poly-points))
(define (run)
(let* ([frame (new frame% [label "Sutherland-Hodgman racket demo"]
[width 320]
[height 320])]
[canvas (new canvas% [parent frame])]
[dc (send canvas get-dc)]
[clipped-poly (clip-to subject-poly-points clip-poly-edges)])
(send frame show #t)
(sleep/yield 1)
(send dc set-pen (make-pen
#:color (send the-color-database find-color "Blue")
#:width 3))
(send dc draw-polygon (make-points subject-poly-points))
(send dc set-pen (make-pen
#:color (send the-color-database find-color "Red")
#:width 4
#:style 'long-dash))
(send dc draw-polygon (make-points clip-poly-points))
(send dc set-pen (make-pen
#:color (send the-color-database find-color "Green")))
(send dc set-brush (make-brush
#:color (send the-color-database find-color "Green")
#:style 'solid))
(send dc draw-polygon (make-points clipped-poly))
clipped-poly))
(run)
Output:
(list
(point 300 300)
(point 250 300)
(point 200 250)
(point 175 300)
(point 125 300)
(point 100 250)
(point 100 200)
(point 100 200)
(point 100 350/3)
(point 125 100)
(point 275 100)
(point 300 350/3))
Raku
(formerly Perl 6)
sub intersection ($L11, $L12, $L21, $L22) {
my ($Δ1x, $Δ1y) = $L11 »-« $L12;
my ($Δ2x, $Δ2y) = $L21 »-« $L22;
my $n1 = $L11[0] * $L12[1] - $L11[1] * $L12[0];
my $n2 = $L21[0] * $L22[1] - $L21[1] * $L22[0];
my $n3 = 1 / ($Δ1x * $Δ2y - $Δ2x * $Δ1y);
(($n1 * $Δ2x - $n2 * $Δ1x) * $n3, ($n1 * $Δ2y - $n2 * $Δ1y) * $n3)
}
sub is-inside ($p1, $p2, $p3) {
($p2[0] - $p1[0]) * ($p3[1] - $p1[1]) > ($p2[1] - $p1[1]) * ($p3[0] - $p1[0])
}
sub sutherland-hodgman (@polygon, @clip) {
my @output = @polygon;
my $clip-point1 = @clip.tail;
for @clip -> $clip-point2 {
my @input = @output;
@output = ();
my $start = @input.tail;
for @input -> $end {
if is-inside($clip-point1, $clip-point2, $end) {
@output.push: intersection($clip-point1, $clip-point2, $start, $end)
unless is-inside($clip-point1, $clip-point2, $start);
@output.push: $end;
} elsif is-inside($clip-point1, $clip-point2, $start) {
@output.push: intersection($clip-point1, $clip-point2, $start, $end);
}
$start = $end;
}
$clip-point1 = $clip-point2;
}
@output
}
my @polygon = (50, 150), (200, 50), (350, 150), (350, 300), (250, 300),
(200, 250), (150, 350), (100, 250), (100, 200);
my @clip = (100, 100), (300, 100), (300, 300), (100, 300);
my @clipped = sutherland-hodgman(@polygon, @clip);
say "Clipped polygon: ", @clipped;
# Output an SVG as well as it is easier to visualize
use SVG;
my $outfile = 'Sutherland-Hodgman-polygon-clipping-perl6.svg'.IO.open(:w);
$outfile.say: SVG.serialize(
svg => [
:400width, :400height,
:rect[ :400width, :400height, :fill<white> ],
:text[ :10x, :20y, "Polygon (blue)" ],
:text[ :10x, :35y, "Clip port (green)" ],
:text[ :10x, :50y, "Clipped polygon (red)" ],
:polyline[ :points(@polygon.join: ','), :style<stroke:blue>, :fill<blue>, :opacity<.3> ],
:polyline[ :points( @clip.join: ','), :style<stroke:green>, :fill<green>, :opacity<.3> ],
:polyline[ :points(@clipped.join: ','), :style<stroke:red>, :fill<red>, :opacity<.5> ],
],
);
- Output:
Clipped polygon: [(100 116.666667) (125 100) (275 100) (300 116.666667) (300 300) (250 300) (200 250) (175 300) (125 300) (100 250)]
Also see output image: offsite SVG image
RATFOR
# Sutherland-Hodgman polygon clipping.
#
# On a POSIX platform, the program can be compiled with f2c and run
# somewhat as follows:
#
# ratfor77 sutherland-hodgman.r > sutherland-hodgman.f
# f2c -C sutherland-hodgman.f
# cc sutherland-hodgman.c -lf2c
# ./a.out
#
# With gfortran, a little differently:
#
# ratfor77 sutherland-hodgman.r > sutherland-hodgman.f
# gfortran -fcheck=all -std=legacy sutherland-hodgman.f
# ./a.out
function evalln (x1, y1, x2, y2, x)
#
# Given the line (x1,y1)--(x2,y2), evaluate it at x.
#
implicit none
real evalln
real x1, y1, x2, y2, x
real dy, dx, slope, xcept
dy = y2 - y1
dx = x2 - x1
slope = dy / dx
xcept = ((dx * y1) - (dy * x1)) / dx
evalln = (slope * x) + xcept
end
subroutine xsctln (x1, y1, x2, y2, x3, y3, x4, y4, x, y)
#
# Given lines (x1,y1)--(x2,y2) and (x3,y3)--(x4,y4), find their
# intersection (x,y).
#
implicit none
real x1, y1, x2, y2, x3, y3, x4, y4, x, y
real evalln
real denom, xnumer, ynumer, xyyx12, xyyx34
if (x1 == x2)
{
x = x1
y = evalln (x3, y3, x4, y4, x1)
}
else if (x3 == x4)
{
x = x3
y = evalln (x1, y1, x2, y2, x3)
}
else
{
denom = ((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4))
xyyx12 = (x1 * y2) - (y1 * x2)
xyyx34 = (x3 * y4) - (y3 * x4)
xnumer = (xyyx12 * (x3 - x4)) - ((x1 - x2) * xyyx34)
ynumer = (xyyx12 * (y3 - y4)) - ((y1 - y2) * xyyx34)
x = xnumer / denom
y = ynumer / denom
}
end
function ptleft (x, y, x1, y1, x2, y2)
#
# Is the point (x,y) left of the edge (x1,y1)--(x2,y2)?
#
implicit none
logical ptleft
real x, y, x1, y1, x2, y2
ptleft = (((x - x1) * (y2 - y1)) - ((x2 - x1) * (y - y1)) < 0)
end
subroutine clpsbe (xs1, ys1, xs2, ys2, xc1, yc1, xc2, yc2, n, pts)
#
# Clip subject edge (xs1,ys1)--(xs2,ys2) with clip edge
# (xc1,yc1)--(xc2,yc2).
#
implicit none
real xs1, ys1, xs2, ys2, xc1, yc1, xc2, yc2
integer n
real pts(2,*), x, y
logical ptleft, s2left, s1left
s2left = ptleft (xs2, ys2, xc1, yc1, xc2, yc2)
s1left = ptleft (xs1, ys1, xc1, yc1, xc2, yc2)
if (s2left)
{
if (s1left)
{
n = n + 1
pts(1,n) = xs2
pts(2,n) = ys2
}
else
{
call xsctln (xs1, ys1, xs2, ys2, xc1, yc1, xc2, yc2, x, y)
n = n + 1
pts(1,n) = x
pts(2,n) = y
n = n + 1
pts(1,n) = xs2
pts(2,n) = ys2
}
}
else if (s1left)
{
call xsctln (xs1, ys1, xs2, ys2, xc1, yc1, xc2, yc2, x, y)
n = n + 1
pts(1,n) = x
pts(2,n) = y
}
end
subroutine sublp (nsub, ptssub, xc1, yc1, xc2, yc2, n, pts)
#
# Loop over the subject points in ptssub, clipping the edges
# therein. Produce a result in pts.
#
implicit none
integer nsub, n
real ptssub(2,*), pts(2,*)
real xc1, yc1, xc2, yc2
real xs1, ys1, xs2, ys2
integer i, j
for (i = 1; i <= nsub; i = i + 1)
{
xs2 = ptssub(1,i)
ys2 = ptssub(2,i)
j = i - 1
if (j == 0) j = nsub
xs1 = ptssub(1,j)
ys1 = ptssub(2,j)
call clpsbe (xs1, ys1, xs2, ys2, xc1, yc1, xc2, yc2, n, pts)
}
end
subroutine clip (nsub, ptssub, nclp, ptsclp, ptswrk)
#
# Loop over the clip points in ptsclp, clipping the subject stored
# in ptssub. Use ptswrk as workspace.
#
implicit none
integer nsub, nclp
real ptssub(2,*), ptsclp(2,*), ptswrk(2,*)
integer i, j, nwrk
real xc1, yc1, xc2, yc2
for (i = 1; i <= nclp; i = i + 1)
{
xc2 = ptsclp(1,i)
yc2 = ptsclp(2,i)
j = i - 1
if (j == 0) j = nclp
xc1 = ptsclp(1,j)
yc1 = ptsclp(2,j)
nwrk = 0
call sublp (nsub, ptssub, xc1, yc1, xc2, yc2, nwrk, ptswrk)
# Copy the new subject over the old subject.
for (j = 1; j <= nwrk; j = j + 1)
{
ptssub(1,j) = ptswrk(1,j)
ptssub(2,j) = ptswrk(2,j)
}
nsub = nwrk
}
end
subroutine wrtpts (eps, n, pts, linclr, filclr)
#
# Write a polygon as PostScript code.
#
implicit none
character*10 linclr, filclr
integer eps, n, i
real pts(2,*)
10 format (F12.6, ' ', F12.6, ' moveto')
20 format (F12.6, ' ', F12.6, ' lineto')
30 format ('closepath')
40 format ('gsave')
50 format ('grestore')
60 format ('fill')
70 format ('stroke')
80 format (A10, ' setrgbcolor')
write (eps, 10) pts(1,1), pts(2,1)
for (i = 2; i <= n; i = i + 1)
write (eps, 20) pts(1,i), pts(2,i)
write (eps, 30)
write (eps, 80) linclr
write (eps, 40)
write (eps, 80) filclr
write (eps, 60)
write (eps, 50)
write (eps, 70)
end
subroutine wrteps (eps, nsub, ptssub, nclp, ptsclp, nres, ptsres)
#
# Write an Encapsulated PostScript file.
#
implicit none
integer eps
integer nsub, nclp, nres
real ptssub(2,*), ptsclp(2,*), ptsres(2,*)
10 format ('%!PS-Adobe-3.0 EPSF-3.0')
20 format ('%%BoundingBox: 40 40 360 360')
30 format ('0 setlinewidth ')
40 format ('2 setlinewidth')
50 format ('[10 8] 0 setdash')
60 format ('%%EOF')
write (eps, 10)
write (eps, 20)
write (eps, 30)
call wrtpts (eps, nclp, ptsclp, '.5 0 0 ', '1 .7 .7 ')
call wrtpts (eps, nsub, ptssub, '0 .2 .5 ', '.4 .7 1 ')
write (eps, 40)
write (eps, 50)
call wrtpts (eps, nres, ptsres, '.5 0 .5 ', '.7 .3 .8 ')
write (eps, 60)
end
define(NMAX,100) # Maximum number of points in a polygon.
define(EPSF,9) # Unit number for the EPS file.
program shclip
implicit none
integer nsub, nclp, nres
real ptssub(2,NMAX), ptsclp(2,NMAX), ptsres(2,NMAX), ptswrk(2,NMAX)
integer i
integer eps
nsub = 9
ptssub(1,1) = 50; ptssub(2,1) = 150
ptssub(1,2) = 200; ptssub(2,2) = 50
ptssub(1,3) = 350; ptssub(2,3) = 150
ptssub(1,4) = 350; ptssub(2,4) = 300
ptssub(1,5) = 250; ptssub(2,5) = 300
ptssub(1,6) = 200; ptssub(2,6) = 250
ptssub(1,7) = 150; ptssub(2,7) = 350
ptssub(1,8) = 100; ptssub(2,8) = 250
ptssub(1,9) = 100; ptssub(2,9) = 200
nclp = 4
ptsclp(1,1) = 100; ptsclp(2,1) = 100
ptsclp(1,2) = 300; ptsclp(2,2) = 100
ptsclp(1,3) = 300; ptsclp(2,3) = 300
ptsclp(1,4) = 100; ptsclp(2,4) = 300
# Copy the subject points to the "result" array.
for (i = 1; i <= nsub; i = i + 1)
{
ptsres(1,i) = ptssub(1,i)
ptsres(2,i) = ptssub(2,i)
}
nres = nsub
call clip (nres, ptsres, nclp, ptsclp, ptswrk)
for (i = 1; i <= nres; i = i + 1)
write (*, 1000) ptsres(1,i), ptsres(2,i)
1000 format ('(', F8.4, ', ', F8.4, ')')
eps = EPSF
open (unit=eps, file='sutherland-hodgman.eps')
call wrteps (eps, nsub, ptssub, nclp, ptsclp, nres, ptsres)
write (*, 1010)
1010 format ('Wrote sutherland-hodgman.eps')
end- Output:
(100.0000, 116.6667) (125.0000, 100.0000) (275.0000, 100.0000) (300.0000, 116.6667) (300.0000, 300.0000) (250.0000, 300.0000) (200.0000, 250.0000) (175.0000, 300.0000) (125.0000, 300.0000) (100.0000, 250.0000) Wrote sutherland-hodgman.eps
Ruby
Point = Struct.new(:x,:y) do
def to_s; "(#{x}, #{y})" end
end
def sutherland_hodgman(subjectPolygon, clipPolygon)
# These inner functions reduce the argument passing to
# "inside" and "intersection".
cp1, cp2, s, e = nil
inside = proc do |p|
(cp2.x-cp1.x)*(p.y-cp1.y) > (cp2.y-cp1.y)*(p.x-cp1.x)
end
intersection = proc do
dcx, dcy = cp1.x-cp2.x, cp1.y-cp2.y
dpx, dpy = s.x-e.x, s.y-e.y
n1 = cp1.x*cp2.y - cp1.y*cp2.x
n2 = s.x*e.y - s.y*e.x
n3 = 1.0 / (dcx*dpy - dcy*dpx)
Point[(n1*dpx - n2*dcx) * n3, (n1*dpy - n2*dcy) * n3]
end
outputList = subjectPolygon
cp1 = clipPolygon.last
for cp2 in clipPolygon
inputList = outputList
outputList = []
s = inputList.last
for e in inputList
if inside[e]
outputList << intersection[] unless inside[s]
outputList << e
elsif inside[s]
outputList << intersection[]
end
s = e
end
cp1 = cp2
end
outputList
end
subjectPolygon = [[50, 150], [200, 50], [350, 150], [350, 300],
[250, 300], [200, 250], [150, 350], [100, 250],
[100, 200]].collect{|pnt| Point[*pnt]}
clipPolygon = [[100, 100], [300, 100], [300, 300], [100, 300]].collect{|pnt| Point[*pnt]}
puts sutherland_hodgman(subjectPolygon, clipPolygon)
- Output:
(100.0, 116.66666666666667) (125.00000000000001, 100.0) (275.0, 100.0) (300.0, 116.66666666666667) (300.0, 299.99999999999994) (250.0, 300.0) (200, 250) (175.0, 300.0) (125.0, 300.0) (100.0, 250.0)
Rust
#[derive(Debug, Clone)]
struct Point {
x: f64,
y: f64,
}
#[derive(Debug, Clone)]
struct Polygon(Vec<Point>);
fn is_inside(p: &Point, cp1: &Point, cp2: &Point) -> bool {
(cp2.x - cp1.x) * (p.y - cp1.y) > (cp2.y - cp1.y) * (p.x - cp1.x)
}
fn compute_intersection(cp1: &Point, cp2: &Point, s: &Point, e: &Point) -> Point {
let dc = Point {
x: cp1.x - cp2.x,
y: cp1.y - cp2.y,
};
let dp = Point {
x: s.x - e.x,
y: s.y - e.y,
};
let n1 = cp1.x * cp2.y - cp1.y * cp2.x;
let n2 = s.x * e.y - s.y * e.x;
let n3 = 1.0 / (dc.x * dp.y - dc.y * dp.x);
Point {
x: (n1 * dp.x - n2 * dc.x) * n3,
y: (n1 * dp.y - n2 * dc.y) * n3,
}
}
fn sutherland_hodgman_clip(subject_polygon: &Polygon, clip_polygon: &Polygon) -> Polygon {
let mut result_ring = subject_polygon.0.clone();
let mut cp1 = clip_polygon.0.last().unwrap();
for cp2 in &clip_polygon.0 {
let input = result_ring;
let mut s = input.last().unwrap();
result_ring = vec![];
for e in &input {
if is_inside(e, cp1, cp2) {
if !is_inside(s, cp1, cp2) {
result_ring.push(compute_intersection(cp1, cp2, s, e));
}
result_ring.push(e.clone());
} else if is_inside(s, cp1, cp2) {
result_ring.push(compute_intersection(cp1, cp2, s, e));
}
s = e;
}
cp1 = cp2;
}
Polygon(result_ring)
}
fn main() {
let _p = |x: f64, y: f64| Point { x, y };
let subject_polygon = Polygon(vec![
_p(50.0, 150.0), _p(200.0, 50.0), _p(350.0, 150.0), _p(350.0, 300.0), _p(250.0, 300.0),
_p(200.0, 250.0), _p(150.0, 350.0), _p(100.0, 250.0), _p(100.0, 200.0),
]);
let clip_polygon = Polygon(vec![
_p(100.0, 100.0),_p(300.0, 100.0),_p(300.0, 300.0),_p(100.0, 300.0),
]);
let result = sutherland_hodgman_clip(&subject_polygon, &clip_polygon);
println!("{:?}", result);
}
- Output:
Polygon([
Point { x: 100, y: 116.66666666666667 }, Point { x: 125.00000000000001, y: 100 }, Point { x: 275, y: 100 },
Point { x: 300, y: 116.66666666666667 }, Point { x: 300, y: 299.99999999999994 }, Point { x: 250, y: 300 },
Point { x: 200, y: 250 }, Point { x: 175, y: 300 }, Point { x: 125, y: 300 }, Point { x: 100, y: 250 }])
Scala
From Java snippet.
import javax.swing.{ JFrame, JPanel }
object SutherlandHodgman extends JFrame with App {
import java.awt.BorderLayout
setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE)
setVisible(true)
val content = getContentPane()
content.setLayout(new BorderLayout())
content.add(SutherlandHodgmanPanel, BorderLayout.CENTER)
setTitle("SutherlandHodgman")
pack()
setLocationRelativeTo(null)
}
object SutherlandHodgmanPanel extends JPanel {
import java.awt.{ Color, Graphics, Graphics2D }
setPreferredSize(new java.awt.Dimension(600, 500))
// subject and clip points are assumed to be valid
val subject = Seq((50D, 150D), (200D, 50D), (350D, 150D), (350D, 300D), (250D, 300D), (200D, 250D), (150D, 350D), (100D, 250D), (100D, 200D))
val clipper = Seq((100D, 100D), (300D, 100D), (300D, 300D), (100D, 300D))
var result = subject
val len = clipper.size
for (i <- 0 until len) {
val len2 = result.size
val input = result
result = Seq()
val A = clipper((i + len - 1) % len)
val B = clipper(i)
for (j <- 0 until len2) {
val P = input((j + len2 - 1) % len2)
val Q = input(j)
if (inside(A, B, Q)) {
if (!inside(A, B, P))
result = result :+ intersection(A, B, P, Q)
result = result :+ Q
}
else if (inside(A, B, P))
result = result :+ intersection(A, B, P, Q)
}
}
override def paintComponent(g: Graphics) {
import java.awt.RenderingHints._
super.paintComponent(g)
val g2 = g.asInstanceOf[Graphics2D]
g2.translate(80, 60)
g2.setStroke(new java.awt.BasicStroke(3))
g2.setRenderingHint(KEY_ANTIALIASING, VALUE_ANTIALIAS_ON)
g2.draw_polygon(subject, Color.blue)
g2.draw_polygon(clipper, Color.red)
g2.draw_polygon(result, Color.green)
}
private def inside(a: (Double, Double), b: (Double, Double), c: (Double, Double)) =
(a._1 - c._1) * (b._2 - c._2) > (a._2 - c._2) * (b._1 - c._1)
private def intersection(a: (Double, Double), b: (Double, Double), p: (Double, Double), q: (Double, Double)) = {
val A1 = b._2 - a._2
val B1 = a._1 - b._1
val C1 = A1 * a._1 + B1 * a._2
val A2 = q._2 - p._2
val B2 = p._1 - q._1
val C2 = A2 * p._1 + B2 * p._2
val det = A1 * B2 - A2 * B1
((B2 * C1 - B1 * C2) / det, (A1 * C2 - A2 * C1) / det)
}
private implicit final class Polygon_drawing(g: Graphics2D) {
def draw_polygon(points: Seq[(Double, Double)], color: Color) {
g.setColor(color)
val len = points.length
val line = new java.awt.geom.Line2D.Double()
for (i <- 0 until len) {
val p1 = points(i)
val p2 = points((i + 1) % len)
line.setLine(p1._1, p1._2, p2._1, p2._2)
g.draw(line)
}
}
}
}
Scheme
;;; Sutherland-Hodgman polygon clipping.
(define (evaluate-line x1 y1 x2 y2 x)
;; Given the straight line between (x1,y1) and (x2,y2), evaluate it
;; at x.
(let ((dy (- y2 y1))
(dx (- x2 x1)))
(let ((slope (/ dy dx))
(intercept (/ (- (* dx y1) (* dy x1)) dx)))
(+ (* slope x) intercept))))
(define (intersection-of-lines x1 y1 x2 y2 x3 y3 x4 y4)
;; Given the line between (x1,y1) and (x2,y2), and the line between
;; (x3,y3) and (x4,y4), find their intersection.
(cond ((= x1 x2) (list x1 (evaluate-line x3 y3 x4 y4 x1)))
((= x3 x4) (list x3 (evaluate-line x1 y1 x2 y2 x3)))
(else (let ((denominator (- (* (- x1 x2) (- y3 y4))
(* (- y1 y2) (- x3 x4))))
(x1*y2-y1*x2 (- (* x1 y2) (* y1 x2)))
(x3*y4-y3*x4 (- (* x3 y4) (* y3 x4))))
(let ((xnumerator (- (* x1*y2-y1*x2 (- x3 x4))
(* (- x1 x2) x3*y4-y3*x4)))
(ynumerator (- (* x1*y2-y1*x2 (- y3 y4))
(* (- y1 y2) x3*y4-y3*x4))))
(list (/ xnumerator denominator)
(/ ynumerator denominator)))))))
(define (intersection-of-edges e1 e2)
;;
;; A point is a list of two coordinates, and an edge is a list of
;; two points.
;;
;; I am not using any SRFI-9 records, or the like, that define
;; actual new types, although I would do so if writing a more
;; serious implementation. Also, I am not using any pattern matcher.
;; A pattern matcher would make this code less tedious with
;; "cadaddaddr" notations.
(let ((point1 (car e1))
(point2 (cadr e1))
(point3 (car e2))
(point4 (cadr e2)))
(let ((x1 (car point1))
(y1 (cadr point1))
(x2 (car point2))
(y2 (cadr point2))
(x3 (car point3))
(y3 (cadr point3))
(x4 (car point4))
(y4 (cadr point4)))
(intersection-of-lines x1 y1 x2 y2 x3 y3 x4 y4))))
(define (point-is-left-of-edge? pt edge)
(let ((x (car pt))
(y (cadr pt))
(x1 (caar edge))
(y1 (cadar edge))
(x2 (caadr edge))
(y2 (cadadr edge)))
;; Outer product of the vectors (x1,y1)-->(x,y) and
;; (x1,y1)-->(x2,y2)
(negative? (- (* (- x x1) (- y2 y1))
(* (- x2 x1) (- y y1))))))
(define (clip-subject-edge subject-edge clip-edge accum)
(define left-of? point-is-left-of-edge?)
(define (intersection)
(intersection-of-edges subject-edge clip-edge))
(let ((s1 (car subject-edge))
(s2 (cadr subject-edge)))
(let ((s2-is-inside? (left-of? s2 clip-edge))
(s1-is-inside? (left-of? s1 clip-edge)))
(if s2-is-inside?
(if s1-is-inside?
(cons s2 accum)
(cons s2 (cons (intersection) accum)))
(if s1-is-inside?
(cons (intersection) accum)
accum)))))
(define (for-each-subject-edge i subject-points clip-edge accum)
(define n (vector-length subject-points))
(if (= i n)
(list->vector (reverse accum))
(let ((s2 (vector-ref subject-points i))
(s1 (vector-ref subject-points
(- (if (zero? i) n i) 1))))
(let ((accum (clip-subject-edge (list s1 s2)
clip-edge accum)))
(for-each-subject-edge (+ i 1) subject-points
clip-edge accum)))))
(define (for-each-clip-edge i subject-points clip-points)
(define n (vector-length clip-points))
(if (= i n)
subject-points
(let ((c2 (vector-ref clip-points i))
(c1 (vector-ref clip-points (- (if (zero? i) n i) 1))))
(let ((subject-points
(for-each-subject-edge 0 subject-points
(list c1 c2) '())))
(for-each-clip-edge (+ i 1) subject-points clip-points)))))
(define (clip subject-points clip-points)
(for-each-clip-edge 0 subject-points clip-points))
(define (write-eps subject-points clip-points result-points)
;; I use only some of the most basic output procedures. Schemes tend
;; to include more advanced means to write output, often resembling
;; those of Common Lisp.
(define (x pt) (exact->inexact (car pt)))
(define (y pt) (exact->inexact (cadr pt)))
(define (moveto pt)
(display (x pt))
(display " ")
(display (y pt))
(display " moveto")
(newline))
(define (lineto pt)
(display (x pt))
(display " ")
(display (y pt))
(display " lineto")
(newline))
(define (setrgbcolor rgb)
(display rgb)
(display " setrgbcolor")
(newline))
(define (simple-word word)
(lambda ()
(display word)
(newline)))
(define closepath (simple-word "closepath"))
(define fill (simple-word "fill"))
(define stroke (simple-word "stroke"))
(define gsave (simple-word "gsave"))
(define grestore (simple-word "grestore"))
(define (showpoly poly line-color fill-color)
(define n (vector-length poly))
(moveto (vector-ref poly 0))
(do ((i 1 (+ i 1)))
((= i n))
(lineto (vector-ref poly i)))
(closepath)
(setrgbcolor line-color)
(gsave)
(setrgbcolor fill-color)
(fill)
(grestore)
(stroke))
(define (code s)
(display s)
(newline))
(code "%!PS-Adobe-3.0 EPSF-3.0")
(code "%%BoundingBox: 40 40 360 360")
(code "0 setlinewidth")
(showpoly clip-points ".5 0 0" "1 .7 .7")
(showpoly subject-points "0 .2 .5" ".4 .7 1")
(code "2 setlinewidth")
(code "[10 8] 0 setdash")
(showpoly result-points ".5 0 .5" ".7 .3 .8")
(code "%%EOF"))
(define (write-eps-to-file outfile subject-points clip-points
result-points)
(with-output-to-file outfile
(lambda ()
(write-eps subject-points clip-points result-points))))
(define subject-points
#((50 150)
(200 50)
(350 150)
(350 300)
(250 300)
(200 250)
(150 350)
(100 250)
(100 200)))
(define clip-points
#((100 100)
(300 100)
(300 300)
(100 300)))
(define result-points (clip subject-points clip-points))
(display result-points)
(newline)
(write-eps-to-file "sutherland-hodgman.eps"
subject-points clip-points result-points)
(display "Wrote sutherland-hodgman.eps")
(newline)
- Output:
#((100 350/3) (125 100) (275 100) (300 350/3) (300 300) (250 300) (200 250) (175 300) (125 300) (100 250)) Wrote sutherland-hodgman.eps
Sidef
class Point(x, y) {
method to_s {
"(#{'%.2f' % x}, #{'%.2f' % y})"
}
}
func sutherland_hodgman(subjectPolygon, clipPolygon) {
var inside = { |cp1, cp2, p|
((cp2.x-cp1.x)*(p.y-cp1.y)) > ((cp2.y-cp1.y)*(p.x-cp1.x))
}
var intersection = { |cp1, cp2, s, e|
var (dcx, dcy) = (cp1.x-cp2.x, cp1.y-cp2.y)
var (dpx, dpy) = (s.x-e.x, s.y-e.y)
var n1 = (cp1.x*cp2.y - cp1.y*cp2.x)
var n2 = (s.x*e.y - s.y*e.x)
var n3 = (1 / (dcx*dpy - dcy*dpx))
Point((n1*dpx - n2*dcx) * n3, (n1*dpy - n2*dcy) * n3)
}
var outputList = subjectPolygon
var cp1 = clipPolygon.last
for cp2 in clipPolygon {
var inputList = outputList
outputList = []
var s = inputList.last
for e in inputList {
if (inside(cp1, cp2, e)) {
outputList << intersection(cp1, cp2, s, e) if !inside(cp1, cp2, s)
outputList << e
}
elsif(inside(cp1, cp2, s)) {
outputList << intersection(cp1, cp2, s, e)
}
s = e
}
cp1 = cp2
}
outputList
}
var subjectPolygon = [
[50, 150], [200, 50], [350, 150], [350, 300],
[250, 300], [200, 250], [150, 350], [100, 250],
[100, 200]
].map{|pnt| Point(pnt...) }
var clipPolygon = [
[100, 100], [300, 100],
[300, 300], [100, 300]
].map{|pnt| Point(pnt...) }
sutherland_hodgman(subjectPolygon, clipPolygon).each { .say }
- Output:
(100.00, 116.67) (125.00, 100.00) (275.00, 100.00) (300.00, 116.67) (300.00, 300.00) (250.00, 300.00) (200.00, 250.00) (175.00, 300.00) (125.00, 300.00) (100.00, 250.00)
Standard ML
(* Sutherland-Hodgman polygon clipping. *)
fun evaluate_line (x1 : real, y1 : real,
x2 : real, y2 : real,
x : real) =
let
val dy = y2 - y1
and dx = x2 - x1
val slope = dy / dx
and intercept = ((dx * y1) - (dy * x1)) / dx
in
(slope * x) + intercept
end
fun intersection_of_lines (x1 : real, y1 : real,
x2 : real, y2 : real,
x3 : real, y3 : real,
x4 : real, y4 : real) =
if Real.== (x1, x2) then
(x1, evaluate_line (x3, y3, x4, y4, x1))
else if Real.== (x3, x4) then
(x3, evaluate_line (x1, y1, x2, y2, x3))
else
let
val denominator =
((x1 - x2) * (y3 - y4)) - ((y1 - y2) * (x3 - x4))
and x1y2_y1x2 = (x1 * y2) - (y1 * x2)
and x3y4_y3x4 = (x3 * y4) - (y3 * x4)
val xnumerator =
(x1y2_y1x2 * (x3 - x4)) - ((x1 - x2) * x3y4_y3x4)
and ynumerator =
(x1y2_y1x2 * (y3 - y4)) - ((y1 - y2) * x3y4_y3x4)
in
(xnumerator / denominator,
ynumerator / denominator)
end
fun intersection_of_edges (((x1, y1), (x2, y2)),
((x3, y3), (x4, y4))) =
intersection_of_lines (x1, y1, x2, y2, x3, y3, x4, y4)
fun point_is_left_of_edge ((x, y), ((x1, y1), (x2, y2))) =
(* Outer product of the vectors (x1,y1)-->(x,y) and
(x1,y1)-->(x2,y2). *)
((x - x1) * (y2 - y1)) - ((x2 - x1) * (y - y1)) < 0.0
fun clip_subject_edge (subject_edge, clip_edge, accum) =
let
fun intersection () =
intersection_of_edges (subject_edge, clip_edge)
val (s1, s2) = subject_edge
val s2_is_inside = point_is_left_of_edge (s2, clip_edge)
and s1_is_inside = point_is_left_of_edge (s1, clip_edge)
in
case (s2_is_inside, s1_is_inside) of
(true, true) => s2 :: accum
| (true, false) => s2 :: intersection () :: accum
| (false, true) => intersection () :: accum
| (false, false) => accum
end
fun for_each_subject_edge (i, subject_points, clip_edge, accum) =
let
val n = Array.length subject_points
in
if i = n then
Array.fromList (rev accum)
else
let
val s2 = Array.sub (subject_points, i)
and s1 = (if i = 0 then
Array.sub (subject_points, n - 1)
else
Array.sub (subject_points, i - 1))
val accum = clip_subject_edge ((s1, s2), clip_edge, accum)
in
for_each_subject_edge (i + 1, subject_points, clip_edge,
accum)
end
end
fun for_each_clip_edge (i, subject_points, clip_points) =
let
val n = Array.length clip_points
in
if i = n then
subject_points
else
let
val c2 = Array.sub (clip_points, i)
and c1 = (if i = 0 then
Array.sub (clip_points, n - 1)
else
Array.sub (clip_points, i - 1))
val subject_points =
for_each_subject_edge (0, subject_points, (c1, c2), [])
in
for_each_clip_edge (i + 1, subject_points, clip_points)
end
end
fun clip (subject_points, clip_points) =
for_each_clip_edge (0, subject_points, clip_points)
fun write_eps (outf, subject_points, clip_points, result_points) =
(* The EPS code that will be generated is based on that which is
generated by the C implementation of this task. *)
let
fun moveto (x, y) =
(TextIO.output (outf, Real.toString x);
TextIO.output (outf, " ");
TextIO.output (outf, Real.toString y);
TextIO.output (outf, " moveto\n"))
fun lineto (x, y) =
(TextIO.output (outf, Real.toString x);
TextIO.output (outf, " ");
TextIO.output (outf, Real.toString y);
TextIO.output (outf, " lineto\n"))
fun setrgbcolor rgb =
(TextIO.output (outf, rgb);
TextIO.output (outf, " setrgbcolor\n"))
fun closepath () = TextIO.output (outf, "closepath\n")
fun fill () = TextIO.output (outf, "fill\n")
fun stroke () = TextIO.output (outf, "stroke\n")
fun gsave () = TextIO.output (outf, "gsave\n")
fun grestore () = TextIO.output (outf, "grestore\n")
fun showpoly (poly, line_color, fill_color) =
let
val n = Array.length poly
in
moveto (Array.sub (poly, 0));
Array.app lineto poly;
closepath ();
setrgbcolor line_color;
gsave ();
setrgbcolor fill_color;
fill ();
grestore ();
stroke ()
end
in
TextIO.output (outf, "%!PS-Adobe-3.0 EPSF-3.0\n");
TextIO.output (outf, "%%BoundingBox: 40 40 360 360\n");
TextIO.output (outf, "0 setlinewidth\n");
showpoly (clip_points, ".5 0 0", "1 .7 .7");
showpoly (subject_points, "0 .2 .5", ".4 .7 1");
TextIO.output (outf, "2 setlinewidth\n");
TextIO.output (outf, "[10 8] 0 setdash\n");
showpoly (result_points, ".5 0 .5", ".7 .3 .8");
TextIO.output (outf, "%%EOF\n")
end
fun write_eps_to_file (outfile, subject_points, clip_points,
result_points) =
let
val outf = TextIO.openOut outfile
in
write_eps (outf, subject_points, clip_points, result_points);
TextIO.closeOut outf
end
val subject_points =
Array.fromList
[(50.0, 150.0),
(200.0, 50.0),
(350.0, 150.0),
(350.0, 300.0),
(250.0, 300.0),
(200.0, 250.0),
(150.0, 350.0),
(100.0, 250.0),
(100.0, 200.0)]
val clip_points =
Array.fromList
[(100.0, 100.0),
(300.0, 100.0),
(300.0, 300.0),
(100.0, 300.0)]
val result_points = clip (subject_points, clip_points)
fun print_point (x, y) =
(TextIO.print " (";
TextIO.print (Real.toString x);
TextIO.print " ";
TextIO.print (Real.toString y);
TextIO.print ")")
;
Array.app print_point result_points;
TextIO.print "\n";
write_eps_to_file ("sutherland-hodgman.eps",
subject_points, clip_points, result_points);
TextIO.print "Wrote sutherland-hodgman.eps\n";
(*
local variables:
mode: SML
sml-indent-level: 2
end:
*)
- Output:
$ mlton sutherland-hodgman.sml && ./sutherland-hodgman (100 116.666666667) (125 100) (275 100) (300 116.666666667) (300 300) (250 300) (200 250) (175 300) (125 300) (100 250) Wrote sutherland-hodgman.eps
Swift
struct Point {
var x: Double
var y: Double
}
struct Polygon {
var points: [Point]
init(points: [Point]) {
self.points = points
}
init(points: [(Double, Double)]) {
self.init(points: points.map({ Point(x: $0.0, y: $0.1) }))
}
}
func isInside(_ p1: Point, _ p2: Point, _ p3: Point) -> Bool {
(p3.x - p2.x) * (p1.y - p2.y) > (p3.y - p2.y) * (p1.x - p2.x)
}
func computeIntersection(_ p1: Point, _ p2: Point, _ s: Point, _ e: Point) -> Point {
let dc = Point(x: p1.x - p2.x, y: p1.y - p2.y)
let dp = Point(x: s.x - e.x, y: s.y - e.y)
let n1 = p1.x * p2.y - p1.y * p2.x
let n2 = s.x * e.y - s.y * e.x
let n3 = 1.0 / (dc.x * dp.y - dc.y * dp.x)
return Point(x: (n1 * dp.x - n2 * dc.x) * n3, y: (n1 * dp.y - n2 * dc.y) * n3)
}
func sutherlandHodgmanClip(subjPoly: Polygon, clipPoly: Polygon) -> Polygon {
var ring = subjPoly.points
var p1 = clipPoly.points.last!
for p2 in clipPoly.points {
let input = ring
var s = input.last!
ring = []
for e in input {
if isInside(e, p1, p2) {
if !isInside(s, p1, p2) {
ring.append(computeIntersection(p1, p2, s, e))
}
ring.append(e)
} else if isInside(s, p1, p2) {
ring.append(computeIntersection(p1, p2, s, e))
}
s = e
}
p1 = p2
}
return Polygon(points: ring)
}
let subj = Polygon(points: [
(50.0, 150.0),
(200.0, 50.0),
(350.0, 150.0),
(350.0, 300.0),
(250.0, 300.0),
(200.0, 250.0),
(150.0, 350.0),
(100.0, 250.0),
(100.0, 200.0)
])
let clip = Polygon(points: [
(100.0, 100.0),
(300.0, 100.0),
(300.0, 300.0),
(100.0, 300.0)
])
print(sutherlandHodgmanClip(subjPoly: subj, clipPoly: clip))
- Output:
Polygon(points: [Point(x: 100.0, y: 116.66666666666667), Point(x: 125.00000000000001, y: 100.0), Point(x: 275.0, y: 100.0), Point(x: 300.0, y: 116.66666666666667), Point(x: 300.0, y: 299.99999999999994), Point(x: 250.0, y: 300.0), Point(x: 200.0, y: 250.0), Point(x: 175.0, y: 300.0), Point(x: 125.0, y: 300.0), Point(x: 100.0, y: 250.0)])
Tcl
# Find intersection of an arbitrary polygon with a convex one.
package require Tcl 8.6
# Does the path (x0,y0)->(x1,y1)->(x2,y2) turn clockwise
# or counterclockwise?
proc cw {x0 y0 x1 y1 x2 y2} {
set dx1 [expr {$x1 - $x0}]; set dy1 [expr {$y1 - $y0}]
set dx2 [expr {$x2 - $x0}]; set dy2 [expr {$y2 - $y0}]
# (0,0,$dx1*$dy2 - $dx2*$dy1) is the crossproduct of
# ($x1-$x0,$y1-$y0,0) and ($x2-$x0,$y2-$y0,0).
# Its z-component is positive if the turn
# is clockwise, negative if the turn is counterclockwise.
set pr1 [expr {$dx1 * $dy2}]
set pr2 [expr {$dx2 * $dy1}]
if {$pr1 > $pr2} {
# Clockwise
return 1
} elseif {$pr1 < $pr2} {
# Counter-clockwise
return -1
} elseif {$dx1*$dx2 < 0 || $dy1*$dy2 < 0} {
# point 0 is the middle point
return 0
} elseif {($dx1*$dx1 + $dy1*$dy1) < ($dx2*$dx2