Line circle intersection: Difference between revisions
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*See [https://mathworld.wolfram.com/Circle-LineIntersection.html Wolfram] for the formulae needed.
=={{header|C}}==
{{trans|Go}}
<lang c>#include <math.h>
#include <stdbool.h>
#include <stdio.h>
const double eps = 1e-14;
typedef struct point_t {
double x, y;
} point;
point make_point(double x, double y) {
point p = { x, y };
return p;
}
void print_point(point p) {
double x = p.x;
double y = p.y;
if (x == 0) {
x = 0;
}
if (y == 0) {
y = 0;
}
printf("(%g, %g)", x, y);
}
double sq(double x) {
return x * x;
}
bool within(double x1, double y1, double x2, double y2, double x, double y) {
double d1 = sqrt(sq(x2 - x1) + sq(y2 - y1)); // distance between end-points
double d2 = sqrt(sq(x - x1) + sq(y - y1)); // distance from point to one end
double d3 = sqrt(sq(x2 - x) + sq(y2 - y)); // distance from point to other end
double delta = d1 - d2 - d3;
return fabs(delta) < eps; // true if delta is less than a small tolerance
}
int rxy(double x1, double y1, double x2, double y2, double x, double y, bool segment) {
if (!segment || within(x1, y1, x2, y2, x, y)) {
print_point(make_point(x, y));
return 1;
} else {
return 0;
}
}
double fx(double A, double B, double C, double x) {
return -(A * x + C) / B;
}
double fy(double A, double B, double C, double y) {
return -(B * y + C) / A;
}
// Prints the intersection points (if any) of a circle, center 'cp' with radius 'r',
// and either an infinite line containing the points 'p1' and 'p2'
// or a segment drawn between those points.
void intersects(point p1, point p2, point cp, double r, bool segment) {
double x0 = cp.x, y0 = cp.y;
double x1 = p1.x, y1 = p1.y;
double x2 = p2.x, y2 = p2.y;
double A = y2 - y1;
double B = x1 - x2;
double C = x2 * y1 - x1 * y2;
double a = sq(A) + sq(B);
double b, c, d;
bool bnz = true;
int cnt = 0;
if (fabs(B) >= eps) {
// if B isn't zero or close to it
b = 2 * (A * C + A * B * y0 - sq(B) * x0);
c = sq(C) + 2 * B * C * y0 - sq(B) * (sq(r) - sq(x0) - sq(y0));
} else {
b = 2 * (B * C + A * B * x0 - sq(A) * y0);
c = sq(C) + 2 * A * C * x0 - sq(A) * (sq(r) - sq(x0) - sq(y0));
bnz = false;
}
d = sq(b) - 4 * a * c; // discriminant
if (d < 0) {
// line & circle don't intersect
printf("[]\n");
return;
}
if (d == 0) {
// line is tangent to circle, so just one intersect at most
if (bnz) {
double x = -b / (2 * a);
double y = fx(A, B, C, x);
cnt = rxy(x1, y1, x2, y2, x, y, segment);
} else {
double y = -b / (2 * a);
double x = fy(A, B, C, y);
cnt = rxy(x1, y1, x2, y2, x, y, segment);
}
} else {
// two intersects at most
d = sqrt(d);
if (bnz) {
double x = (-b + d) / (2 * a);
double y = fx(A, B, C, x);
cnt = rxy(x1, y1, x2, y2, x, y, segment);
x = (-b - d) / (2 * a);
y = fx(A, B, C, x);
cnt += rxy(x1, y1, x2, y2, x, y, segment);
} else {
double y = (-b + d) / (2 * a);
double x = fy(A, B, C, y);
cnt = rxy(x1, y1, x2, y2, x, y, segment);
y = (-b - d) / (2 * a);
x = fy(A, B, C, y);
cnt += rxy(x1, y1, x2, y2, x, y, segment);
}
}
if (cnt <= 0) {
printf("[]");
}
}
int main() {
point cp = make_point(3, -5);
double r = 3.0;
printf("The intersection points (if any) between:\n");
printf(" A circle, center (3, -5) with radius 3, and:\n");
printf(" a line containing the points (-10, 11) and (10, -9) is/are:\n");
printf(" ");
intersects(make_point(-10, 11), make_point(10, -9), cp, r, false);
printf("\n a segment starting at (-10, 11) and ending at (-11, 12) is/are\n");
printf(" ");
intersects(make_point(-10, 11), make_point(-11, 12), cp, r, true);
printf("\n a horizontal line containing the points (3, -2) and (7, -2) is/are:\n");
printf(" ");
intersects(make_point(3, -2), make_point(7, -2), cp, r, false);
printf("\n");
cp = make_point(0, 0);
r = 4.0;
printf(" A circle, center (0, 0) with radius 4, and:\n");
printf(" a vertical line containing the points (0, -3) and (0, 6) is/are:\n");
printf(" ");
intersects(make_point(0, -3), make_point(0, 6), cp, r, false);
printf("\n a vertical segment starting at (0, -3) and ending at (0, 6) is/are:\n");
printf(" ");
intersects(make_point(0, -3), make_point(0, 6), cp, r, true);
printf("\n");
cp = make_point(4,2);
r = 5.0;
printf(" A circle, center (4, 2) with radius 5, and:\n");
printf(" a line containing the points (6, 3) and (10, 7) is/are:\n");
printf(" ");
intersects(make_point(6, 3), make_point(10, 7), cp, r, false);
printf("\n a segment starting at (7, 4) and ending at (11, 8) is/are:\n");
printf(" ");
intersects(make_point(7, 4), make_point(11, 8), cp, r, true);
printf("\n");
return 0;
}</lang>
{{out}}
<pre>The intersection points (if any) between:
A circle, center (3, -5) with radius 3, and:
a line containing the points (-10, 11) and (10, -9) is/are:
(6, -5)(3, -2)
a segment starting at (-10, 11) and ending at (-11, 12) is/are
[]
a horizontal line containing the points (3, -2) and (7, -2) is/are:
(3, -2)
A circle, center (0, 0) with radius 4, and:
a vertical line containing the points (0, -3) and (0, 6) is/are:
(0, 4)(0, -4)
a vertical segment starting at (0, -3) and ending at (0, 6) is/are:
(0, 4)
A circle, center (4, 2) with radius 5, and:
a line containing the points (6, 3) and (10, 7) is/are:
(8, 5)(1, -2)
a segment starting at (7, 4) and ending at (11, 8) is/are:
(8, 5)</pre>
=={{header|Go}}==
Line 187 ⟶ 374:
[(8, 5)]
</pre>
=={{header|Haskell}}==
<lang haskell>import Data.Tuple.Curry
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