diff options
Diffstat (limited to 'content/geometry/circle.cpp')
| -rw-r--r-- | content/geometry/circle.cpp | 33 |
1 files changed, 33 insertions, 0 deletions
diff --git a/content/geometry/circle.cpp b/content/geometry/circle.cpp new file mode 100644 index 0000000..155b55c --- /dev/null +++ b/content/geometry/circle.cpp @@ -0,0 +1,33 @@ +// berechnet die Schnittpunkte von zwei Kreisen +// (Kreise dürfen nicht gleich sein!) +vector<pt> circleIntersection(pt c1, double r1, + pt c2, double r2) { + double d = abs(c1 - c2); + if (d < abs(r1 - r2) || d > abs(r1 + r2)) return {}; + double a = (r1 * r1 - r2 * r2 + d * d) / (2 * d); + pt p = (c2 - c1) * a / d + c1; + if (d == abs(r1 - r2) || d == abs(r1 + r2)) return {p}; + double h = sqrt(r1 * r1 - a * a); + return {p + pt{0, 1} * (c2 - c1) * h / d, + p - pt{0, 1} * (c2 - c1) * h / d}; +} + +// berechnet die Schnittpunkte zwischen +// einem Kreis(Kugel) und einem Strahl (2D und 3D) +vector<pt> circleRayIntersection(pt center, double r, + pt orig, pt dir) { + vector<pt> result; + double a = norm(dir); + double b = 2 * dot(dir, orig - center); + double c = norm(orig - center) - r * r; + double discr = b * b - 4 * a * c; + if (discr >= 0) { + //t in [0, 1] => Schnitt mit Segment [orig, orig + dir] + double t1 = -(b + sqrt(discr)) / (2 * a); + double t2 = -(b - sqrt(discr)) / (2 * a); + if (t1 >= 0) result.push_back(t1 * dir + orig); + if (t2 >= 0 && abs(t1 - t2) > EPS) { + result.push_back(t2 * dir + orig); + }} + return result; +} |