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#include "geo3d/cross_point.hpp"
#include "geo3d/base.hpp" // 0: 交点なし // 1: 一意な交点 // 2:2 つ以上の交点 template <typename T> int count_cross(Line_3d<T> L1, Line_3d<T> L2) { static_assert(!std::is_floating_point<T>::value); if (L1.is_parallel(L2)) { if (L1.contain(L2.a)) return 2; return 0; } Point_3d<T> norm = L1.d.cross(L2.d); return ((L1.a - L2.a).dot(norm) == 0 ? 1 : 0); } // count_cross == 1 のときにだけ呼ぶこと template <typename REAL, typename T> Point_3d<REAL> cross_point(Line_3d<T> L1, Line_3d<T> L2) { Point_3d<T> d1 = L1.d; Point_3d<T> d2 = L2.d; Point_3d<T> a = L2.a - L1.a; REAL t1 = [&]() -> REAL { FOR(3) { d1 = {d1.y, d1.z, d1.x}; d2 = {d2.y, d2.z, d2.x}; a = {a.y, a.z, a.x}; T det = d1.x * d2.y - d1.y * d2.x; if (det != 0) { return REAL(a.x * d2.y - a.y * d2.x) / REAL(det); } } assert(0); }(); REAL x = REAL(L1.a.x) + t1 * REAL(L1.d.x); REAL y = REAL(L1.a.y) + t1 * REAL(L1.d.y); REAL z = REAL(L1.a.z) + t1 * REAL(L1.d.z); return {x, y, z}; }
#line 2 "geo3d/base.hpp" template <typename T> struct Point_3d { T x, y, z; Point_3d() = default; template <typename A, typename B, typename C> Point_3d(A x, B y, C z) : x(x), y(y), z(z) {} Point_3d operator+(Point_3d p) const { return {x + p.x, y + p.y, z + p.z}; } Point_3d operator-(Point_3d p) const { return {x - p.x, y - p.y, z - p.z}; } Point_3d operator*(T t) const { return {x * t, y * t, z * t}; } bool operator==(Point_3d p) const { return x == p.x && y == p.y && z == p.z; } bool operator!=(Point_3d p) const { return x != p.x || y != p.y || z == p.z; } Point_3d operator-() const { return {-x, -y, -z}; } bool is_parallel(Point_3d p) const { return x * p.y == y * p.x && y * p.z == z * p.y && z * p.x == x * p.z; } T dot(Point_3d other) { return x * other.x + y * other.y + z * other.z; } double norm() { return sqrt(x * x + y * y + z * z); } Point_3d cross(Point_3d other) { return Point_3d(y * other.z - z * other.y, z * other.x - x * other.z, x * other.y - y * other.x); } }; template <typename T> struct Line_3d { // a + td Point_3d<T> a, d; Line_3d(Point_3d<T> A, Point_3d<T> B) : a(A), d(B - A) { assert(d.dot(d) != 0); } bool is_parallel(Line_3d<T> other) { Point_3d<T> n = d.cross(other.d); return (n.x == T(0) && n.y == T(0) && n.z == T(0)); } bool contain(Point_3d<T> p) { p = p - a; p = p.cross(d); return (p.x == T(0) && p.y == T(0) && p.z == T(0)); } }; #line 2 "geo3d/cross_point.hpp" // 0: 交点なし // 1: 一意な交点 // 2:2 つ以上の交点 template <typename T> int count_cross(Line_3d<T> L1, Line_3d<T> L2) { static_assert(!std::is_floating_point<T>::value); if (L1.is_parallel(L2)) { if (L1.contain(L2.a)) return 2; return 0; } Point_3d<T> norm = L1.d.cross(L2.d); return ((L1.a - L2.a).dot(norm) == 0 ? 1 : 0); } // count_cross == 1 のときにだけ呼ぶこと template <typename REAL, typename T> Point_3d<REAL> cross_point(Line_3d<T> L1, Line_3d<T> L2) { Point_3d<T> d1 = L1.d; Point_3d<T> d2 = L2.d; Point_3d<T> a = L2.a - L1.a; REAL t1 = [&]() -> REAL { FOR(3) { d1 = {d1.y, d1.z, d1.x}; d2 = {d2.y, d2.z, d2.x}; a = {a.y, a.z, a.x}; T det = d1.x * d2.y - d1.y * d2.x; if (det != 0) { return REAL(a.x * d2.y - a.y * d2.x) / REAL(det); } } assert(0); }(); REAL x = REAL(L1.a.x) + t1 * REAL(L1.d.x); REAL y = REAL(L1.a.y) + t1 * REAL(L1.d.y); REAL z = REAL(L1.a.z) + t1 * REAL(L1.d.z); return {x, y, z}; }