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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);
return 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}; }
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));
}
};
template <typename T>
struct Plane {
// ax + by + cz == d
T a, b, c, d;
Point_3d<T> normal_vec;
Plane(Point_3d<T> A, Point_3d<T> B, Point_3d<T> C) {
Point_3d<T> AB = B - A;
Point_3d<T> AC = C - A;
normal_vec = AB.cross(AC);
a = normal_vec.x, b = normal_vec.y, c = normal_vec.z;
d = normal_vec.dot(A);
}
int side(Point_3d<T> p) {
T x = normal_vec.dot(p) - d;
if (x == 0) return 0;
return (x > 0 ? 1 : -1);
}
template <typename Re>
Point_3d<Re> cross_point(Line_3d<T> L) {
// a + td
T x = normal_vec.dot(L.a);
T y = normal_vec.dot(L.d);
Re t = Re(d - x) / y;
Point_3d<Re> ANS;
ANS.x = L.a.x + t * L.d.x;
ANS.y = L.a.y + t * L.d.y;
ANS.z = L.a.z + t * L.d.z;
return ANS;
}
};
#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);
return 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};
}