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#include "geo3d/base.hpp"
#pragma once 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/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)); } };