/* This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>. */ // Copyright 2010 Michael Smith, all rights reserved. // Derived closely from: /**************************************** * 3D Vector Classes * By Bill Perone (billperone@yahoo.com) * Original: 9-16-2002 * Revised: 19-11-2003 * 11-12-2003 * 18-12-2003 * 06-06-2004 * * Copyright 2003, This code is provided "as is" and you can use it freely as long as * credit is given to Bill Perone in the application it is used in * * Notes: * if a*b = 0 then a & b are orthogonal * a%b = -b%a * a*(b%c) = (a%b)*c * a%b = a(cast to matrix)*b * (a%b).length() = area of parallelogram formed by a & b * (a%b).length() = a.length()*b.length() * sin(angle between a & b) * (a%b).length() = 0 if angle between a & b = 0 or a.length() = 0 or b.length() = 0 * a * (b%c) = volume of parallelpiped formed by a, b, c * vector triple product: a%(b%c) = b*(a*c) - c*(a*b) * scalar triple product: a*(b%c) = c*(a%b) = b*(c%a) * vector quadruple product: (a%b)*(c%d) = (a*c)*(b*d) - (a*d)*(b*c) * if a is unit vector along b then a%b = -b%a = -b(cast to matrix)*a = 0 * vectors a1...an are linearly dependent if there exists a vector of scalars (b) where a1*b1 + ... + an*bn = 0 * or if the matrix (A) * b = 0 * ****************************************/ #pragma once #ifndef MATH_CHECK_INDEXES #define MATH_CHECK_INDEXES 0 #endif #include <cmath> #include <float.h> #include <string.h> #if MATH_CHECK_INDEXES #include <assert.h> #endif #include "rotations.h" #include "ftype.h" template <typename T> class Matrix3; template <typename T> class Vector2; template <typename T> class Vector3 { public: T x, y, z; // trivial ctor constexpr Vector3<T>() : x(0) , y(0) , z(0) {} // setting ctor constexpr Vector3<T>(const T x0, const T y0, const T z0) : x(x0) , y(y0) , z(z0) {} //Create a Vector3 from a Vector2 with z constexpr Vector3<T>(const Vector2<T> &v0, const T z0) : x(v0.x) , y(v0.y) , z(z0) {} // test for equality bool operator ==(const Vector3<T> &v) const; // test for inequality bool operator !=(const Vector3<T> &v) const; // negation Vector3<T> operator -(void) const; // addition Vector3<T> operator +(const Vector3<T> &v) const; // subtraction Vector3<T> operator -(const Vector3<T> &v) const; // uniform scaling Vector3<T> operator *(const T num) const; // uniform scaling Vector3<T> operator /(const T num) const; // addition Vector3<T> &operator +=(const Vector3<T> &v); // subtraction Vector3<T> &operator -=(const Vector3<T> &v); // uniform scaling Vector3<T> &operator *=(const T num); // uniform scaling Vector3<T> &operator /=(const T num); // non-uniform scaling Vector3<T> &operator *=(const Vector3<T> &v) { x *= v.x; y *= v.y; z *= v.z; return *this; } // allow a vector3 to be used as an array, 0 indexed T & operator[](uint8_t i) { T *_v = &x; #if MATH_CHECK_INDEXES assert(i >= 0 && i < 3); #endif return _v[i]; } const T & operator[](uint8_t i) const { const T *_v = &x; #if MATH_CHECK_INDEXES assert(i >= 0 && i < 3); #endif return _v[i]; } // dot product T operator *(const Vector3<T> &v) const; // dot product for Lua T dot(const Vector3<T> &v) const { return *this * v; } // multiply a row vector by a matrix, to give a row vector Vector3<T> operator *(const Matrix3<T> &m) const; // multiply a column vector by a row vector, returning a 3x3 matrix Matrix3<T> mul_rowcol(const Vector3<T> &v) const; // cross product Vector3<T> operator %(const Vector3<T> &v) const; // cross product for Lua Vector3<T> cross(const Vector3<T> &v) const { return *this % v; } // scale a vector3 Vector3<T> scale(const T v) const { return *this * v; } // computes the angle between this vector and another vector T angle(const Vector3<T> &v2) const; // check if any elements are NAN bool is_nan(void) const WARN_IF_UNUSED; // check if any elements are infinity bool is_inf(void) const WARN_IF_UNUSED; // check if all elements are zero bool is_zero(void) const WARN_IF_UNUSED { return (fabsf(x) < FLT_EPSILON) && (fabsf(y) < FLT_EPSILON) && (fabsf(z) < FLT_EPSILON); } // rotate by a standard rotation void rotate(enum Rotation rotation); void rotate_inverse(enum Rotation rotation); // rotate vector by angle in radians in xy plane leaving z untouched void rotate_xy(T rotation_rad); // return xy components of a vector3 as a vector2. // this returns a reference to the original vector3 xy data const Vector2<T> &xy() const { return *(const Vector2<T> *)this; } Vector2<T> &xy() { return *(Vector2<T> *)this; } // gets the length of this vector squared T length_squared() const { return (T)(*this * *this); } // gets the length of this vector T length(void) const; // limit xy component vector to a given length. returns true if vector was limited bool limit_length_xy(T max_length); // normalizes this vector void normalize() { *this /= length(); } // zero the vector void zero() { x = y = z = 0; } // returns the normalized version of this vector Vector3<T> normalized() const { return *this/length(); } // reflects this vector about n void reflect(const Vector3<T> &n) { Vector3<T> orig(*this); project(n); *this = *this*2 - orig; } // projects this vector onto v void project(const Vector3<T> &v) { *this= v * (*this * v)/(v*v); } // returns this vector projected onto v Vector3<T> projected(const Vector3<T> &v) const { return v * (*this * v)/(v*v); } // distance from the tip of this vector to another vector squared (so as to avoid the sqrt calculation) T distance_squared(const Vector3<T> &v) const { const T dist_x = x-v.x; const T dist_y = y-v.y; const T dist_z = z-v.z; return (dist_x*dist_x + dist_y*dist_y + dist_z*dist_z); } // distance from the tip of this vector to a line segment specified by two vectors T distance_to_segment(const Vector3<T> &seg_start, const Vector3<T> &seg_end) const; // extrapolate position given bearing and pitch (in degrees) and distance void offset_bearing(T bearing, T pitch, T distance); /* conversion to/from double */ Vector3<float> tofloat() const { return Vector3<float>{float(x),float(y),float(z)}; } Vector3<double> todouble() const { return Vector3<double>{x,y,z}; } // given a position p1 and a velocity v1 produce a vector // perpendicular to v1 maximising distance from p1. If p1 is the // zero vector the return from the function will always be the // zero vector - that should be checked for. static Vector3<T> perpendicular(const Vector3<T> &p1, const Vector3<T> &v1) { const T d = p1 * v1; if (fabsf(d) < FLT_EPSILON) { return p1; } const Vector3<T> parallel = (v1 * d) / v1.length_squared(); Vector3<T> perpendicular = p1 - parallel; return perpendicular; } // Shortest distance between point(p) to a point contained in the line segment defined by w1,w2 static T closest_distance_between_line_and_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p); // Point in the line segment defined by w1,w2 which is closest to point(p) static Vector3<T> point_on_line_closest_to_other_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p); // This implementation is borrowed from: http://geomalgorithms.com/a07-_distance.html // INPUT: 4 points corresponding to start and end of two line segments // OUTPUT: closest point on segment 2, from segment 1, gets passed on reference as "closest_point" static void segment_to_segment_closest_point(const Vector3<T>& seg1_start, const Vector3<T>& seg1_end, const Vector3<T>& seg2_start, const Vector3<T>& seg2_end, Vector3<T>& closest_point); // Returns true if the passed 3D segment passes through a plane defined by plane normal, and a point on the plane static bool segment_plane_intersect(const Vector3<T>& seg_start, const Vector3<T>& seg_end, const Vector3<T>& plane_normal, const Vector3<T>& plane_point); }; typedef Vector3<int16_t> Vector3i; typedef Vector3<uint16_t> Vector3ui; typedef Vector3<int32_t> Vector3l; typedef Vector3<uint32_t> Vector3ul; typedef Vector3<float> Vector3f; typedef Vector3<double> Vector3d;