/* 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 . */ // Copyright 2010 Michael Smith, all rights reserved. // Derived closely from: /**************************************** * 2D Vector Classes * By Bill Perone (billperone@yahoo.com) * Original: 9-16-2002 * Revised: 19-11-2003 * 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 ****************************************/ #pragma once #include #include template struct Vector2 { T x, y; // trivial ctor constexpr Vector2() : x(0) , y(0) {} // setting ctor constexpr Vector2(const T x0, const T y0) : x(x0) , y(y0) {} // function call operator void operator ()(const T x0, const T y0) { x= x0; y= y0; } // test for equality bool operator ==(const Vector2 &v) const; // test for inequality bool operator !=(const Vector2 &v) const; // negation Vector2 operator -(void) const; // addition Vector2 operator +(const Vector2 &v) const; // subtraction Vector2 operator -(const Vector2 &v) const; // uniform scaling Vector2 operator *(const T num) const; // uniform scaling Vector2 operator /(const T num) const; // addition Vector2 &operator +=(const Vector2 &v); // subtraction Vector2 &operator -=(const Vector2 &v); // uniform scaling Vector2 &operator *=(const T num); // uniform scaling Vector2 &operator /=(const T num); // dot product T operator *(const Vector2 &v) const; // cross product T operator %(const Vector2 &v) const; // computes the angle between this vector and another vector // returns 0 if the vectors are parallel, and M_PI if they are antiparallel float angle(const Vector2 &v2) const; // computes the angle of this vector in radians, from 0 to 2pi, // from a unit vector(1,0); a (1,1) vector's angle is +M_PI/4 float angle(void) 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); } // allow a vector2 to be used as an array, 0 indexed T & operator[](uint8_t i) { T *_v = &x; #if MATH_CHECK_INDEXES assert(i >= 0 && i < 2); #endif return _v[i]; } const T & operator[](uint8_t i) const { const T *_v = &x; #if MATH_CHECK_INDEXES assert(i >= 0 && i < 2); #endif return _v[i]; } // zero the vector void zero() { x = y = 0; } // gets the length of this vector squared float length_squared() const; // gets the length of this vector float length(void) const; // normalizes this vector void normalize(); // returns the normalized vector Vector2 normalized() const; // reflects this vector about n void reflect(const Vector2 &n); // projects this vector onto v void project(const Vector2 &v); // returns this vector projected onto v Vector2 projected(const Vector2 &v); // adjust position by a given bearing (in degrees) and distance void offset_bearing(float bearing, float distance); // given a position p1 and a velocity v1 produce a vector // perpendicular to v1 maximising distance from p1 static Vector2 perpendicular(const Vector2 &pos_delta, const Vector2 &v1); /* * Returns the point closest to p on the line segment (v,w). * * Comments and implementation taken from * http://stackoverflow.com/questions/849211/shortest-distance-between-a-point-and-a-line-segment */ static Vector2 closest_point(const Vector2 &p, const Vector2 &v, const Vector2 &w); /* * Returns the point closest to p on the line segment (0,w). * * this is a simplification of closest point with a general segment, with v=(0,0) */ static Vector2 closest_point(const Vector2 &p, const Vector2 &w); // w1 and w2 define a line segment // p is a point // returns the square of the closest distance between the line segment and the point static float closest_distance_between_line_and_point_squared(const Vector2 &w1, const Vector2 &w2, const Vector2 &p); // w1 and w2 define a line segment // p is a point // returns the closest distance between the line segment and the point static float closest_distance_between_line_and_point(const Vector2 &w1, const Vector2 &w2, const Vector2 &p); // a1->a2 and b2->v2 define two line segments // returns the square of the closest distance between the two line segments static float closest_distance_between_lines_squared(const Vector2 &a1, const Vector2 &a2, const Vector2 &b1, const Vector2 &b2); // w defines a line segment from the origin // p is a point // returns the square of the closest distance between the radial and the point static float closest_distance_between_radial_and_point_squared(const Vector2 &w, const Vector2 &p); // w defines a line segment from the origin // p is a point // returns the closest distance between the radial and the point static float closest_distance_between_radial_and_point(const Vector2 &w, const Vector2 &p); // find the intersection between two line segments // returns true if they intersect, false if they do not // the point of intersection is returned in the intersection argument static bool segment_intersection(const Vector2& seg1_start, const Vector2& seg1_end, const Vector2& seg2_start, const Vector2& seg2_end, Vector2& intersection) WARN_IF_UNUSED; // find the intersection between a line segment and a circle // returns true if they intersect and intersection argument is updated with intersection closest to seg_start static bool circle_segment_intersection(const Vector2& seg_start, const Vector2& seg_end, const Vector2& circle_center, float radius, Vector2& intersection) WARN_IF_UNUSED; // check if a point falls on the line segment from seg_start to seg_end static bool point_on_segment(const Vector2& point, const Vector2& seg_start, const Vector2& seg_end) WARN_IF_UNUSED { const float expected_run = seg_end.x-seg_start.x; const float intersection_run = point.x-seg_start.x; // check slopes are identical: if (fabsf(expected_run) < FLT_EPSILON) { if (fabsf(intersection_run) > FLT_EPSILON) { return false; } } else { const float expected_slope = (seg_end.y-seg_start.y)/expected_run; const float intersection_slope = (point.y-seg_start.y)/intersection_run; if (fabsf(expected_slope - intersection_slope) > FLT_EPSILON) { return false; } } // check for presence in bounding box if (seg_start.x < seg_end.x) { if (point.x < seg_start.x || point.x > seg_end.x) { return false; } } else { if (point.x < seg_end.x || point.x > seg_start.x) { return false; } } if (seg_start.y < seg_end.y) { if (point.y < seg_start.y || point.y > seg_end.y) { return false; } } else { if (point.y < seg_end.y || point.y > seg_start.y) { return false; } } return true; } }; typedef Vector2 Vector2i; typedef Vector2 Vector2ui; typedef Vector2 Vector2l; typedef Vector2 Vector2ul; typedef Vector2 Vector2f;