/* Copyright (c) 2013 Scott Lembcke and Howling Moon Software * * Permission is hereby granted, free of charge, to any person obtaining a copy * of this software and associated documentation files (the "Software"), to deal * in the Software without restriction, including without limitation the rights * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the Software is * furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE * SOFTWARE. */ #ifndef CHIPMUNK_VECT_H #define CHIPMUNK_VECT_H #include "chipmunk_types.h" /// @defgroup cpVect cpVect /// Chipmunk's 2D vector type along with a handy 2D vector math lib. /// @{ /// Constant for the zero vector. static const cpVect cpvzero = {0.0f,0.0f}; /// Convenience constructor for cpVect structs. static inline cpVect cpv(const cpFloat x, const cpFloat y) { cpVect v = {x, y}; return v; } /// Check if two vectors are equal. (Be careful when comparing floating point numbers!) static inline cpBool cpveql(const cpVect v1, const cpVect v2) { return (v1.x == v2.x && v1.y == v2.y); } /// Add two vectors static inline cpVect cpvadd(const cpVect v1, const cpVect v2) { return cpv(v1.x + v2.x, v1.y + v2.y); } /// Subtract two vectors. static inline cpVect cpvsub(const cpVect v1, const cpVect v2) { return cpv(v1.x - v2.x, v1.y - v2.y); } /// Negate a vector. static inline cpVect cpvneg(const cpVect v) { return cpv(-v.x, -v.y); } /// Scalar multiplication. static inline cpVect cpvmult(const cpVect v, const cpFloat s) { return cpv(v.x*s, v.y*s); } /// Vector dot product. static inline cpFloat cpvdot(const cpVect v1, const cpVect v2) { return v1.x*v2.x + v1.y*v2.y; } /// 2D vector cross product analog. /// The cross product of 2D vectors results in a 3D vector with only a z component. /// This function returns the magnitude of the z value. static inline cpFloat cpvcross(const cpVect v1, const cpVect v2) { return v1.x*v2.y - v1.y*v2.x; } /// Returns a perpendicular vector. (90 degree rotation) static inline cpVect cpvperp(const cpVect v) { return cpv(-v.y, v.x); } /// Returns a perpendicular vector. (-90 degree rotation) static inline cpVect cpvrperp(const cpVect v) { return cpv(v.y, -v.x); } /// Returns the vector projection of v1 onto v2. static inline cpVect cpvproject(const cpVect v1, const cpVect v2) { return cpvmult(v2, cpvdot(v1, v2)/cpvdot(v2, v2)); } /// Returns the unit length vector for the given angle (in radians). static inline cpVect cpvforangle(const cpFloat a) { return cpv(cpfcos(a), cpfsin(a)); } /// Returns the angular direction v is pointing in (in radians). static inline cpFloat cpvtoangle(const cpVect v) { return cpfatan2(v.y, v.x); } /// Uses complex number multiplication to rotate v1 by v2. Scaling will occur if v1 is not a unit vector. static inline cpVect cpvrotate(const cpVect v1, const cpVect v2) { return cpv(v1.x*v2.x - v1.y*v2.y, v1.x*v2.y + v1.y*v2.x); } /// Inverse of cpvrotate(). static inline cpVect cpvunrotate(const cpVect v1, const cpVect v2) { return cpv(v1.x*v2.x + v1.y*v2.y, v1.y*v2.x - v1.x*v2.y); } /// Returns the squared length of v. Faster than cpvlength() when you only need to compare lengths. static inline cpFloat cpvlengthsq(const cpVect v) { return cpvdot(v, v); } /// Returns the length of v. static inline cpFloat cpvlength(const cpVect v) { return cpfsqrt(cpvdot(v, v)); } /// Linearly interpolate between v1 and v2. static inline cpVect cpvlerp(const cpVect v1, const cpVect v2, const cpFloat t) { return cpvadd(cpvmult(v1, 1.0f - t), cpvmult(v2, t)); } /// Returns a normalized copy of v. static inline cpVect cpvnormalize(const cpVect v) { // Neat trick I saw somewhere to avoid div/0. return cpvmult(v, 1.0f/(cpvlength(v) + CPFLOAT_MIN)); } /// Spherical linearly interpolate between v1 and v2. static inline cpVect cpvslerp(const cpVect v1, const cpVect v2, const cpFloat t) { cpFloat dot = cpvdot(cpvnormalize(v1), cpvnormalize(v2)); cpFloat omega = cpfacos(cpfclamp(dot, -1.0f, 1.0f)); if(omega < 1e-3){ // If the angle between two vectors is very small, lerp instead to avoid precision issues. return cpvlerp(v1, v2, t); } else { cpFloat denom = 1.0f/cpfsin(omega); return cpvadd(cpvmult(v1, cpfsin((1.0f - t)*omega)*denom), cpvmult(v2, cpfsin(t*omega)*denom)); } } /// Spherical linearly interpolate between v1 towards v2 by no more than angle a radians static inline cpVect cpvslerpconst(const cpVect v1, const cpVect v2, const cpFloat a) { cpFloat dot = cpvdot(cpvnormalize(v1), cpvnormalize(v2)); cpFloat omega = cpfacos(cpfclamp(dot, -1.0f, 1.0f)); return cpvslerp(v1, v2, cpfmin(a, omega)/omega); } /// Clamp v to length len. static inline cpVect cpvclamp(const cpVect v, const cpFloat len) { return (cpvdot(v,v) > len*len) ? cpvmult(cpvnormalize(v), len) : v; } /// Linearly interpolate between v1 towards v2 by distance d. static inline cpVect cpvlerpconst(cpVect v1, cpVect v2, cpFloat d) { return cpvadd(v1, cpvclamp(cpvsub(v2, v1), d)); } /// Returns the distance between v1 and v2. static inline cpFloat cpvdist(const cpVect v1, const cpVect v2) { return cpvlength(cpvsub(v1, v2)); } /// Returns the squared distance between v1 and v2. Faster than cpvdist() when you only need to compare distances. static inline cpFloat cpvdistsq(const cpVect v1, const cpVect v2) { return cpvlengthsq(cpvsub(v1, v2)); } /// Returns true if the distance between v1 and v2 is less than dist. static inline cpBool cpvnear(const cpVect v1, const cpVect v2, const cpFloat dist) { return cpvdistsq(v1, v2) < dist*dist; } /// @} /// @defgroup cpMat2x2 cpMat2x2 /// 2x2 matrix type used for tensors and such. /// @{ // NUKE static inline cpMat2x2 cpMat2x2New(cpFloat a, cpFloat b, cpFloat c, cpFloat d) { cpMat2x2 m = {a, b, c, d}; return m; } static inline cpVect cpMat2x2Transform(cpMat2x2 m, cpVect v) { return cpv(v.x*m.a + v.y*m.b, v.x*m.c + v.y*m.d); } ///@} #endif