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