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cpVect.h
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cpVect.h
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/* 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