axmol/chipmunk/include/chipmunk/cpVect.h

/* Copyright (c) 2007 Scott Lembcke
 * 
 * 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.
 */

/// 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;
}

// non-inlined functions

/// Returns the length of v.
cpFloat cpvlength(const cpVect v);

/// Spherical linearly interpolate between v1 and v2.
cpVect cpvslerp(const cpVect v1, const cpVect v2, const cpFloat t);

/// Spherical linearly interpolate between v1 towards v2 by no more than angle a radians
cpVect cpvslerpconst(const cpVect v1, const cpVect v2, const cpFloat a);

/// Returns the unit length vector for the given angle (in radians).
cpVect cpvforangle(const cpFloat a);

/// Returns the angular direction v is pointing in (in radians).
cpFloat cpvtoangle(const cpVect v);

/**
	Returns a string representation of v. Intended mostly for debugging purposes and not production use.
	
	@attention The string points to a static local and is reset every time the function is called.
	If you want to print more than one vector you will have to split up your printing onto separate lines.
*/
char *cpvstr(const cpVect 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);
}

/// Negate a vector.
static inline cpVect
cpvneg(const cpVect v)
{
	return cpv(-v.x, -v.y);
}

/// Subtract two vectors.
static inline cpVect
cpvsub(const cpVect v1, const cpVect v2)
{
	return cpv(v1.x - v2.x, v1.y - v2.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));
}

/// 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);
}

/// 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)
{
	return cpvmult(v, 1.0f/cpvlength(v));
}

/// Returns a normalized copy of v or cpvzero if v was already cpvzero. Protects against divide by zero errors.
static inline cpVect
cpvnormalize_safe(const cpVect v)
{
	return (v.x == 0.0f && v.y == 0.0f ? cpvzero : cpvnormalize(v));
}

/// 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;
}