assimp/include/aiQuaternion.h

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Open Asset Import Library (ASSIMP)
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/** @file Quaternion structure, including operators when compiling in C++ */
#ifndef AI_QUATERNION_H_INC
#define AI_QUATERNION_H_INC

#include <math.h>
#include "aiTypes.h"

#ifdef __cplusplus
extern "C" {
#endif

// ---------------------------------------------------------------------------
/** Represents a quaternion in a 4D vector. */
struct aiQuaternion
{
#ifdef __cplusplus
	aiQuaternion() : w(0.0f), x(0.0f), y(0.0f), z(0.0f) {}
	aiQuaternion(float _w, float _x, float _y, float _z) : w(_w), x(_x), y(_y), z(_z) {}

	/** Construct from rotation matrix. Result is undefined if the matrix is not orthonormal. */
	aiQuaternion( const aiMatrix3x3& pRotMatrix);

	/** Construct from euler angles */
	aiQuaternion( float rotx, float roty, float rotz);

	/** Construct from an axis-angle pair */
	aiQuaternion( aiVector3D axis, float angle);

	/** Construct from a normalized quaternion stored in a vec3 */
	aiQuaternion( aiVector3D normalized);

	/** Returns a matrix representation of the quaternion */
	aiMatrix3x3 GetMatrix() const;


	bool operator== (const aiQuaternion& o) const
		{return x == o.x && y == o.y && z == o.z && w == o.w;}

	bool operator!= (const aiQuaternion& o) const
		{return !(*this == o);}

	/** Normalize the quaternion */
	aiQuaternion& Normalize();

	/** Multiply two quaternions */
	aiQuaternion operator* (const aiQuaternion& two) const;

	/** Performs a spherical interpolation between two quaternions and writes the result into the third.
	 * @param pOut Target object to received the interpolated rotation.
	 * @param pStart Start rotation of the interpolation at factor == 0.
	 * @param pEnd End rotation, factor == 1.
	 * @param pFactor Interpolation factor between 0 and 1. Values outside of this range yield undefined results.
	 */
	static void Interpolate( aiQuaternion& pOut, const aiQuaternion& pStart, const aiQuaternion& pEnd, float pFactor);

#endif // __cplusplus

	//! w,x,y,z components of the quaternion
	float w, x, y, z;	
} ;


#ifdef __cplusplus

// ---------------------------------------------------------------------------
// Constructs a quaternion from a rotation matrix
inline aiQuaternion::aiQuaternion( const aiMatrix3x3 &pRotMatrix)
{
	float t = 1 + pRotMatrix.a1 + pRotMatrix.b2 + pRotMatrix.c3;

	// large enough
	if( t > 0.001f)
	{
		float s = sqrt( t) * 2.0f;
		x = (pRotMatrix.b3 - pRotMatrix.c2) / s;
		y = (pRotMatrix.c1 - pRotMatrix.a3) / s;
		z = (pRotMatrix.a2 - pRotMatrix.b1) / s;
		w = 0.25f * s;
	} // else we have to check several cases
	else if( pRotMatrix.a1 > pRotMatrix.b2 && pRotMatrix.a1 > pRotMatrix.c3 )  
	{	
    // Column 0: 
		float s = sqrt( 1.0f + pRotMatrix.a1 - pRotMatrix.b2 - pRotMatrix.c3) * 2.0f;
		x = 0.25f * s;
		y = (pRotMatrix.a2 + pRotMatrix.b1) / s;
		z = (pRotMatrix.c1 + pRotMatrix.a3) / s;
		w = (pRotMatrix.b3 - pRotMatrix.c2) / s;
	} 
	else if( pRotMatrix.b2 > pRotMatrix.c3) 
	{ 
    // Column 1: 
		float s = sqrt( 1.0f + pRotMatrix.b2 - pRotMatrix.a1 - pRotMatrix.c3) * 2.0f;
		x = (pRotMatrix.a2 + pRotMatrix.b1) / s;
		y = 0.25f * s;
		z = (pRotMatrix.b3 + pRotMatrix.c2) / s;
		w = (pRotMatrix.c1 - pRotMatrix.a3) / s;
	} else 
	{ 
    // Column 2:
		float s = sqrt( 1.0f + pRotMatrix.c3 - pRotMatrix.a1 - pRotMatrix.b2) * 2.0f;
		x = (pRotMatrix.c1 + pRotMatrix.a3) / s;
		y = (pRotMatrix.b3 + pRotMatrix.c2) / s;
		z = 0.25f * s;
		w = (pRotMatrix.a2 - pRotMatrix.b1) / s;
	}
}

// ---------------------------------------------------------------------------
// Construction from euler angles
inline aiQuaternion::aiQuaternion( float fPitch, float fYaw, float fRoll )
{
	const float fSinPitch(sin(fPitch*0.5F));
	const float fCosPitch(cos(fPitch*0.5F));
	const float fSinYaw(sin(fYaw*0.5F));
	const float fCosYaw(cos(fYaw*0.5F));
	const float fSinRoll(sin(fRoll*0.5F));
	const float fCosRoll(cos(fRoll*0.5F));
	const float fCosPitchCosYaw(fCosPitch*fCosYaw);
	const float fSinPitchSinYaw(fSinPitch*fSinYaw);
	x = fSinRoll * fCosPitchCosYaw     - fCosRoll * fSinPitchSinYaw;
	y = fCosRoll * fSinPitch * fCosYaw + fSinRoll * fCosPitch * fSinYaw;
	z = fCosRoll * fCosPitch * fSinYaw - fSinRoll * fSinPitch * fCosYaw;
	w = fCosRoll * fCosPitchCosYaw     + fSinRoll * fSinPitchSinYaw;
}

// ---------------------------------------------------------------------------
// Returns a matrix representation of the quaternion
inline aiMatrix3x3 aiQuaternion::GetMatrix() const
{
	aiMatrix3x3 resMatrix;
	resMatrix.a1 = 1.0f - 2.0f * (y * y + z * z);
	resMatrix.a2 = 2.0f * (x * y + z * w);
	resMatrix.a3 = 2.0f * (x * z - y * w);
	resMatrix.b1 = 2.0f * (x * y - z * w);
	resMatrix.b2 = 1.0f - 2.0f * (x * x + z * z);
	resMatrix.b3 = 2.0f * (y * z + x * w);
	resMatrix.c1 = 2.0f * (x * z + y * w);
	resMatrix.c2 = 2.0f * (y * z - x * w);
	resMatrix.c3 = 1.0f - 2.0f * (x * x + y * y);

	return resMatrix;
}

// ---------------------------------------------------------------------------
// Construction from an axis-angle pair
inline aiQuaternion::aiQuaternion( aiVector3D axis, float angle)
{
	axis.Normalize();

	const float sin_a = sin( angle / 2 );
    const float cos_a = cos( angle / 2 );
    x    = axis.x * sin_a;
    y    = axis.y * sin_a;
    z    = axis.z * sin_a;
    w    = cos_a;
}
// ---------------------------------------------------------------------------
// Construction from am existing, normalized quaternion
inline aiQuaternion::aiQuaternion( aiVector3D normalized)
{
	x = normalized.x;
	y = normalized.y;
	z = normalized.z;

	float t = 1.0f - (normalized.x * normalized.x) - 
		(normalized.y * normalized.y) - (normalized.z * normalized.z);

	if (t < 0.0f)
		w = 0.0f;
	else w = sqrt (t);

}

// ---------------------------------------------------------------------------
// Performs a spherical interpolation between two quaternions 
// Implementation adopted from the gmtl project. All others I found on the net fail in some cases.
// Congrats, gmtl!
inline void aiQuaternion::Interpolate( aiQuaternion& pOut, const aiQuaternion& pStart, const aiQuaternion& pEnd, float pFactor)
{
  // calc cosine theta
  float cosom = pStart.x * pEnd.x + pStart.y * pEnd.y + pStart.z * pEnd.z + pStart.w * pEnd.w;

  // adjust signs (if necessary)
  aiQuaternion end = pEnd;
  if( cosom < 0.0f)
  {
    cosom = -cosom;
    end.x = -end.x;   // Reverse all signs
    end.y = -end.y;
    end.z = -end.z;
    end.w = -end.w;
  } 

  // Calculate coefficients
  float sclp, sclq;
  if( (1.0f - cosom) > 0.0001f) // 0.0001 -> some epsillon
  {
    // Standard case (slerp)
    float omega, sinom;
    omega = acos( cosom); // extract theta from dot product's cos theta
    sinom = sin( omega);
    sclp  = sin( (1.0f - pFactor) * omega) / sinom;
    sclq  = sin( pFactor * omega) / sinom;
  } else
  {
    // Very close, do linear interp (because it's faster)
    sclp = 1.0f - pFactor;
    sclq = pFactor;
  }

  pOut.x = sclp * pStart.x + sclq * end.x;
  pOut.y = sclp * pStart.y + sclq * end.y;
  pOut.z = sclp * pStart.z + sclq * end.z;
  pOut.w = sclp * pStart.w + sclq * end.w;
}

// ---------------------------------------------------------------------------
inline aiQuaternion& aiQuaternion::Normalize()
{
	// compute the magnitude and divide through it
	const float mag = x*x+y*y+z*z+w*w;
	if (mag)
	{
		x /= mag;
		y /= mag;
		z /= mag;
		w /= mag;
	}
	return *this;
}

// ---------------------------------------------------------------------------
inline aiQuaternion aiQuaternion::operator* (const aiQuaternion& t) const
{
	return aiQuaternion(w*t.w - x*t.x - y*t.y - z*t.z,
		w*t.x + x*t.w + y*t.z - z*t.y,
		w*t.y + y*t.w + z*t.x - x*t.z,
		w*t.z + z*t.w + x*t.y - y*t.x);
}

} // end extern "C"
#endif // __cplusplus

#endif // AI_QUATERNION_H_INC