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/** @file aiMatrix3x3.inl
* @brief Inline implementation of the 3x3 matrix operators
*/
#ifndef AI_MATRIX3x3_INL_INC
#define AI_MATRIX3x3_INL_INC
#include "aiMatrix3x3.h"
#ifdef __cplusplus
#include "aiMatrix4x4.h"
#include <algorithm>
#include <limits>
// ------------------------------------------------------------------------------------------------
// Construction from a 4x4 matrix. The remaining parts of the matrix are ignored.
inline aiMatrix3x3::aiMatrix3x3( const aiMatrix4x4& pMatrix)
{
a1 = pMatrix.a1; a2 = pMatrix.a2; a3 = pMatrix.a3;
b1 = pMatrix.b1; b2 = pMatrix.b2; b3 = pMatrix.b3;
c1 = pMatrix.c1; c2 = pMatrix.c2; c3 = pMatrix.c3;
}
// ------------------------------------------------------------------------------------------------
inline aiMatrix3x3& aiMatrix3x3::operator *= (const aiMatrix3x3& m)
{
*this = aiMatrix3x3(m.a1 * a1 + m.b1 * a2 + m.c1 * a3,
m.a2 * a1 + m.b2 * a2 + m.c2 * a3,
m.a3 * a1 + m.b3 * a2 + m.c3 * a3,
m.a1 * b1 + m.b1 * b2 + m.c1 * b3,
m.a2 * b1 + m.b2 * b2 + m.c2 * b3,
m.a3 * b1 + m.b3 * b2 + m.c3 * b3,
m.a1 * c1 + m.b1 * c2 + m.c1 * c3,
m.a2 * c1 + m.b2 * c2 + m.c2 * c3,
m.a3 * c1 + m.b3 * c2 + m.c3 * c3);
return *this;
}
// ------------------------------------------------------------------------------------------------
inline aiMatrix3x3 aiMatrix3x3::operator* (const aiMatrix3x3& m) const
{
aiMatrix3x3 temp( *this);
temp *= m;
return temp;
}
// ------------------------------------------------------------------------------------------------
inline float* aiMatrix3x3::operator[] (unsigned int p_iIndex)
{
return &this->a1 + p_iIndex * 3;
}
// ------------------------------------------------------------------------------------------------
inline const float* aiMatrix3x3::operator[] (unsigned int p_iIndex) const
{
return &this->a1 + p_iIndex * 3;
}
// ------------------------------------------------------------------------------------------------
inline bool aiMatrix3x3::operator== (const aiMatrix4x4 m) const
{
return a1 == m.a1 && a2 == m.a2 && a3 == m.a3 &&
b1 == m.b1 && b2 == m.b2 && b3 == m.b3 &&
c1 == m.c1 && c2 == m.c2 && c3 == m.c3;
}
// ------------------------------------------------------------------------------------------------
inline bool aiMatrix3x3::operator!= (const aiMatrix4x4 m) const
{
return !(*this == m);
}
// ------------------------------------------------------------------------------------------------
inline aiMatrix3x3& aiMatrix3x3::Transpose()
{
// (float&) don't remove, GCC complains cause of packed fields
std::swap( (float&)a2, (float&)b1);
std::swap( (float&)a3, (float&)c1);
std::swap( (float&)b3, (float&)c2);
return *this;
}
// ----------------------------------------------------------------------------------------
inline float aiMatrix3x3::Determinant() const
{
return a1*b2*c3 - a1*b3*c2 + a2*b3*c1 - a2*b1*c3 + a3*b1*c2 - a3*b2*c1;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix3x3& aiMatrix3x3::Inverse()
{
// Compute the reciprocal determinant
float det = Determinant();
if(det == 0.0f)
{
// Matrix not invertible. Setting all elements to nan is not really
// correct in a mathematical sense but it is easy to debug for the
// programmer.
const float nan = std::numeric_limits<float>::quiet_NaN();
*this = aiMatrix3x3( nan,nan,nan,nan,nan,nan,nan,nan,nan);
return *this;
}
float invdet = 1.0f / det;
aiMatrix3x3 res;
res.a1 = invdet * (b2 * c3 - b3 * c2);
res.a2 = -invdet * (a2 * c3 - a3 * c2);
res.a3 = invdet * (a2 * b3 - a3 * b2);
res.b1 = -invdet * (b1 * c3 - b3 * c1);
res.b2 = invdet * (a1 * c3 - a3 * c1);
res.b3 = -invdet * (a1 * b3 - a3 * b1);
res.c1 = invdet * (b1 * c2 - b2 * c1);
res.c2 = -invdet * (a1 * c2 - a2 * c1);
res.c3 = invdet * (a1 * b2 - a2 * b1);
*this = res;
return *this;
}
// ------------------------------------------------------------------------------------------------
inline aiMatrix3x3& aiMatrix3x3::RotationZ(float a, aiMatrix3x3& out)
{
out.a1 = out.b2 = ::cos(a);
out.b1 = ::sin(a);
out.a2 = - out.b1;
out.a3 = out.b3 = out.c1 = out.c2 = 0.f;
out.c3 = 1.f;
return out;
}
// ------------------------------------------------------------------------------------------------
// Returns a rotation matrix for a rotation around an arbitrary axis.
inline aiMatrix3x3& aiMatrix3x3::Rotation( float a, const aiVector3D& axis, aiMatrix3x3& out)
{
float c = cos( a), s = sin( a), t = 1 - c;
float x = axis.x, y = axis.y, z = axis.z;
// Many thanks to MathWorld and Wikipedia
out.a1 = t*x*x + c; out.a2 = t*x*y - s*z; out.a3 = t*x*z + s*y;
out.b1 = t*x*y + s*z; out.b2 = t*y*y + c; out.b3 = t*y*z - s*x;
out.c1 = t*x*z - s*y; out.c2 = t*y*z + s*x; out.c3 = t*z*z + c;
return out;
}
// ------------------------------------------------------------------------------------------------
inline aiMatrix3x3& aiMatrix3x3::Translation( const aiVector2D& v, aiMatrix3x3& out)
{
out = aiMatrix3x3();
out.a3 = v.x;
out.b3 = v.y;
return out;
}
// ----------------------------------------------------------------------------------------
/** A function for creating a rotation matrix that rotates a vector called
* "from" into another vector called "to".
* Input : from[3], to[3] which both must be *normalized* non-zero vectors
* Output: mtx[3][3] -- a 3x3 matrix in colum-major form
* Authors: Tomas Möller, John Hughes
* "Efficiently Building a Matrix to Rotate One Vector to Another"
* Journal of Graphics Tools, 4(4):1-4, 1999
*/
// ----------------------------------------------------------------------------------------
inline aiMatrix3x3& aiMatrix3x3::FromToMatrix(const aiVector3D& from,
const aiVector3D& to, aiMatrix3x3& mtx)
{
const float e = from * to;
const float f = (e < 0)? -e:e;
if (f > 1.0 - 0.00001f) /* "from" and "to"-vector almost parallel */
{
aiVector3D u,v; /* temporary storage vectors */
aiVector3D x; /* vector most nearly orthogonal to "from" */
x.x = (from.x > 0.0)? from.x : -from.x;
x.y = (from.y > 0.0)? from.y : -from.y;
x.z = (from.z > 0.0)? from.z : -from.z;
if (x.x < x.y)
{
if (x.x < x.z)
{
x.x = 1.0; x.y = x.z = 0.0;
}
else
{
x.z = 1.0; x.y = x.z = 0.0;
}
}
else
{
if (x.y < x.z)
{
x.y = 1.0; x.x = x.z = 0.0;
}
else
{
x.z = 1.0; x.x = x.y = 0.0;
}
}
u.x = x.x - from.x; u.y = x.y - from.y; u.z = x.z - from.z;
v.x = x.x - to.x; v.y = x.y - to.y; v.z = x.z - to.z;
const float c1 = 2.0f / (u * u);
const float c2 = 2.0f / (v * v);
const float c3 = c1 * c2 * (u * v);
for (unsigned int i = 0; i < 3; i++)
{
for (unsigned int j = 0; j < 3; j++)
{
mtx[i][j] = - c1 * u[i] * u[j] - c2 * v[i] * v[j]
+ c3 * v[i] * u[j];
}
mtx[i][i] += 1.0;
}
}
else /* the most common case, unless "from"="to", or "from"=-"to" */
{
const aiVector3D v = from ^ to;
/* ... use this hand optimized version (9 mults less) */
const float h = 1.0f/(1.0f + e); /* optimization by Gottfried Chen */
const float hvx = h * v.x;
const float hvz = h * v.z;
const float hvxy = hvx * v.y;
const float hvxz = hvx * v.z;
const float hvyz = hvz * v.y;
mtx[0][0] = e + hvx * v.x;
mtx[0][1] = hvxy - v.z;
mtx[0][2] = hvxz + v.y;
mtx[1][0] = hvxy + v.z;
mtx[1][1] = e + h * v.y * v.y;
mtx[1][2] = hvyz - v.x;
mtx[2][0] = hvxz - v.y;
mtx[2][1] = hvyz + v.x;
mtx[2][2] = e + hvz * v.z;
}
return mtx;
}
#endif // __cplusplus
#endif // AI_MATRIX3x3_INL_INC
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