337 lines
12 KiB
C++
337 lines
12 KiB
C++
/*
|
||
---------------------------------------------------------------------------
|
||
Open Asset Import Library (assimp)
|
||
---------------------------------------------------------------------------
|
||
|
||
Copyright (c) 2006-2016, assimp team
|
||
|
||
All rights reserved.
|
||
|
||
Redistribution and use of this software in source and binary forms,
|
||
with or without modification, are permitted provided that the following
|
||
conditions are met:
|
||
|
||
* Redistributions of source code must retain the above
|
||
copyright notice, this list of conditions and the
|
||
following disclaimer.
|
||
|
||
* Redistributions in binary form must reproduce the above
|
||
copyright notice, this list of conditions and the
|
||
following disclaimer in the documentation and/or other
|
||
materials provided with the distribution.
|
||
|
||
* Neither the name of the assimp team, nor the names of its
|
||
contributors may be used to endorse or promote products
|
||
derived from this software without specific prior
|
||
written permission of the assimp team.
|
||
|
||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||
---------------------------------------------------------------------------
|
||
*/
|
||
|
||
/** @file matrix3x3.inl
|
||
* @brief Inline implementation of the 3x3 matrix operators
|
||
*/
|
||
#ifndef AI_MATRIX3x3_INL_INC
|
||
#define AI_MATRIX3x3_INL_INC
|
||
|
||
#ifdef __cplusplus
|
||
#include "matrix3x3.h"
|
||
|
||
#include "matrix4x4.h"
|
||
#include <algorithm>
|
||
#include <cmath>
|
||
#include <limits>
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
// Construction from a 4x4 matrix. The remaining parts of the matrix are ignored.
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>::aiMatrix3x3t( const aiMatrix4x4t<TReal>& 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;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::operator *= (const aiMatrix3x3t<TReal>& m)
|
||
{
|
||
*this = aiMatrix3x3t<TReal>(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;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
template <typename TOther>
|
||
aiMatrix3x3t<TReal>::operator aiMatrix3x3t<TOther> () const
|
||
{
|
||
return aiMatrix3x3t<TOther>(static_cast<TOther>(a1),static_cast<TOther>(a2),static_cast<TOther>(a3),
|
||
static_cast<TOther>(b1),static_cast<TOther>(b2),static_cast<TOther>(b3),
|
||
static_cast<TOther>(c1),static_cast<TOther>(c2),static_cast<TOther>(c3));
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal> aiMatrix3x3t<TReal>::operator* (const aiMatrix3x3t<TReal>& m) const
|
||
{
|
||
aiMatrix3x3t<TReal> temp( *this);
|
||
temp *= m;
|
||
return temp;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline TReal* aiMatrix3x3t<TReal>::operator[] (unsigned int p_iIndex)
|
||
{
|
||
return &this->a1 + p_iIndex * 3;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline const TReal* aiMatrix3x3t<TReal>::operator[] (unsigned int p_iIndex) const
|
||
{
|
||
return &this->a1 + p_iIndex * 3;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline bool aiMatrix3x3t<TReal>::operator== (const aiMatrix4x4t<TReal>& 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;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline bool aiMatrix3x3t<TReal>::operator!= (const aiMatrix4x4t<TReal>& m) const
|
||
{
|
||
return !(*this == m);
|
||
}
|
||
|
||
// ---------------------------------------------------------------------------
|
||
template<typename TReal>
|
||
inline bool aiMatrix3x3t<TReal>::Equal(const aiMatrix4x4t<TReal>& m, TReal epsilon) const {
|
||
return
|
||
std::abs(a1 - m.a1) <= epsilon &&
|
||
std::abs(a2 - m.a2) <= epsilon &&
|
||
std::abs(a3 - m.a3) <= epsilon &&
|
||
std::abs(b1 - m.b1) <= epsilon &&
|
||
std::abs(b2 - m.b2) <= epsilon &&
|
||
std::abs(b3 - m.b3) <= epsilon &&
|
||
std::abs(c1 - m.c1) <= epsilon &&
|
||
std::abs(c2 - m.c2) <= epsilon &&
|
||
std::abs(c3 - m.c3) <= epsilon;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Transpose()
|
||
{
|
||
// (TReal&) don't remove, GCC complains cause of packed fields
|
||
std::swap( (TReal&)a2, (TReal&)b1);
|
||
std::swap( (TReal&)a3, (TReal&)c1);
|
||
std::swap( (TReal&)b3, (TReal&)c2);
|
||
return *this;
|
||
}
|
||
|
||
// ----------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline TReal aiMatrix3x3t<TReal>::Determinant() const
|
||
{
|
||
return a1*b2*c3 - a1*b3*c2 + a2*b3*c1 - a2*b1*c3 + a3*b1*c2 - a3*b2*c1;
|
||
}
|
||
|
||
// ----------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Inverse()
|
||
{
|
||
// Compute the reciprocal determinant
|
||
TReal det = Determinant();
|
||
if(det == static_cast<TReal>(0.0))
|
||
{
|
||
// Matrix not invertible. Setting all elements to nan is not really
|
||
// correct in a mathematical sense; but at least qnans are easy to
|
||
// spot. XXX we might throw an exception instead, which would
|
||
// be even much better to spot :/.
|
||
const TReal nan = std::numeric_limits<TReal>::quiet_NaN();
|
||
*this = aiMatrix3x3t<TReal>( nan,nan,nan,nan,nan,nan,nan,nan,nan);
|
||
|
||
return *this;
|
||
}
|
||
|
||
TReal invdet = static_cast<TReal>(1.0) / det;
|
||
|
||
aiMatrix3x3t<TReal> 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;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::RotationZ(TReal a, aiMatrix3x3t<TReal>& out)
|
||
{
|
||
out.a1 = out.b2 = std::cos(a);
|
||
out.b1 = std::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.
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Rotation( TReal a, const aiVector3t<TReal>& axis, aiMatrix3x3t<TReal>& out)
|
||
{
|
||
TReal c = std::cos( a), s = std::sin( a), t = 1 - c;
|
||
TReal 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;
|
||
}
|
||
|
||
// ------------------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Translation( const aiVector2t<TReal>& v, aiMatrix3x3t<TReal>& out)
|
||
{
|
||
out = aiMatrix3x3t<TReal>();
|
||
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 M<>ller, John Hughes
|
||
* "Efficiently Building a Matrix to Rotate One Vector to Another"
|
||
* Journal of Graphics Tools, 4(4):1-4, 1999
|
||
*/
|
||
// ----------------------------------------------------------------------------------------
|
||
template <typename TReal>
|
||
inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::FromToMatrix(const aiVector3t<TReal>& from,
|
||
const aiVector3t<TReal>& to, aiMatrix3x3t<TReal>& mtx)
|
||
{
|
||
const TReal e = from * to;
|
||
const TReal f = (e < 0)? -e:e;
|
||
|
||
if (f > static_cast<TReal>(1.0) - static_cast<TReal>(0.00001)) /* "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 = static_cast<TReal>(1.0);
|
||
x.y = x.z = static_cast<TReal>(0.0);
|
||
}
|
||
else
|
||
{
|
||
x.z = static_cast<TReal>(1.0);
|
||
x.x = x.y = static_cast<TReal>(0.0);
|
||
}
|
||
}
|
||
else
|
||
{
|
||
if (x.y < x.z)
|
||
{
|
||
x.y = static_cast<TReal>(1.0);
|
||
x.x = x.z = static_cast<TReal>(0.0);
|
||
}
|
||
else
|
||
{
|
||
x.z = static_cast<TReal>(1.0);
|
||
x.x = x.y = static_cast<TReal>(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 TReal c1 = static_cast<TReal>(2.0) / (u * u);
|
||
const TReal c2 = static_cast<TReal>(2.0) / (v * v);
|
||
const TReal 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] += static_cast<TReal>(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 TReal h = static_cast<TReal>(1.0)/(static_cast<TReal>(1.0) + e); /* optimization by Gottfried Chen */
|
||
const TReal hvx = h * v.x;
|
||
const TReal hvz = h * v.z;
|
||
const TReal hvxy = hvx * v.y;
|
||
const TReal hvxz = hvx * v.z;
|
||
const TReal 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
|