assimp/include/aiMatrix4x4.inl

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/*
---------------------------------------------------------------------------
Open Asset Import Library (ASSIMP)
---------------------------------------------------------------------------
Copyright (c) 2006-2008, ASSIMP Development 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 Development 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 aiMatrix4x4.inl
* @brief Inline implementation of the 4x4 matrix operators
*/
#ifndef AI_MATRIX4x4_INL_INC
#define AI_MATRIX4x4_INL_INC
#include "aiMatrix4x4.h"
#ifdef __cplusplus
#include "aiMatrix3x3.h"
#include <algorithm>
#include <limits>
#include <math.h>
#include "aiAssert.h"
#include "aiQuaternion.h"
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4::aiMatrix4x4( const aiMatrix3x3& m)
{
a1 = m.a1; a2 = m.a2; a3 = m.a3; a4 = 0.0f;
b1 = m.b1; b2 = m.b2; b3 = m.b3; b4 = 0.0f;
c1 = m.c1; c2 = m.c2; c3 = m.c3; c4 = 0.0f;
d1 = 0.0f; d2 = 0.0f; d3 = 0.0f; d4 = 1.0f;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::operator *= (const aiMatrix4x4& m)
{
*this = aiMatrix4x4(
m.a1 * a1 + m.b1 * a2 + m.c1 * a3 + m.d1 * a4,
m.a2 * a1 + m.b2 * a2 + m.c2 * a3 + m.d2 * a4,
m.a3 * a1 + m.b3 * a2 + m.c3 * a3 + m.d3 * a4,
m.a4 * a1 + m.b4 * a2 + m.c4 * a3 + m.d4 * a4,
m.a1 * b1 + m.b1 * b2 + m.c1 * b3 + m.d1 * b4,
m.a2 * b1 + m.b2 * b2 + m.c2 * b3 + m.d2 * b4,
m.a3 * b1 + m.b3 * b2 + m.c3 * b3 + m.d3 * b4,
m.a4 * b1 + m.b4 * b2 + m.c4 * b3 + m.d4 * b4,
m.a1 * c1 + m.b1 * c2 + m.c1 * c3 + m.d1 * c4,
m.a2 * c1 + m.b2 * c2 + m.c2 * c3 + m.d2 * c4,
m.a3 * c1 + m.b3 * c2 + m.c3 * c3 + m.d3 * c4,
m.a4 * c1 + m.b4 * c2 + m.c4 * c3 + m.d4 * c4,
m.a1 * d1 + m.b1 * d2 + m.c1 * d3 + m.d1 * d4,
m.a2 * d1 + m.b2 * d2 + m.c2 * d3 + m.d2 * d4,
m.a3 * d1 + m.b3 * d2 + m.c3 * d3 + m.d3 * d4,
m.a4 * d1 + m.b4 * d2 + m.c4 * d3 + m.d4 * d4);
return *this;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4 aiMatrix4x4::operator* (const aiMatrix4x4& m) const
{
aiMatrix4x4 temp( *this);
temp *= m;
return temp;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::Transpose()
{
// (float&) don't remove, GCC complains cause of packed fields
std::swap( (float&)b1, (float&)a2);
std::swap( (float&)c1, (float&)a3);
std::swap( (float&)c2, (float&)b3);
std::swap( (float&)d1, (float&)a4);
std::swap( (float&)d2, (float&)b4);
std::swap( (float&)d3, (float&)c4);
return *this;
}
// ----------------------------------------------------------------------------------------
inline float aiMatrix4x4::Determinant() const
{
return a1*b2*c3*d4 - a1*b2*c4*d3 + a1*b3*c4*d2 - a1*b3*c2*d4
+ a1*b4*c2*d3 - a1*b4*c3*d2 - a2*b3*c4*d1 + a2*b3*c1*d4
- a2*b4*c1*d3 + a2*b4*c3*d1 - a2*b1*c3*d4 + a2*b1*c4*d3
+ a3*b4*c1*d2 - a3*b4*c2*d1 + a3*b1*c2*d4 - a3*b1*c4*d2
+ a3*b2*c4*d1 - a3*b2*c1*d4 - a4*b1*c2*d3 + a4*b1*c3*d2
- a4*b2*c3*d1 + a4*b2*c1*d3 - a4*b3*c1*d2 + a4*b3*c2*d1;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::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 = aiMatrix4x4(
nan,nan,nan,nan,
nan,nan,nan,nan,
nan,nan,nan,nan,
nan,nan,nan,nan);
return *this;
}
float invdet = 1.0f / det;
aiMatrix4x4 res;
res.a1 = invdet * (b2 * (c3 * d4 - c4 * d3) + b3 * (c4 * d2 - c2 * d4) + b4 * (c2 * d3 - c3 * d2));
res.a2 = -invdet * (a2 * (c3 * d4 - c4 * d3) + a3 * (c4 * d2 - c2 * d4) + a4 * (c2 * d3 - c3 * d2));
res.a3 = invdet * (a2 * (b3 * d4 - b4 * d3) + a3 * (b4 * d2 - b2 * d4) + a4 * (b2 * d3 - b3 * d2));
res.a4 = -invdet * (a2 * (b3 * c4 - b4 * c3) + a3 * (b4 * c2 - b2 * c4) + a4 * (b2 * c3 - b3 * c2));
res.b1 = -invdet * (b1 * (c3 * d4 - c4 * d3) + b3 * (c4 * d1 - c1 * d4) + b4 * (c1 * d3 - c3 * d1));
res.b2 = invdet * (a1 * (c3 * d4 - c4 * d3) + a3 * (c4 * d1 - c1 * d4) + a4 * (c1 * d3 - c3 * d1));
res.b3 = -invdet * (a1 * (b3 * d4 - b4 * d3) + a3 * (b4 * d1 - b1 * d4) + a4 * (b1 * d3 - b3 * d1));
res.b4 = invdet * (a1 * (b3 * c4 - b4 * c3) + a3 * (b4 * c1 - b1 * c4) + a4 * (b1 * c3 - b3 * c1));
res.c1 = invdet * (b1 * (c2 * d4 - c4 * d2) + b2 * (c4 * d1 - c1 * d4) + b4 * (c1 * d2 - c2 * d1));
res.c2 = -invdet * (a1 * (c2 * d4 - c4 * d2) + a2 * (c4 * d1 - c1 * d4) + a4 * (c1 * d2 - c2 * d1));
res.c3 = invdet * (a1 * (b2 * d4 - b4 * d2) + a2 * (b4 * d1 - b1 * d4) + a4 * (b1 * d2 - b2 * d1));
res.c4 = -invdet * (a1 * (b2 * c4 - b4 * c2) + a2 * (b4 * c1 - b1 * c4) + a4 * (b1 * c2 - b2 * c1));
res.d1 = -invdet * (b1 * (c2 * d3 - c3 * d2) + b2 * (c3 * d1 - c1 * d3) + b3 * (c1 * d2 - c2 * d1));
res.d2 = invdet * (a1 * (c2 * d3 - c3 * d2) + a2 * (c3 * d1 - c1 * d3) + a3 * (c1 * d2 - c2 * d1));
res.d3 = -invdet * (a1 * (b2 * d3 - b3 * d2) + a2 * (b3 * d1 - b1 * d3) + a3 * (b1 * d2 - b2 * d1));
res.d4 = invdet * (a1 * (b2 * c3 - b3 * c2) + a2 * (b3 * c1 - b1 * c3) + a3 * (b1 * c2 - b2 * c1));
*this = res;
return *this;
}
// ----------------------------------------------------------------------------------------
inline float* aiMatrix4x4::operator[](unsigned int p_iIndex)
{
return &this->a1 + p_iIndex * 4;
}
// ----------------------------------------------------------------------------------------
inline const float* aiMatrix4x4::operator[](unsigned int p_iIndex) const
{
return &this->a1 + p_iIndex * 4;
}
// ----------------------------------------------------------------------------------------
inline bool aiMatrix4x4::operator== (const aiMatrix4x4 m) const
{
return (a1 == m.a1 && a2 == m.a2 && a3 == m.a3 && a4 == m.a4 &&
b1 == m.b1 && b2 == m.b2 && b3 == m.b3 && b4 == m.b4 &&
c1 == m.c1 && c2 == m.c2 && c3 == m.c3 && c4 == m.c4 &&
d1 == m.d1 && d2 == m.d2 && d3 == m.d3 && d4 == m.d4);
}
// ----------------------------------------------------------------------------------------
inline bool aiMatrix4x4::operator!= (const aiMatrix4x4 m) const
{
return !(*this == m);
}
// ----------------------------------------------------------------------------------------
inline void aiMatrix4x4::Decompose (aiVector3D& scaling, aiQuaternion& rotation,
aiVector3D& position) const
{
const aiMatrix4x4& _this = *this;
// extract translation
position.x = _this[0][3];
position.y = _this[1][3];
position.z = _this[2][3];
// extract the rows of the matrix
aiVector3D vRows[3] = {
aiVector3D(_this[0][0],_this[1][0],_this[2][0]),
aiVector3D(_this[0][1],_this[1][1],_this[2][1]),
aiVector3D(_this[0][2],_this[1][2],_this[2][2])
};
// extract the scaling factors
scaling.x = vRows[0].Length();
scaling.y = vRows[1].Length();
scaling.z = vRows[2].Length();
// and remove all scaling from the matrix
if(scaling.x)
{
vRows[0] /= scaling.x;
}
if(scaling.y)
{
vRows[1] /= scaling.y;
}
if(scaling.z)
{
vRows[2] /= scaling.z;
}
// build a 3x3 rotation matrix
aiMatrix3x3 m(vRows[0].x,vRows[1].x,vRows[2].x,
vRows[0].y,vRows[1].y,vRows[2].y,
vRows[0].z,vRows[1].z,vRows[2].z);
// and generate the rotation quaternion from it
rotation = aiQuaternion(m);
}
// ----------------------------------------------------------------------------------------
inline void aiMatrix4x4::DecomposeNoScaling (aiQuaternion& rotation,
aiVector3D& position) const
{
const aiMatrix4x4& _this = *this;
// extract translation
position.x = _this[0][3];
position.y = _this[1][3];
position.z = _this[2][3];
// extract rotation
rotation = aiQuaternion((aiMatrix3x3)_this);
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::FromEulerAnglesXYZ(const aiVector3D& blubb)
{
return FromEulerAnglesXYZ(blubb.x,blubb.y,blubb.z);
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::FromEulerAnglesXYZ(float x, float y, float z)
{
aiMatrix4x4& _this = *this;
float cr = cos( x );
float sr = sin( x );
float cp = cos( y );
float sp = sin( y );
float cy = cos( z );
float sy = sin( z );
_this.a1 = cp*cy ;
_this.a2 = cp*sy;
_this.a3 = -sp ;
float srsp = sr*sp;
float crsp = cr*sp;
_this.b1 = srsp*cy-cr*sy ;
_this.b2 = srsp*sy+cr*cy ;
_this.b3 = sr*cp ;
_this.c1 = crsp*cy+sr*sy ;
_this.c2 = crsp*sy-sr*cy ;
_this.c3 = cr*cp ;
return *this;
}
// ----------------------------------------------------------------------------------------
inline bool aiMatrix4x4::IsIdentity() const
{
// Use a small epsilon to solve floating-point inaccuracies
const static float epsilon = 10e-3f;
return (a2 <= epsilon && a2 >= -epsilon &&
a3 <= epsilon && a3 >= -epsilon &&
a4 <= epsilon && a4 >= -epsilon &&
b1 <= epsilon && b1 >= -epsilon &&
b3 <= epsilon && b3 >= -epsilon &&
b4 <= epsilon && b4 >= -epsilon &&
c1 <= epsilon && c1 >= -epsilon &&
c2 <= epsilon && c2 >= -epsilon &&
c4 <= epsilon && c4 >= -epsilon &&
d1 <= epsilon && d1 >= -epsilon &&
d2 <= epsilon && d2 >= -epsilon &&
d3 <= epsilon && d3 >= -epsilon &&
a1 <= 1.f+epsilon && a1 >= 1.f-epsilon &&
b2 <= 1.f+epsilon && b2 >= 1.f-epsilon &&
c3 <= 1.f+epsilon && c3 >= 1.f-epsilon &&
d4 <= 1.f+epsilon && d4 >= 1.f-epsilon);
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::RotationX(float a, aiMatrix4x4& out)
{
/*
| 1 0 0 0 |
M = | 0 cos(A) -sin(A) 0 |
| 0 sin(A) cos(A) 0 |
| 0 0 0 1 | */
out = aiMatrix4x4();
out.b2 = out.c3 = cos(a);
out.b3 = -(out.c2 = sin(a));
return out;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::RotationY(float a, aiMatrix4x4& out)
{
/*
| cos(A) 0 sin(A) 0 |
M = | 0 1 0 0 |
| -sin(A) 0 cos(A) 0 |
| 0 0 0 1 |
*/
out = aiMatrix4x4();
out.a1 = out.c3 = cos(a);
out.c1 = -(out.a3 = sin(a));
return out;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::RotationZ(float a, aiMatrix4x4& out)
{
/*
| cos(A) -sin(A) 0 0 |
M = | sin(A) cos(A) 0 0 |
| 0 0 1 0 |
| 0 0 0 1 | */
out = aiMatrix4x4();
out.a1 = out.b2 = cos(a);
out.a2 = -(out.b1 = sin(a));
return out;
}
// ----------------------------------------------------------------------------------------
// Returns a rotation matrix for a rotation around an arbitrary axis.
inline aiMatrix4x4& aiMatrix4x4::Rotation( float a, const aiVector3D& axis, aiMatrix4x4& 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;
out.a4 = out.b4 = out.c4 = 0.0f;
out.d1 = out.d2 = out.d3 = 0.0f;
out.d4 = 1.0f;
return out;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::Translation( const aiVector3D& v, aiMatrix4x4& out)
{
out = aiMatrix4x4();
out.a4 = v.x;
out.b4 = v.y;
out.c4 = v.z;
return out;
}
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::Scaling( const aiVector3D& v, aiMatrix4x4& out)
{
out = aiMatrix4x4();
out.a1 = v.x;
out.b2 = v.y;
out.c3 = v.z;
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
*/
// ----------------------------------------------------------------------------------------
inline aiMatrix4x4& aiMatrix4x4::FromToMatrix(const aiVector3D& from,
const aiVector3D& to, aiMatrix4x4& mtx)
{
aiMatrix3x3 m3;
aiMatrix3x3::FromToMatrix(from,to,m3);
mtx = aiMatrix4x4(m3);
return mtx;
}
#endif // __cplusplus
#endif // AI_MATRIX4x4_INL_INC