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assimp/include/aiMatrix4x4.inl

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/** @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 void aiMatrix4x4::FromEulerAnglesXYZ(const aiVector3D& blubb)
{
FromEulerAnglesXYZ(blubb.x,blubb.y,blubb.z);
}
// ---------------------------------------------------------------------------
inline void 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 ;
}
// ---------------------------------------------------------------------------
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 &&
c3 <= epsilon && c3 >= -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;
}
// ---------------------------------------------------------------------------
/** 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)
{
const aiVector3D v = from ^ to;
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" */
{
/* ... 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_MATRIX4x4_INL_INC
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