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OpenSceneGraph/src/osg/Matrix_implementation.cpp
Robert Osfield a799cdca2f From Tim Daust, "I fixed the getScale functions in matrixf and 
matrixd.  It was returning the values of the diagonal
of the matrix, which only returns the scale if there
is not a rotation.  I fixed this by returning the
length of the  vectors that form the basis.
  I also added a function to orthonormalize the
rotation component of the matrix. I seem to always run
into situations where non uniform (or even uniform)
scale complicate my calculations, and I thought other
members of the community could use this function as
well."
2005-05-31 06:21:16 +00:00

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/* -*-c++-*- OpenSceneGraph - Copyright (C) 1998-2005 Robert Osfield
*
* This library is open source and may be redistributed and/or modified under
* the terms of the OpenSceneGraph Public License (OSGPL) version 0.0 or
* (at your option) any later version. The full license is in LICENSE file
* included with this distribution, and on the openscenegraph.org website.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* OpenSceneGraph Public License for more details.
*/
#include <osg/Quat>
#include <osg/Notify>
#include <osg/Math>
#include <osg/Timer>
#include <osg/GL>
#include <stdlib.h>
using namespace osg;
#define SET_ROW(row, v1, v2, v3, v4 ) \
_mat[(row)][0] = (v1); \
_mat[(row)][1] = (v2); \
_mat[(row)][2] = (v3); \
_mat[(row)][3] = (v4);
#define INNER_PRODUCT(a,b,r,c) \
((a)._mat[r][0] * (b)._mat[0][c]) \
+((a)._mat[r][1] * (b)._mat[1][c]) \
+((a)._mat[r][2] * (b)._mat[2][c]) \
+((a)._mat[r][3] * (b)._mat[3][c])
Matrix_implementation::Matrix_implementation( value_type a00, value_type a01, value_type a02, value_type a03,
value_type a10, value_type a11, value_type a12, value_type a13,
value_type a20, value_type a21, value_type a22, value_type a23,
value_type a30, value_type a31, value_type a32, value_type a33)
{
SET_ROW(0, a00, a01, a02, a03 )
SET_ROW(1, a10, a11, a12, a13 )
SET_ROW(2, a20, a21, a22, a23 )
SET_ROW(3, a30, a31, a32, a33 )
}
void Matrix_implementation::set( value_type a00, value_type a01, value_type a02, value_type a03,
value_type a10, value_type a11, value_type a12, value_type a13,
value_type a20, value_type a21, value_type a22, value_type a23,
value_type a30, value_type a31, value_type a32, value_type a33)
{
SET_ROW(0, a00, a01, a02, a03 )
SET_ROW(1, a10, a11, a12, a13 )
SET_ROW(2, a20, a21, a22, a23 )
SET_ROW(3, a30, a31, a32, a33 )
}
#define QX q._v[0]
#define QY q._v[1]
#define QZ q._v[2]
#define QW q._v[3]
void Matrix_implementation::set(const Quat& q_in)
{
Quat q(q_in);
double length2 = q.length2();
if (length2!=1.0 && length2!=0)
{
// normalize quat if required.
q /= sqrt(length2);
}
// Source: Gamasutra, Rotating Objects Using Quaternions
//
//http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
double wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// calculate coefficients
x2 = QX + QX;
y2 = QY + QY;
z2 = QZ + QZ;
xx = QX * x2;
xy = QX * y2;
xz = QX * z2;
yy = QY * y2;
yz = QY * z2;
zz = QZ * z2;
wx = QW * x2;
wy = QW * y2;
wz = QW * z2;
// Note. Gamasutra gets the matrix assignments inverted, resulting
// in left-handed rotations, which is contrary to OpenGL and OSG's
// methodology. The matrix assignment has been altered in the next
// few lines of code to do the right thing.
// Don Burns - Oct 13, 2001
_mat[0][0] = 1.0 - (yy + zz);
_mat[1][0] = xy - wz;
_mat[2][0] = xz + wy;
_mat[3][0] = 0.0;
_mat[0][1] = xy + wz;
_mat[1][1] = 1.0 - (xx + zz);
_mat[2][1] = yz - wx;
_mat[3][1] = 0.0;
_mat[0][2] = xz - wy;
_mat[1][2] = yz + wx;
_mat[2][2] = 1.0 - (xx + yy);
_mat[3][2] = 0.0;
_mat[0][3] = 0.0;
_mat[1][3] = 0.0;
_mat[2][3] = 0.0;
_mat[3][3] = 1.0;
}
void Matrix_implementation::get( Quat& q ) const
{
// Source: Gamasutra, Rotating Objects Using Quaternions
//
//http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
value_type tr, s;
value_type tq[4];
int i, j, k;
int nxt[3] = {1, 2, 0};
tr = _mat[0][0] + _mat[1][1] + _mat[2][2]+1.0;
// check the diagonal
if (tr > 0.0)
{
s = (value_type)sqrt (tr);
QW = s / 2.0;
s = 0.5 / s;
QX = (_mat[1][2] - _mat[2][1]) * s;
QY = (_mat[2][0] - _mat[0][2]) * s;
QZ = (_mat[0][1] - _mat[1][0]) * s;
}
else
{
// diagonal is negative
i = 0;
if (_mat[1][1] > _mat[0][0])
i = 1;
if (_mat[2][2] > _mat[i][i])
i = 2;
j = nxt[i];
k = nxt[j];
s = (value_type)sqrt ((_mat[i][i] - (_mat[j][j] + _mat[k][k])) + 1.0);
tq[i] = s * 0.5;
if (s != 0.0)
s = 0.5 / s;
tq[3] = (_mat[j][k] - _mat[k][j]) * s;
tq[j] = (_mat[i][j] + _mat[j][i]) * s;
tq[k] = (_mat[i][k] + _mat[k][i]) * s;
QX = tq[0];
QY = tq[1];
QZ = tq[2];
QW = tq[3];
}
}
int Matrix_implementation::compare(const Matrix_implementation& m) const
{
const Matrix_implementation::value_type* lhs = reinterpret_cast<const Matrix_implementation::value_type*>(_mat);
const Matrix_implementation::value_type* end_lhs = lhs+16;
const Matrix_implementation::value_type* rhs = reinterpret_cast<const Matrix_implementation::value_type*>(m._mat);
for(;lhs!=end_lhs;++lhs,++rhs)
{
if (*lhs < *rhs) return -1;
if (*rhs < *lhs) return 1;
}
return 0;
}
void Matrix_implementation::setTrans( value_type tx, value_type ty, value_type tz )
{
_mat[3][0] = tx;
_mat[3][1] = ty;
_mat[3][2] = tz;
}
void Matrix_implementation::setTrans( const Vec3f& v )
{
_mat[3][0] = v[0];
_mat[3][1] = v[1];
_mat[3][2] = v[2];
}
void Matrix_implementation::setTrans( const Vec3d& v )
{
_mat[3][0] = v[0];
_mat[3][1] = v[1];
_mat[3][2] = v[2];
}
void Matrix_implementation::makeIdentity()
{
SET_ROW(0, 1, 0, 0, 0 )
SET_ROW(1, 0, 1, 0, 0 )
SET_ROW(2, 0, 0, 1, 0 )
SET_ROW(3, 0, 0, 0, 1 )
}
void Matrix_implementation::makeScale( const Vec3f& v )
{
makeScale(v[0], v[1], v[2] );
}
void Matrix_implementation::makeScale( const Vec3d& v )
{
makeScale(v[0], v[1], v[2] );
}
void Matrix_implementation::makeScale( value_type x, value_type y, value_type z )
{
SET_ROW(0, x, 0, 0, 0 )
SET_ROW(1, 0, y, 0, 0 )
SET_ROW(2, 0, 0, z, 0 )
SET_ROW(3, 0, 0, 0, 1 )
}
void Matrix_implementation::makeTranslate( const Vec3f& v )
{
makeTranslate( v[0], v[1], v[2] );
}
void Matrix_implementation::makeTranslate( const Vec3d& v )
{
makeTranslate( v[0], v[1], v[2] );
}
void Matrix_implementation::makeTranslate( value_type x, value_type y, value_type z )
{
SET_ROW(0, 1, 0, 0, 0 )
SET_ROW(1, 0, 1, 0, 0 )
SET_ROW(2, 0, 0, 1, 0 )
SET_ROW(3, x, y, z, 1 )
}
void Matrix_implementation::makeRotate( const Vec3f& from, const Vec3f& to )
{
Quat quat;
quat.makeRotate(from,to);
set(quat);
}
void Matrix_implementation::makeRotate( const Vec3d& from, const Vec3d& to )
{
Quat quat;
quat.makeRotate(from,to);
set(quat);
}
void Matrix_implementation::makeRotate( value_type angle, const Vec3f& axis )
{
Quat quat;
quat.makeRotate( angle, axis);
set(quat);
}
void Matrix_implementation::makeRotate( value_type angle, const Vec3d& axis )
{
Quat quat;
quat.makeRotate( angle, axis);
set(quat);
}
void Matrix_implementation::makeRotate( value_type angle, value_type x, value_type y, value_type z )
{
Quat quat;
quat.makeRotate( angle, x, y, z);
set(quat);
}
void Matrix_implementation::makeRotate( const Quat& quat )
{
set(quat);
}
void Matrix_implementation::makeRotate( value_type angle1, const Vec3f& axis1,
value_type angle2, const Vec3f& axis2,
value_type angle3, const Vec3f& axis3)
{
Quat quat;
quat.makeRotate(angle1, axis1,
angle2, axis2,
angle3, axis3);
set(quat);
}
void Matrix_implementation::makeRotate( value_type angle1, const Vec3d& axis1,
value_type angle2, const Vec3d& axis2,
value_type angle3, const Vec3d& axis3)
{
Quat quat;
quat.makeRotate(angle1, axis1,
angle2, axis2,
angle3, axis3);
set(quat);
}
void Matrix_implementation::mult( const Matrix_implementation& lhs, const Matrix_implementation& rhs )
{
if (&lhs==this)
{
postMult(rhs);
return;
}
if (&rhs==this)
{
preMult(lhs);
return;
}
// PRECONDITION: We assume neither &lhs nor &rhs == this
// if it did, use preMult or postMult instead
_mat[0][0] = INNER_PRODUCT(lhs, rhs, 0, 0);
_mat[0][1] = INNER_PRODUCT(lhs, rhs, 0, 1);
_mat[0][2] = INNER_PRODUCT(lhs, rhs, 0, 2);
_mat[0][3] = INNER_PRODUCT(lhs, rhs, 0, 3);
_mat[1][0] = INNER_PRODUCT(lhs, rhs, 1, 0);
_mat[1][1] = INNER_PRODUCT(lhs, rhs, 1, 1);
_mat[1][2] = INNER_PRODUCT(lhs, rhs, 1, 2);
_mat[1][3] = INNER_PRODUCT(lhs, rhs, 1, 3);
_mat[2][0] = INNER_PRODUCT(lhs, rhs, 2, 0);
_mat[2][1] = INNER_PRODUCT(lhs, rhs, 2, 1);
_mat[2][2] = INNER_PRODUCT(lhs, rhs, 2, 2);
_mat[2][3] = INNER_PRODUCT(lhs, rhs, 2, 3);
_mat[3][0] = INNER_PRODUCT(lhs, rhs, 3, 0);
_mat[3][1] = INNER_PRODUCT(lhs, rhs, 3, 1);
_mat[3][2] = INNER_PRODUCT(lhs, rhs, 3, 2);
_mat[3][3] = INNER_PRODUCT(lhs, rhs, 3, 3);
}
void Matrix_implementation::preMult( const Matrix_implementation& other )
{
// brute force method requiring a copy
//Matrix_implementation tmp(other* *this);
// *this = tmp;
// more efficient method just use a value_type[4] for temporary storage.
value_type t[4];
for(int col=0; col<4; ++col) {
t[0] = INNER_PRODUCT( other, *this, 0, col );
t[1] = INNER_PRODUCT( other, *this, 1, col );
t[2] = INNER_PRODUCT( other, *this, 2, col );
t[3] = INNER_PRODUCT( other, *this, 3, col );
_mat[0][col] = t[0];
_mat[1][col] = t[1];
_mat[2][col] = t[2];
_mat[3][col] = t[3];
}
}
void Matrix_implementation::postMult( const Matrix_implementation& other )
{
// brute force method requiring a copy
//Matrix_implementation tmp(*this * other);
// *this = tmp;
// more efficient method just use a value_type[4] for temporary storage.
value_type t[4];
for(int row=0; row<4; ++row)
{
t[0] = INNER_PRODUCT( *this, other, row, 0 );
t[1] = INNER_PRODUCT( *this, other, row, 1 );
t[2] = INNER_PRODUCT( *this, other, row, 2 );
t[3] = INNER_PRODUCT( *this, other, row, 3 );
SET_ROW(row, t[0], t[1], t[2], t[3] )
}
}
#undef INNER_PRODUCT
// orthoNormalize the 3x3 rotation matrix
void Matrix_implementation::orthoNormalize(const Matrix_implementation& rhs)
{
value_type x_colMag = (rhs._mat[0][0] * rhs._mat[0][0]) + (rhs._mat[1][0] * rhs._mat[1][0]) + (rhs._mat[2][0] * rhs._mat[2][0]);
value_type y_colMag = (rhs._mat[0][1] * rhs._mat[0][1]) + (rhs._mat[1][1] * rhs._mat[1][1]) + (rhs._mat[2][1] * rhs._mat[2][1]);
value_type z_colMag = (rhs._mat[0][2] * rhs._mat[0][2]) + (rhs._mat[1][2] * rhs._mat[1][2]) + (rhs._mat[2][2] * rhs._mat[2][2]);
if(!equivalent((double)x_colMag, 1.0) && !equivalent((double)x_colMag, 0.0))
{
x_colMag = sqrt(x_colMag);
_mat[0][0] = rhs._mat[0][0] / x_colMag;
_mat[1][0] = rhs._mat[1][0] / x_colMag;
_mat[2][0] = rhs._mat[2][0] / x_colMag;
}
else
{
_mat[0][0] = rhs._mat[0][0];
_mat[1][0] = rhs._mat[1][0];
_mat[2][0] = rhs._mat[2][0];
}
if(!equivalent((double)y_colMag, 1.0) && !equivalent((double)y_colMag, 0.0))
{
y_colMag = sqrt(y_colMag);
_mat[0][1] = rhs._mat[0][1] / y_colMag;
_mat[1][1] = rhs._mat[1][1] / y_colMag;
_mat[2][1] = rhs._mat[2][1] / y_colMag;
}
else
{
_mat[0][1] = rhs._mat[0][1];
_mat[1][1] = rhs._mat[1][1];
_mat[2][1] = rhs._mat[2][1];
}
if(!equivalent((double)z_colMag, 1.0) && !equivalent((double)z_colMag, 0.0))
{
z_colMag = sqrt(z_colMag);
_mat[0][2] = rhs._mat[0][2] / z_colMag;
_mat[1][2] = rhs._mat[1][2] / z_colMag;
_mat[2][2] = rhs._mat[2][2] / z_colMag;
}
else
{
_mat[0][2] = rhs._mat[0][2];
_mat[1][2] = rhs._mat[1][2];
_mat[2][2] = rhs._mat[2][2];
}
_mat[3][0] = rhs._mat[3][0];
_mat[3][1] = rhs._mat[3][1];
_mat[3][2] = rhs._mat[3][2];
_mat[0][3] = rhs._mat[0][3];
_mat[1][3] = rhs._mat[1][3];
_mat[2][3] = rhs._mat[2][3];
_mat[3][3] = rhs._mat[3][3];
}
bool Matrix_implementation::invert( const Matrix_implementation& rhs)
{
#if 1
return invert_4x4_new(rhs);
#else
static const osg::Timer& timer = *Timer::instance();
Matrix_implementation a;
Matrix_implementation b;
Timer_t t1 = timer.tick();
a.invert_4x4_new(rhs);
Timer_t t2 = timer.tick();
b.invert_4x4_orig(rhs);
Timer_t t3 = timer.tick();
static double new_time = 0.0;
static double orig_time = 0.0;
static double count = 0.0;
new_time += timer.delta_u(t1,t2);
orig_time += timer.delta_u(t2,t3);
++count;
std::cout<<"Average new="<<new_time/count<<" orig = "<<orig_time/count<<std::endl;
std::cout<<"new matrix invert time="<<timer.delta_u(t1,t2)<<" "<<a<<std::endl;
std::cout<<"orig matrix invert time="<<timer.delta_u(t2,t3)<<" "<<b<<std::endl;
set(b);
return true;
#endif
}
/******************************************
Matrix inversion technique:
Given a matrix mat, we want to invert it.
mat = [ r00 r01 r02 a
r10 r11 r12 b
r20 r21 r22 c
tx ty tz d ]
We note that this matrix can be split into three matrices.
mat = rot * trans * corr, where rot is rotation part, trans is translation part, and corr is the correction due to perspective (if any).
rot = [ r00 r01 r02 0
r10 r11 r12 0
r20 r21 r22 0
0 0 0 1 ]
trans = [ 1 0 0 0
0 1 0 0
0 0 1 0
tx ty tz 1 ]
corr = [ 1 0 0 px
0 1 0 py
0 0 1 pz
0 0 0 s ]
where the elements of corr are obtained from linear combinations of the elements of rot, trans, and mat.
So the inverse is mat' = (trans * corr)' * rot', where rot' must be computed the traditional way, which is easy since it is only a 3x3 matrix.
This problem is simplified if [px py pz s] = [0 0 0 1], which will happen if mat was composed only of rotations, scales, and translations (which is common). In this case, we can ignore corr entirely which saves on a lot of computations.
******************************************/
bool Matrix_implementation::invert_4x4_new( const Matrix_implementation& mat )
{
if (&mat==this)
{
Matrix_implementation tm(mat);
return invert_4x4_new(tm);
}
register value_type r00, r01, r02,
r10, r11, r12,
r20, r21, r22;
// Copy rotation components directly into registers for speed
r00 = mat._mat[0][0]; r01 = mat._mat[0][1]; r02 = mat._mat[0][2];
r10 = mat._mat[1][0]; r11 = mat._mat[1][1]; r12 = mat._mat[1][2];
r20 = mat._mat[2][0]; r21 = mat._mat[2][1]; r22 = mat._mat[2][2];
// Partially compute inverse of rot
_mat[0][0] = r11*r22 - r12*r21;
_mat[0][1] = r02*r21 - r01*r22;
_mat[0][2] = r01*r12 - r02*r11;
// Compute determinant of rot from 3 elements just computed
register value_type one_over_det = 1.0/(r00*_mat[0][0] + r10*_mat[0][1] + r20*_mat[0][2]);
r00 *= one_over_det; r10 *= one_over_det; r20 *= one_over_det; // Saves on later computations
// Finish computing inverse of rot
_mat[0][0] *= one_over_det;
_mat[0][1] *= one_over_det;
_mat[0][2] *= one_over_det;
_mat[0][3] = 0.0;
_mat[1][0] = r12*r20 - r10*r22; // Have already been divided by det
_mat[1][1] = r00*r22 - r02*r20; // same
_mat[1][2] = r02*r10 - r00*r12; // same
_mat[1][3] = 0.0;
_mat[2][0] = r10*r21 - r11*r20; // Have already been divided by det
_mat[2][1] = r01*r20 - r00*r21; // same
_mat[2][2] = r00*r11 - r01*r10; // same
_mat[2][3] = 0.0;
_mat[3][3] = 1.0;
// We no longer need the rxx or det variables anymore, so we can reuse them for whatever we want. But we will still rename them for the sake of clarity.
#define d r22
d = mat._mat[3][3];
if( osg::square(d-1.0) > 1.0e-6 ) // Involves perspective, so we must
{ // compute the full inverse
Matrix_implementation TPinv;
_mat[3][0] = _mat[3][1] = _mat[3][2] = 0.0;
#define px r00
#define py r01
#define pz r02
#define one_over_s one_over_det
#define a r10
#define b r11
#define c r12
a = mat._mat[0][3]; b = mat._mat[1][3]; c = mat._mat[2][3];
px = _mat[0][0]*a + _mat[0][1]*b + _mat[0][2]*c;
py = _mat[1][0]*a + _mat[1][1]*b + _mat[1][2]*c;
pz = _mat[2][0]*a + _mat[2][1]*b + _mat[2][2]*c;
#undef a
#undef b
#undef c
#define tx r10
#define ty r11
#define tz r12
tx = mat._mat[3][0]; ty = mat._mat[3][1]; tz = mat._mat[3][2];
one_over_s = 1.0/(d - (tx*px + ty*py + tz*pz));
tx *= one_over_s; ty *= one_over_s; tz *= one_over_s; // Reduces number of calculations later on
// Compute inverse of trans*corr
TPinv._mat[0][0] = tx*px + 1.0;
TPinv._mat[0][1] = ty*px;
TPinv._mat[0][2] = tz*px;
TPinv._mat[0][3] = -px * one_over_s;
TPinv._mat[1][0] = tx*py;
TPinv._mat[1][1] = ty*py + 1.0;
TPinv._mat[1][2] = tz*py;
TPinv._mat[1][3] = -py * one_over_s;
TPinv._mat[2][0] = tx*pz;
TPinv._mat[2][1] = ty*pz;
TPinv._mat[2][2] = tz*pz + 1.0;
TPinv._mat[2][3] = -pz * one_over_s;
TPinv._mat[3][0] = -tx;
TPinv._mat[3][1] = -ty;
TPinv._mat[3][2] = -tz;
TPinv._mat[3][3] = one_over_s;
preMult(TPinv); // Finish computing full inverse of mat
#undef px
#undef py
#undef pz
#undef one_over_s
#undef d
}
else // Rightmost column is [0; 0; 0; 1] so it can be ignored
{
tx = mat._mat[3][0]; ty = mat._mat[3][1]; tz = mat._mat[3][2];
// Compute translation components of mat'
_mat[3][0] = -(tx*_mat[0][0] + ty*_mat[1][0] + tz*_mat[2][0]);
_mat[3][1] = -(tx*_mat[0][1] + ty*_mat[1][1] + tz*_mat[2][1]);
_mat[3][2] = -(tx*_mat[0][2] + ty*_mat[1][2] + tz*_mat[2][2]);
#undef tx
#undef ty
#undef tz
}
return true;
}
template <class T>
inline T SGL_ABS(T a)
{
return (a >= 0 ? a : -a);
}
#ifndef SGL_SWAP
#define SGL_SWAP(a,b,temp) ((temp)=(a),(a)=(b),(b)=(temp))
#endif
bool Matrix_implementation::invert_4x4_orig( const Matrix_implementation& mat )
{
if (&mat==this) {
Matrix_implementation tm(mat);
return invert_4x4_orig(tm);
}
unsigned int indxc[4], indxr[4], ipiv[4];
unsigned int i,j,k,l,ll;
unsigned int icol = 0;
unsigned int irow = 0;
double temp, pivinv, dum, big;
// copy in place this may be unnecessary
*this = mat;
for (j=0; j<4; j++) ipiv[j]=0;
for(i=0;i<4;i++)
{
big=0.0;
for (j=0; j<4; j++)
if (ipiv[j] != 1)
for (k=0; k<4; k++)
{
if (ipiv[k] == 0)
{
if (SGL_ABS(operator()(j,k)) >= big)
{
big = SGL_ABS(operator()(j,k));
irow=j;
icol=k;
}
}
else if (ipiv[k] > 1)
return false;
}
++(ipiv[icol]);
if (irow != icol)
for (l=0; l<4; l++) SGL_SWAP(operator()(irow,l),
operator()(icol,l),
temp);
indxr[i]=irow;
indxc[i]=icol;
if (operator()(icol,icol) == 0)
return false;
pivinv = 1.0/operator()(icol,icol);
operator()(icol,icol) = 1;
for (l=0; l<4; l++) operator()(icol,l) *= pivinv;
for (ll=0; ll<4; ll++)
if (ll != icol)
{
dum=operator()(ll,icol);
operator()(ll,icol) = 0;
for (l=0; l<4; l++) operator()(ll,l) -= operator()(icol,l)*dum;
}
}
for (int lx=4; lx>0; --lx)
{
if (indxr[lx-1] != indxc[lx-1])
for (k=0; k<4; k++) SGL_SWAP(operator()(k,indxr[lx-1]),
operator()(k,indxc[lx-1]),temp);
}
return true;
}
void Matrix_implementation::makeOrtho(double left, double right,
double bottom, double top,
double zNear, double zFar)
{
// note transpose of Matrix_implementation wr.t OpenGL documentation, since the OSG use post multiplication rather than pre.
double tx = -(right+left)/(right-left);
double ty = -(top+bottom)/(top-bottom);
double tz = -(zFar+zNear)/(zFar-zNear);
SET_ROW(0, 2.0/(right-left), 0.0, 0.0, 0.0 )
SET_ROW(1, 0.0, 2.0/(top-bottom), 0.0, 0.0 )
SET_ROW(2, 0.0, 0.0, -2.0/(zFar-zNear), 0.0 )
SET_ROW(3, tx, ty, tz, 1.0 )
}
bool Matrix_implementation::getOrtho(double& left, double& right,
double& bottom, double& top,
double& zNear, double& zFar) const
{
if (_mat[0][3]!=0.0 || _mat[1][3]!=0.0 || _mat[2][3]!=0.0 || _mat[3][3]!=1.0) return false;
zNear = (_mat[3][2]+1.0) / _mat[2][2];
zFar = (_mat[3][2]-1.0) / _mat[2][2];
left = -(1.0+_mat[3][0]) / _mat[0][0];
right = (1.0-_mat[3][0]) / _mat[0][0];
bottom = -(1.0+_mat[3][1]) / _mat[1][1];
top = (1.0-_mat[3][1]) / _mat[1][1];
return true;
}
void Matrix_implementation::makeFrustum(double left, double right,
double bottom, double top,
double zNear, double zFar)
{
// note transpose of Matrix_implementation wr.t OpenGL documentation, since the OSG use post multiplication rather than pre.
double A = (right+left)/(right-left);
double B = (top+bottom)/(top-bottom);
double C = -(zFar+zNear)/(zFar-zNear);
double D = -2.0*zFar*zNear/(zFar-zNear);
SET_ROW(0, 2.0*zNear/(right-left), 0.0, 0.0, 0.0 )
SET_ROW(1, 0.0, 2.0*zNear/(top-bottom), 0.0, 0.0 )
SET_ROW(2, A, B, C, -1.0 )
SET_ROW(3, 0.0, 0.0, D, 0.0 )
}
bool Matrix_implementation::getFrustum(double& left, double& right,
double& bottom, double& top,
double& zNear, double& zFar) const
{
if (_mat[0][3]!=0.0 || _mat[1][3]!=0.0 || _mat[2][3]!=-1.0 || _mat[3][3]!=0.0) return false;
zNear = _mat[3][2] / (_mat[2][2]-1.0);
zFar = _mat[3][2] / (1.0+_mat[2][2]);
left = zNear * (_mat[2][0]-1.0) / _mat[0][0];
right = zNear * (1.0+_mat[2][0]) / _mat[0][0];
top = zNear * (1.0+_mat[2][1]) / _mat[1][1];
bottom = zNear * (_mat[2][1]-1.0) / _mat[1][1];
return true;
}
void Matrix_implementation::makePerspective(double fovy,double aspectRatio,
double zNear, double zFar)
{
// calculate the appropriate left, right etc.
double tan_fovy = tan(DegreesToRadians(fovy*0.5));
double right = tan_fovy * aspectRatio * zNear;
double left = -right;
double top = tan_fovy * zNear;
double bottom = -top;
makeFrustum(left,right,bottom,top,zNear,zFar);
}
bool Matrix_implementation::getPerspective(double& fovy,double& aspectRatio,
double& zNear, double& zFar) const
{
double right = 0.0;
double left = 0.0;
double top = 0.0;
double bottom = 0.0;
if (getFrustum(left,right,bottom,top,zNear,zFar))
{
fovy = RadiansToDegrees(atan(top/zNear)-atan(bottom/zNear));
aspectRatio = (right-left)/(top-bottom);
return true;
}
return false;
}
void Matrix_implementation::makeLookAt(const Vec3d& eye,const Vec3d& center,const Vec3d& up)
{
Vec3d f(center-eye);
f.normalize();
Vec3d s(f^up);
s.normalize();
Vec3d u(s^f);
u.normalize();
set(
s[0], u[0], -f[0], 0.0,
s[1], u[1], -f[1], 0.0,
s[2], u[2], -f[2], 0.0,
0.0, 0.0, 0.0, 1.0);
preMult(Matrix_implementation::translate(-eye));
}
void Matrix_implementation::getLookAt(Vec3f& eye,Vec3f& center,Vec3f& up,value_type lookDistance) const
{
Matrix_implementation inv;
inv.invert(*this);
eye = osg::Vec3f(0.0,0.0,0.0)*inv;
up = transform3x3(*this,osg::Vec3f(0.0,1.0,0.0));
center = transform3x3(*this,osg::Vec3f(0.0,0.0,-1));
center.normalize();
center = eye + center*lookDistance;
}
void Matrix_implementation::getLookAt(Vec3d& eye,Vec3d& center,Vec3d& up,value_type lookDistance) const
{
Matrix_implementation inv;
inv.invert(*this);
eye = osg::Vec3d(0.0,0.0,0.0)*inv;
up = transform3x3(*this,osg::Vec3d(0.0,1.0,0.0));
center = transform3x3(*this,osg::Vec3d(0.0,0.0,-1));
center.normalize();
center = eye + center*lookDistance;
}
#undef SET_ROW
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