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vcglib/vcg/math/matrix44.h

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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program 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 *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
#ifndef VCG_USE_EIGEN
#include "deprecated_matrix44.h"
#else
#ifndef __VCGLIB_MATRIX44
#define __VCGLIB_MATRIX44
#include "eigen.h"
#include <vcg/space/point3.h>
#include <vcg/space/point4.h>
#include <memory.h>
#include <vector>
namespace vcg{
template<class Scalar> class Matrix44;
}
namespace Eigen{
template<typename Scalar>
struct ei_traits<vcg::Matrix44<Scalar> > : ei_traits<Eigen::Matrix<Scalar,4,4,RowMajor> > {};
}
namespace vcg {
/*
Annotations:
Opengl stores matrix in column-major order. That is, the matrix is stored as:
a0 a4 a8 a12
a1 a5 a9 a13
a2 a6 a10 a14
a3 a7 a11 a15
Usually in opengl (see opengl specs) vectors are 'column' vectors
so usually matrix are PRE-multiplied for a vector.
So the command glTranslate generate a matrix that
is ready to be premultipled for a vector:
1 0 0 tx
0 1 0 ty
0 0 1 tz
0 0 0 1
Matrix44 stores matrix in row-major order i.e.
a0 a1 a2 a3
a4 a5 a6 a7
a8 a9 a10 a11
a12 a13 a14 a15
So for the use of that matrix in opengl with their supposed meaning you have to transpose them before feeding to glMultMatrix.
This mechanism is hidden by the templated function defined in wrap/gl/math.h;
If your machine has the ARB_transpose_matrix extension it will use the appropriate;
The various gl-like command SetRotate, SetTranslate assume that you are making matrix
for 'column' vectors.
*/
/** This class represents a 4x4 matrix. T is the kind of element in the matrix.
*/
template<typename _Scalar>
class Matrix44 : public Eigen::Matrix<_Scalar,4,4,Eigen::RowMajor> // FIXME col or row major !
{
typedef Eigen::Matrix<_Scalar,4,4,Eigen::RowMajor> _Base;
using _Base::coeff;
using _Base::coeffRef;
using _Base::ElementAt;
using _Base::setZero;
public:
_EIGEN_GENERIC_PUBLIC_INTERFACE(Matrix44,_Base);
typedef _Scalar ScalarType;
VCG_EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Matrix44)
Matrix44() : Base() {}
~Matrix44() {}
Matrix44(const Matrix44 &m) : Base(m) {}
Matrix44(const Scalar * v ) : Base(Eigen::Map<Eigen::Matrix<Scalar,4,4,Eigen::RowMajor> >(v)) {}
template<typename OtherDerived>
Matrix44(const Eigen::MatrixBase<OtherDerived>& other) : Base(other) {}
const typename Base::RowXpr operator[](int i) const { return Base::row(i); }
typename Base::RowXpr operator[](int i) { return Base::row(i); }
typename Base::ColXpr GetColumn4(const int& i) const { return Base::col(i); }
const Eigen::Block<Base,3,1> GetColumn3(const int& i) const { return this->template block<3,1>(0,i); }
typename Base::RowXpr GetRow4(const int& i) const { return Base::row(i); }
Eigen::Block<Base,1,3> GetRow3(const int& i) const { return this->template block<1,3>(i,0); }
template <class Matrix44Type>
void ToMatrix(Matrix44Type & m) const { m = (*this).template cast<typename Matrix44Type::Scalar>(); }
void ToEulerAngles(Scalar &alpha, Scalar &beta, Scalar &gamma);
template <class Matrix44Type>
void FromMatrix(const Matrix44Type & m) { for(int i = 0; i < 16; i++) Base::data()[i] = m.data()[i]; }
void FromEulerAngles(Scalar alpha, Scalar beta, Scalar gamma);
void SetDiagonal(const Scalar k);
Matrix44 &SetScale(const Scalar sx, const Scalar sy, const Scalar sz);
Matrix44 &SetScale(const Point3<Scalar> &t);
Matrix44 &SetTranslate(const Point3<Scalar> &t);
Matrix44 &SetTranslate(const Scalar sx, const Scalar sy, const Scalar sz);
Matrix44 &SetShearXY(const Scalar sz);
Matrix44 &SetShearXZ(const Scalar sy);
Matrix44 &SetShearYZ(const Scalar sx);
///use radiants for angle.
Matrix44 &SetRotateDeg(Scalar AngleDeg, const Point3<Scalar> & axis);
Matrix44 &SetRotateRad(Scalar AngleRad, const Point3<Scalar> & axis);
template <class Q> void Import(const Matrix44<Q> &m) {
for(int i = 0; i < 16; i++)
Base::data()[i] = (Scalar)(m.data()[i]);
}
template <class Q>
static inline Matrix44 Construct( const Matrix44<Q> & b )
{
Matrix44 tmp; tmp.FromMatrix(b);
return tmp;
}
};
/** Class for solving A * x = b. */
template <class T> class LinearSolve: public Matrix44<T> {
public:
LinearSolve(const Matrix44<T> &m);
Point4<T> Solve(const Point4<T> &b); // solve A <20> x = b
///If you need to solve some equation you can use this function instead of Matrix44 one for speed.
T Determinant() const;
protected:
///Holds row permutation.
int index[4]; //hold permutation
///Hold sign of row permutation (used for determinant sign)
T d;
bool Decompose();
};
/*** Postmultiply */
//template <class T> Point3<T> operator*(const Point3<T> &p, const Matrix44<T> &m);
///Premultiply
template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p);
//return NULL matrix if not invertible
template <class T> Matrix44<T> &Invert(Matrix44<T> &m);
template <class T> Matrix44<T> Inverse(const Matrix44<T> &m);
typedef Matrix44<short> Matrix44s;
typedef Matrix44<int> Matrix44i;
typedef Matrix44<float> Matrix44f;
typedef Matrix44<double> Matrix44d;
//template <class T> T &Matrix44<T>::operator[](const int i) {
// assert(i >= 0 && i < 16);
// return ((T *)_a)[i];
//}
//
//template <class T> const T &Matrix44<T>::operator[](const int i) const {
// assert(i >= 0 && i < 16);
// return ((T *)_a)[i];
//}
template < class PointType , class T > void operator*=( std::vector<PointType> &vert, const Matrix44<T> & m ) {
typename std::vector<PointType>::iterator ii;
for(ii=vert.begin();ii!=vert.end();++ii)
(*ii).P()=m * (*ii).P();
}
template <class T>
void Matrix44<T>::ToEulerAngles(Scalar &alpha, Scalar &beta, Scalar &gamma)
{
alpha = atan2(coeff(1,2), coeff(2,2));
beta = asin(-coeff(0,2));
gamma = atan2(coeff(0,1), coeff(1,1));
}
template <class T>
void Matrix44<T>::FromEulerAngles(Scalar alpha, Scalar beta, Scalar gamma)
{
this->SetZero();
T cosalpha = cos(alpha);
T cosbeta = cos(beta);
T cosgamma = cos(gamma);
T sinalpha = sin(alpha);
T sinbeta = sin(beta);
T singamma = sin(gamma);
ElementAt(0,0) = cosbeta * cosgamma;
ElementAt(1,0) = -cosalpha * singamma + sinalpha * sinbeta * cosgamma;
ElementAt(2,0) = sinalpha * singamma + cosalpha * sinbeta * cosgamma;
ElementAt(0,1) = cosbeta * singamma;
ElementAt(1,1) = cosalpha * cosgamma + sinalpha * sinbeta * singamma;
ElementAt(2,1) = -sinalpha * cosgamma + cosalpha * sinbeta * singamma;
ElementAt(0,2) = -sinbeta;
ElementAt(1,2) = sinalpha * cosbeta;
ElementAt(2,2) = cosalpha * cosbeta;
ElementAt(3,3) = 1;
}
template <class T> void Matrix44<T>::SetDiagonal(const Scalar k) {
setZero();
ElementAt(0, 0) = k;
ElementAt(1, 1) = k;
ElementAt(2, 2) = k;
ElementAt(3, 3) = 1;
}
template <class T> Matrix44<T> &Matrix44<T>::SetScale(const Point3<Scalar> &t) {
SetScale(t[0], t[1], t[2]);
return *this;
}
template <class T> Matrix44<T> &Matrix44<T>::SetScale(const Scalar sx, const Scalar sy, const Scalar sz) {
setZero();
ElementAt(0, 0) = sx;
ElementAt(1, 1) = sy;
ElementAt(2, 2) = sz;
ElementAt(3, 3) = 1;
return *this;
}
template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const Point3<Scalar> &t) {
SetTranslate(t[0], t[1], t[2]);
return *this;
}
template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const Scalar tx, const Scalar ty, const Scalar tz) {
Base::setIdentity();
ElementAt(0, 3) = tx;
ElementAt(1, 3) = ty;
ElementAt(2, 3) = tz;
return *this;
}
template <class T> Matrix44<T> &Matrix44<T>::SetRotateDeg(Scalar AngleDeg, const Point3<Scalar> & axis) {
return SetRotateRad(math::ToRad(AngleDeg),axis);
}
template <class T> Matrix44<T> &Matrix44<T>::SetRotateRad(Scalar AngleRad, const Point3<Scalar> & axis) {
//angle = angle*(T)3.14159265358979323846/180; e' in radianti!
T c = math::Cos(AngleRad);
T s = math::Sin(AngleRad);
T q = 1-c;
Point3<T> t = axis;
t.Normalize();
ElementAt(0,0) = t[0]*t[0]*q + c;
ElementAt(0,1) = t[0]*t[1]*q - t[2]*s;
ElementAt(0,2) = t[0]*t[2]*q + t[1]*s;
ElementAt(0,3) = 0;
ElementAt(1,0) = t[1]*t[0]*q + t[2]*s;
ElementAt(1,1) = t[1]*t[1]*q + c;
ElementAt(1,2) = t[1]*t[2]*q - t[0]*s;
ElementAt(1,3) = 0;
ElementAt(2,0) = t[2]*t[0]*q -t[1]*s;
ElementAt(2,1) = t[2]*t[1]*q +t[0]*s;
ElementAt(2,2) = t[2]*t[2]*q +c;
ElementAt(2,3) = 0;
ElementAt(3,0) = 0;
ElementAt(3,1) = 0;
ElementAt(3,2) = 0;
ElementAt(3,3) = 1;
return *this;
}
/* Shear Matrixes
XY
1 k 0 0 x x+ky
0 1 0 0 y y
0 0 1 0 z z
0 0 0 1 1 1
1 0 k 0 x x+kz
0 1 0 0 y y
0 0 1 0 z z
0 0 0 1 1 1
1 1 0 0 x x
0 1 k 0 y y+kz
0 0 1 0 z z
0 0 0 1 1 1
*/
template <class T> Matrix44<T> & Matrix44<T>::SetShearXY( const Scalar sh) {// shear the X coordinate as the Y coordinate change
Base::setIdentity();
ElementAt(0,1) = sh;
return *this;
}
template <class T> Matrix44<T> & Matrix44<T>::SetShearXZ( const Scalar sh) {// shear the X coordinate as the Z coordinate change
Base::setIdentity();
ElementAt(0,2) = sh;
return *this;
}
template <class T> Matrix44<T> &Matrix44<T>::SetShearYZ( const Scalar sh) {// shear the Y coordinate as the Z coordinate change
Base::setIdentity();
ElementAt(1,2) = sh;
return *this;
}
/*
Given a non singular, non projective matrix (e.g. with the last row equal to [0,0,0,1] )
This procedure decompose it in a sequence of
Scale,Shear,Rotation e Translation
- ScaleV and Tranv are obiviously scaling and translation.
- ShearV contains three scalars with, respectively
ShearXY, ShearXZ e ShearYZ
- RotateV contains the rotations (in degree!) around the x,y,z axis
The input matrix is modified leaving inside it a simple roto translation.
To obtain the original matrix the above transformation have to be applied in the strict following way:
OriginalMatrix = Trn * Rtx*Rty*Rtz * ShearYZ*ShearXZ*ShearXY * Scl
Example Code:
double srv() { return (double(rand()%40)-20)/2.0; } // small random value
srand(time(0));
Point3d ScV(10+srv(),10+srv(),10+srv()),ScVOut(-1,-1,-1);
Point3d ShV(srv(),srv(),srv()),ShVOut(-1,-1,-1);
Point3d RtV(10+srv(),srv(),srv()),RtVOut(-1,-1,-1);
Point3d TrV(srv(),srv(),srv()),TrVOut(-1,-1,-1);
Matrix44d Scl; Scl.SetScale(ScV);
Matrix44d Sxy; Sxy.SetShearXY(ShV[0]);
Matrix44d Sxz; Sxz.SetShearXZ(ShV[1]);
Matrix44d Syz; Syz.SetShearYZ(ShV[2]);
Matrix44d Rtx; Rtx.SetRotate(math::ToRad(RtV[0]),Point3d(1,0,0));
Matrix44d Rty; Rty.SetRotate(math::ToRad(RtV[1]),Point3d(0,1,0));
Matrix44d Rtz; Rtz.SetRotate(math::ToRad(RtV[2]),Point3d(0,0,1));
Matrix44d Trn; Trn.SetTranslate(TrV);
Matrix44d StartM = Trn * Rtx*Rty*Rtz * Syz*Sxz*Sxy *Scl;
Matrix44d ResultM=StartM;
Decompose(ResultM,ScVOut,ShVOut,RtVOut,TrVOut);
Scl.SetScale(ScVOut);
Sxy.SetShearXY(ShVOut[0]);
Sxz.SetShearXZ(ShVOut[1]);
Syz.SetShearYZ(ShVOut[2]);
Rtx.SetRotate(math::ToRad(RtVOut[0]),Point3d(1,0,0));
Rty.SetRotate(math::ToRad(RtVOut[1]),Point3d(0,1,0));
Rtz.SetRotate(math::ToRad(RtVOut[2]),Point3d(0,0,1));
Trn.SetTranslate(TrVOut);
// Now Rebuild is equal to StartM
Matrix44d RebuildM = Trn * Rtx*Rty*Rtz * Syz*Sxz*Sxy * Scl ;
*/
template <class T>
bool Decompose(Matrix44<T> &M, Point3<T> &ScaleV, Point3<T> &ShearV, Point3<T> &RotV,Point3<T> &TranV)
{
if(!(M(3,0)==0 && M(3,1)==0 && M(3,2)==0 && M(3,3)==1) ) // the matrix is projective
return false;
if(math::Abs(M.Determinant())<1e-10) return false; // matrix should be at least invertible...
// First Step recover the traslation
TranV=M.GetColumn3(3);
// Second Step Recover Scale and Shearing interleaved
ScaleV[0]=Norm(M.GetColumn3(0));
Point3<T> R[3];
R[0]=M.GetColumn3(0);
R[0].Normalize();
ShearV[0]=R[0].dot(M.GetColumn3(1)); // xy shearing
R[1]= M.GetColumn3(1)-R[0]*ShearV[0];
assert(math::Abs(R[1].dot(R[0]))<1e-10);
ScaleV[1]=Norm(R[1]); // y scaling
R[1]=R[1]/ScaleV[1];
ShearV[0]=ShearV[0]/ScaleV[1];
ShearV[1]=R[0].dot(M.GetColumn3(2)); // xz shearing
R[2]= M.GetColumn3(2)-R[0]*ShearV[1];
assert(math::Abs(R[2].dot(R[0]))<1e-10);
R[2] = R[2]-R[1]*(R[2].dot(R[1]));
assert(math::Abs(R[2].dot(R[1]))<1e-10);
assert(math::Abs(R[2].dot(R[0]))<1e-10);
ScaleV[2]=Norm(R[2]);
ShearV[1]=ShearV[1]/ScaleV[2];
R[2]=R[2]/ScaleV[2];
assert(math::Abs(R[2].dot(R[1]))<1e-10);
assert(math::Abs(R[2].dot(R[0]))<1e-10);
ShearV[2]=R[1].dot(M.GetColumn3(2)); // yz shearing
ShearV[2]=ShearV[2]/ScaleV[2];
int i,j;
for(i=0;i<3;++i)
for(j=0;j<3;++j)
M(i,j)=R[j][i];
// Third and last step: Recover the rotation
//now the matrix should be a pure rotation matrix so its determinant is +-1
double det=M.Determinant();
if(math::Abs(det)<1e-10) return false; // matrix should be at least invertible...
assert(math::Abs(math::Abs(det)-1.0)<1e-10); // it should be +-1...
if(det<0) {
ScaleV *= -1;
M *= -1;
}
double alpha,beta,gamma; // rotations around the x,y and z axis
beta=asin( M(0,2));
double cosbeta=cos(beta);
if(math::Abs(cosbeta) > 1e-5)
{
alpha=asin(-M(1,2)/cosbeta);
if((M(2,2)/cosbeta) < 0 ) alpha=M_PI-alpha;
gamma=asin(-M(0,1)/cosbeta);
if((M(0,0)/cosbeta)<0) gamma = M_PI-gamma;
}
else
{
alpha=asin(-M(1,0));
if(M(1,1)<0) alpha=M_PI-alpha;
gamma=0;
}
RotV[0]=math::ToDeg(alpha);
RotV[1]=math::ToDeg(beta);
RotV[2]=math::ToDeg(gamma);
return true;
}
template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p) {
T w;
Point3<T> s;
s[0] = m.ElementAt(0, 0)*p[0] + m.ElementAt(0, 1)*p[1] + m.ElementAt(0, 2)*p[2] + m.ElementAt(0, 3);
s[1] = m.ElementAt(1, 0)*p[0] + m.ElementAt(1, 1)*p[1] + m.ElementAt(1, 2)*p[2] + m.ElementAt(1, 3);
s[2] = m.ElementAt(2, 0)*p[0] + m.ElementAt(2, 1)*p[1] + m.ElementAt(2, 2)*p[2] + m.ElementAt(2, 3);
w = m.ElementAt(3, 0)*p[0] + m.ElementAt(3, 1)*p[1] + m.ElementAt(3, 2)*p[2] + m.ElementAt(3, 3);
if(w!= 0) s /= w;
return s;
}
// template <class T> Point3<T> operator*(const Point3<T> &p, const Matrix44<T> &m) {
// T w;
// Point3<T> s;
// s[0] = m.ElementAt(0, 0)*p[0] + m.ElementAt(1, 0)*p[1] + m.ElementAt(2, 0)*p[2] + m.ElementAt(3, 0);
// s[1] = m.ElementAt(0, 1)*p[0] + m.ElementAt(1, 1)*p[1] + m.ElementAt(2, 1)*p[2] + m.ElementAt(3, 1);
// s[2] = m.ElementAt(0, 2)*p[0] + m.ElementAt(1, 2)*p[1] + m.ElementAt(2, 2)*p[2] + m.ElementAt(3, 2);
// w = m.ElementAt(0, 3)*p[0] + m.ElementAt(1, 3)*p[1] + m.ElementAt(2, 3)*p[2] + m.ElementAt(3, 3);
// if(w != 0) s /= w;
// return s;
// }
/*
To invert a matrix you can
either invert the matrix inplace calling
vcg::Invert(yourMatrix);
or get the inverse matrix of a given matrix without touching it:
invertedMatrix = vcg::Inverse(untouchedMatrix);
*/
template <class T> Matrix44<T> & Invert(Matrix44<T> &m) {
return m = m.lu().inverse();
}
template <class T> Matrix44<T> Inverse(const Matrix44<T> &m) {
return m.lu().inverse();
}
} //namespace
#endif
#endif
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