682 lines
19 KiB
C++
682 lines
19 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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#ifndef __VCGLIB_MATRIX44
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#define __VCGLIB_MATRIX44
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#include <memory.h>
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#include <vcg/math/base.h>
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#include <vcg/space/point3.h>
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#include <vcg/space/point4.h>
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#include <vector>
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#include <iostream>
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#include <eigenlib/Eigen/Core>
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#include <eigenlib/Eigen/LU>
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namespace vcg {
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/*
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Annotations:
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Opengl stores matrix in column-major order. That is, the matrix is stored as:
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a0 a4 a8 a12
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a1 a5 a9 a13
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a2 a6 a10 a14
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a3 a7 a11 a15
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Usually in opengl (see opengl specs) vectors are 'column' vectors
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so usually matrix are PRE-multiplied for a vector.
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So the command glTranslate generate a matrix that
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is ready to be premultipled for a vector:
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1 0 0 tx
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0 1 0 ty
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0 0 1 tz
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0 0 0 1
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Matrix44 stores matrix in row-major order i.e.
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a0 a1 a2 a3
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a4 a5 a6 a7
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a8 a9 a10 a11
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a12 a13 a14 a15
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So for the use of that matrix in opengl with their supposed meaning you have to transpose them before feeding to glMultMatrix.
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This mechanism is hidden by the templated function defined in wrap/gl/math.h;
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If your machine has the ARB_transpose_matrix extension it will use the appropriate;
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The various gl-like command SetRotate, SetTranslate assume that you are making matrix
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for 'column' vectors.
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*/
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/** This class represent a 4x4 matrix. T is the kind of element in the matrix.
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*/
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template <class T> class Matrix44 {
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protected:
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T _a[16];
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public:
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typedef T ScalarType;
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///@{
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/** $name Constructors
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* No automatic casting and default constructor is empty
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*/
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Matrix44() {}
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~Matrix44() {}
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Matrix44(const Matrix44 &m);
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Matrix44(const T v[]);
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T &ElementAt(const int row, const int col);
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T ElementAt(const int row, const int col) const;
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//T &operator[](const int i);
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//const T &operator[](const int i) const;
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T *V();
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const T *V() const ;
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T *operator[](const int i);
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const T *operator[](const int i) const;
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// return a copy of the i-th column
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Point4<T> GetColumn4(const int& i)const{
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assert(i>=0 && i<4);
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return Point4<T>(ElementAt(0,i),ElementAt(1,i),ElementAt(2,i),ElementAt(3,i));
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//return Point4<T>(_a[i],_a[i+4],_a[i+8],_a[i+12]);
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}
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Point3<T> GetColumn3(const int& i)const{
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assert(i>=0 && i<4);
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return Point3<T>(ElementAt(0,i),ElementAt(1,i),ElementAt(2,i));
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}
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Point4<T> GetRow4(const int& i)const{
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assert(i>=0 && i<4);
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return Point4<T>(ElementAt(i,0),ElementAt(i,1),ElementAt(i,2),ElementAt(i,3));
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// return *((Point4<T>*)(&_a[i<<2])); alternativa forse + efficiente
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}
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Point3<T> GetRow3(const int& i)const{
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assert(i>=0 && i<4);
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return Point3<T>(ElementAt(i,0),ElementAt(i,1),ElementAt(i,2));
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// return *((Point4<T>*)(&_a[i<<2])); alternativa forse + efficiente
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}
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Matrix44 operator+(const Matrix44 &m) const;
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Matrix44 operator-(const Matrix44 &m) const;
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Matrix44 operator*(const Matrix44 &m) const;
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Point4<T> operator*(const Point4<T> &v) const;
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bool operator==(const Matrix44 &m) const;
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bool operator!= (const Matrix44 &m) const;
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Matrix44 operator-() const;
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Matrix44 operator*(const T k) const;
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void operator+=(const Matrix44 &m);
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void operator-=(const Matrix44 &m);
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void operator*=( const Matrix44 & m );
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void operator*=( const T k );
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template <class Matrix44Type>
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void ToMatrix(Matrix44Type & m) const {for(int i = 0; i < 16; i++) m.V()[i]=V()[i];}
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void ToEulerAngles(T &alpha, T &beta, T &gamma);
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template <class Matrix44Type>
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void FromMatrix(const Matrix44Type & m){for(int i = 0; i < 16; i++) V()[i]=m.V()[i];}
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template <class EigenMatrix44Type>
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void ToEigenMatrix(EigenMatrix44Type & m) const {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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m(i,j)=(*this)[i][j];
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}
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template <class EigenMatrix44Type>
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void FromEigenMatrix(const EigenMatrix44Type & m){
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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ElementAt(i,j)=m(i,j);
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}
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void FromEulerAngles(T alpha, T beta, T gamma);
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void SetZero();
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void SetIdentity();
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void SetDiagonal(const T k);
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Matrix44 &SetScale(const T sx, const T sy, const T sz);
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Matrix44 &SetScale(const Point3<T> &t);
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Matrix44<T>& SetColumn(const unsigned int ii,const Point4<T> &t);
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Matrix44<T>& SetColumn(const unsigned int ii,const Point3<T> &t);
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Matrix44 &SetTranslate(const Point3<T> &t);
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Matrix44 &SetTranslate(const T sx, const T sy, const T sz);
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Matrix44 &SetShearXY(const T sz);
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Matrix44 &SetShearXZ(const T sy);
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Matrix44 &SetShearYZ(const T sx);
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///use radiants for angle.
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Matrix44 &SetRotateDeg(T AngleDeg, const Point3<T> & axis);
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Matrix44 &SetRotateRad(T AngleRad, const Point3<T> & axis);
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T Determinant() const;
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template <class Q> void Import(const Matrix44<Q> &m) {
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for(int i = 0; i < 16; i++)
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_a[i] = (T)(m.V()[i]);
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}
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template <class Q>
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static inline Matrix44 Construct( const Matrix44<Q> & b )
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{
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Matrix44<T> tmp; tmp.FromMatrix(b);
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return tmp;
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}
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static inline const Matrix44 &Identity( )
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{
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static Matrix44<T> tmp; tmp.SetIdentity();
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return tmp;
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}
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// for the transistion to eigen
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Matrix44 transpose() const
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{
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Matrix44 res = *this;
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Transpose(res);
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return res;
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}
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void transposeInPlace() { Transpose(*this); }
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void print() {
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unsigned int i, j, p;
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for (i=0, p=0; i<4; i++, p+=4)
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{
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std::cout << "[\t";
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for (j=0; j<4; j++)
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std::cout << _a[p+j] << "\t";
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std::cout << "]\n";
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}
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std::cout << "\n";
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}
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};
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/** Class for solving A * x = b. */
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template <class T> class LinearSolve: public Matrix44<T> {
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public:
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LinearSolve(const Matrix44<T> &m);
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Point4<T> Solve(const Point4<T> &b); // solve A <20> x = b
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///If you need to solve some equation you can use this function instead of Matrix44 one for speed.
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T Determinant() const;
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protected:
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///Holds row permutation.
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int index[4]; //hold permutation
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///Hold sign of row permutation (used for determinant sign)
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T d;
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bool Decompose();
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};
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/*** Postmultiply */
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//template <class T> Point3<T> operator*(const Point3<T> &p, const Matrix44<T> &m);
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///Premultiply
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template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p);
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template <class T> Matrix44<T> &Transpose(Matrix44<T> &m);
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//return NULL matrix if not invertible
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template <class T> Matrix44<T> Inverse(const Matrix44<T> &m);
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typedef Matrix44<short> Matrix44s;
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typedef Matrix44<int> Matrix44i;
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typedef Matrix44<float> Matrix44f;
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typedef Matrix44<double> Matrix44d;
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template <class T> Matrix44<T>::Matrix44(const Matrix44<T> &m) {
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memcpy((T *)_a, (T *)m._a, 16 * sizeof(T));
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}
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template <class T> Matrix44<T>::Matrix44(const T v[]) {
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memcpy((T *)_a, v, 16 * sizeof(T));
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}
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template <class T> T &Matrix44<T>::ElementAt(const int row, const int col) {
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assert(row >= 0 && row < 4);
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assert(col >= 0 && col < 4);
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return _a[(row<<2) + col];
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}
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template <class T> T Matrix44<T>::ElementAt(const int row, const int col) const {
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assert(row >= 0 && row < 4);
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assert(col >= 0 && col < 4);
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return _a[(row<<2) + col];
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}
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//template <class T> T &Matrix44<T>::operator[](const int i) {
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// assert(i >= 0 && i < 16);
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// return ((T *)_a)[i];
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//}
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//
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//template <class T> const T &Matrix44<T>::operator[](const int i) const {
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// assert(i >= 0 && i < 16);
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// return ((T *)_a)[i];
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//}
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template <class T> T *Matrix44<T>::operator[](const int i) {
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assert(i >= 0 && i < 4);
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return _a+i*4;
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}
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template <class T> const T *Matrix44<T>::operator[](const int i) const {
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assert(i >= 0 && i < 4);
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return _a+i*4;
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}
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template <class T> T *Matrix44<T>::V() { return _a;}
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template <class T> const T *Matrix44<T>::V() const { return _a;}
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template <class T> Matrix44<T> Matrix44<T>::operator+(const Matrix44 &m) const {
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Matrix44<T> ret;
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for(int i = 0; i < 16; i++)
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ret.V()[i] = V()[i] + m.V()[i];
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return ret;
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}
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template <class T> Matrix44<T> Matrix44<T>::operator-(const Matrix44 &m) const {
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Matrix44<T> ret;
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for(int i = 0; i < 16; i++)
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ret.V()[i] = V()[i] - m.V()[i];
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return ret;
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}
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template <class T> Matrix44<T> Matrix44<T>::operator*(const Matrix44 &m) const {
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Matrix44 ret;
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++) {
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T t = 0.0;
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for(int k = 0; k < 4; k++)
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t += ElementAt(i, k) * m.ElementAt(k, j);
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ret.ElementAt(i, j) = t;
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}
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return ret;
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}
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template <class T> Point4<T> Matrix44<T>::operator*(const Point4<T> &v) const {
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Point4<T> ret;
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for(int i = 0; i < 4; i++){
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T t = 0.0;
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for(int k = 0; k < 4; k++)
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t += ElementAt(i,k) * v[k];
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ret[i] = t;
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}
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return ret;
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}
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template <class T> bool Matrix44<T>::operator==(const Matrix44 &m) const {
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for(int i = 0; i < 4; ++i)
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for(int j = 0; j < 4; ++j)
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if(ElementAt(i,j) != m.ElementAt(i,j))
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return false;
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return true;
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}
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template <class T> bool Matrix44<T>::operator!=(const Matrix44 &m) const {
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for(int i = 0; i < 4; ++i)
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for(int j = 0; j < 4; ++j)
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if(ElementAt(i,j) != m.ElementAt(i,j))
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return true;
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return false;
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}
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template <class T> Matrix44<T> Matrix44<T>::operator-() const {
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Matrix44<T> res;
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for(int i = 0; i < 16; i++)
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res.V()[i] = -V()[i];
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return res;
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}
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template <class T> Matrix44<T> Matrix44<T>::operator*(const T k) const {
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Matrix44<T> res;
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for(int i = 0; i < 16; i++)
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res.V()[i] =V()[i] * k;
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return res;
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}
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template <class T> void Matrix44<T>::operator+=(const Matrix44 &m) {
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for(int i = 0; i < 16; i++)
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V()[i] += m.V()[i];
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}
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template <class T> void Matrix44<T>::operator-=(const Matrix44 &m) {
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for(int i = 0; i < 16; i++)
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V()[i] -= m.V()[i];
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}
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template <class T> void Matrix44<T>::operator*=( const Matrix44 & m ) {
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*this = *this *m;
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}
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template < class PointType , class T > void operator*=( std::vector<PointType> &vert, const Matrix44<T> & m ) {
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typename std::vector<PointType>::iterator ii;
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for(ii=vert.begin();ii!=vert.end();++ii)
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(*ii).P()=m * (*ii).P();
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}
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template <class T> void Matrix44<T>::operator*=( const T k ) {
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for(int i = 0; i < 16; i++)
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_a[i] *= k;
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}
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template <class T>
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void Matrix44<T>::ToEulerAngles(T &alpha, T &beta, T &gamma)
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{
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alpha = atan2(ElementAt(1,2), ElementAt(2,2));
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beta = asin(-ElementAt(0,2));
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gamma = atan2(ElementAt(0,1), ElementAt(0,0));
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}
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template <class T>
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void Matrix44<T>::FromEulerAngles(T alpha, T beta, T gamma)
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{
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this->SetZero();
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T cosalpha = cos(alpha);
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T cosbeta = cos(beta);
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T cosgamma = cos(gamma);
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T sinalpha = sin(alpha);
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T sinbeta = sin(beta);
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T singamma = sin(gamma);
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ElementAt(0,0) = cosbeta * cosgamma;
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ElementAt(1,0) = -cosalpha * singamma + sinalpha * sinbeta * cosgamma;
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ElementAt(2,0) = sinalpha * singamma + cosalpha * sinbeta * cosgamma;
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ElementAt(0,1) = cosbeta * singamma;
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ElementAt(1,1) = cosalpha * cosgamma + sinalpha * sinbeta * singamma;
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ElementAt(2,1) = -sinalpha * cosgamma + cosalpha * sinbeta * singamma;
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ElementAt(0,2) = -sinbeta;
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ElementAt(1,2) = sinalpha * cosbeta;
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ElementAt(2,2) = cosalpha * cosbeta;
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ElementAt(3,3) = 1;
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}
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template <class T> void Matrix44<T>::SetZero() {
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memset((T *)_a, 0, 16 * sizeof(T));
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}
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template <class T> void Matrix44<T>::SetIdentity() {
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SetDiagonal(1);
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}
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template <class T> void Matrix44<T>::SetDiagonal(const T k) {
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SetZero();
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ElementAt(0, 0) = k;
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ElementAt(1, 1) = k;
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ElementAt(2, 2) = k;
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ElementAt(3, 3) = 1;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetScale(const Point3<T> &t) {
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SetScale(t[0], t[1], t[2]);
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetScale(const T sx, const T sy, const T sz) {
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SetZero();
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ElementAt(0, 0) = sx;
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ElementAt(1, 1) = sy;
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ElementAt(2, 2) = sz;
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ElementAt(3, 3) = 1;
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const Point3<T> &t) {
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SetTranslate(t[0], t[1], t[2]);
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const T tx, const T ty, const T tz) {
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SetIdentity();
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ElementAt(0, 3) = tx;
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ElementAt(1, 3) = ty;
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ElementAt(2, 3) = tz;
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetColumn(const unsigned int ii,const Point3<T> &t) {
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assert( ii < 4 );
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ElementAt(0, ii) = t.X();
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ElementAt(1, ii) = t.Y();
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ElementAt(2, ii) = t.Z();
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetColumn(const unsigned int ii,const Point4<T> &t) {
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assert( ii < 4 );
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ElementAt(0, ii) = t[0];
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ElementAt(1, ii) = t[1];
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ElementAt(2, ii) = t[2];
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ElementAt(3, ii) = t[3];
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return *this;
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetRotateDeg(T AngleDeg, const Point3<T> & axis) {
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return SetRotateRad(math::ToRad(AngleDeg),axis);
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}
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template <class T> Matrix44<T> &Matrix44<T>::SetRotateRad(T AngleRad, const Point3<T> & axis) {
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//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;
|
||
}
|
||
|
||
/*
|
||
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 and 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]*M.GetColumn3(1); // xy shearing
|
||
R[1]= M.GetColumn3(1)-R[0]*ShearV[0];
|
||
assert(math::Abs(R[1]*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]*M.GetColumn3(2); // xz shearing
|
||
R[2]= M.GetColumn3(2)-R[0]*ShearV[1];
|
||
assert(math::Abs(R[2]*R[0])<1e-10);
|
||
|
||
R[2] = R[2]-R[1]*(R[2]*R[1]);
|
||
assert(math::Abs(R[2]*R[1])<1e-10);
|
||
assert(math::Abs(R[2]*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]*R[1])<1e-10);
|
||
assert(math::Abs(R[2]*R[0])<1e-10);
|
||
|
||
ShearV[2]=R[1]*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> T Matrix44<T>::Determinant() const {
|
||
Eigen::Matrix4d mm;
|
||
this->ToEigenMatrix(mm);
|
||
return mm.determinant();
|
||
}
|
||
|
||
|
||
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> Matrix44<T> &Transpose(Matrix44<T> &m) {
|
||
for(int i = 1; i < 4; i++)
|
||
for(int j = 0; j < i; j++) {
|
||
std::swap(m.ElementAt(i, j), m.ElementAt(j, i));
|
||
}
|
||
return m;
|
||
}
|
||
|
||
template <class T> Matrix44<T> Inverse(const Matrix44<T> &m) {
|
||
Eigen::Matrix4d mm,mmi;
|
||
m.ToEigenMatrix(mm);
|
||
mmi=mm.inverse();
|
||
Matrix44<T> res;
|
||
res.FromEigenMatrix(mmi);
|
||
return res;
|
||
}
|
||
|
||
} //namespace
|
||
#endif
|
||
|
||
|