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/****************************************************************************
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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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/****************************************************************************
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History
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$LOG$
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****************************************************************************/
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#ifndef __VCGLIB_MATRIX44
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#define __VCGLIB_MATRIX44
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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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e.g. glTranslate generate a matrix that is
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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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and the Translate Function generate:
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1 0 0 0
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0 1 0 0
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0 0 1 0
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tx ty tz 1
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Le funzioni Translate e Rotate vanno usate con la Apply,
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che moltiplica vettore (inteso come riga) per la matrice
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*/
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#include <math.h>
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#include <string.h>
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#include "../space/Point3.h"
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#include "../space/Point4.h"
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namespace vcg {
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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 scalar;
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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 &element(const int row, const int col);
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T element(const int row, const int col) const;
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T &operator[](const int i);
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T operator[](const int i) 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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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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void SetZero();
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void SetIdentity();
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void SetDiagonal(const T k);
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void SetScale(const T sx, const T sy, const T sz);
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void SetTranslate(const Point3<T> &t);
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void SetTranslate(const T sx, const T sy, const T sz);
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void SetRotate(T angle, const Point3<T> & axis); //use radiants for angle.
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T Determinant() const;
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};
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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(Point4<T> &b); // solve A · x = b
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T Determinant() const;
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protected:
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int index[4]; //hold permutation
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T d; //hold sign of permutation
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void Decompose();
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};
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template <class T> Point4<T> operator*(const Matrix44<T> &m, const Point4<T> &p);
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template <class T> Point4<T> operator*(const Point4<T> &p, const Matrix44<T> &m);
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template <class T> Matrix44<T> &Transpose(Matrix44<T> &m);
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template <class T> Matrix44<T> &Invert(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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//Implementazione
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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> T &Matrix44<T>::element(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>::element(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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template <class T> 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> 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[i] = operator[](i) + m[i];
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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[i] = operator[](i) - m[i];
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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 += element[i][k] * m.element[k][j];
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ret.element[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 += element[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 < 16; i++)
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if(operator[](i) != m[i])
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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 < 16; i++)
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if(operator[](i) != m[i])
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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[i] = -operator[](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[i] = operator[](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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operator[](i) += m[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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operator[](i) -= m[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 < 4; i++) {
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Point4<T> t(0, 0, 0, 0);
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for(int k = 0; k < 4; k++) {
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for(int j = 0; j < 4; j++) {
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t[k] += element(i, k) * m.element(k, j);
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}
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}
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for(int l = 0; l < 4; l++)
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element(i, l) = t[l];
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}
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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 < 4; i++)
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operator[](i) *= k;
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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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element(0, 0) = k;
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element(1, 1) = k;
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element(2, 2) = k;
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element(3, 3) = 1;
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}
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template <class T> void Matrix44<T>::SetScale(const T sx, const T sy, const T sz) {
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SetZero();
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element(0, 0) = sx;
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element(1, 1) = sy;
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element(2, 2) = sz;
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element(3, 3) = 1;
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}
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template <class T> void Matrix44<T>::SetTranslate(const Point3<T> &t) {
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SetTranslate(t[0], t[1], t[2]);
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}
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template <class T> void Matrix44<T>::SetTranslate(const T sx, const T sy, const T sz) {
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SetIdentity();
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element(3, 0) = sx;
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element(3, 1) = sy;
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element(3, 2) = sz;
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}
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template <class T> void Matrix44<T>::SetRotate(T angle, const Point3<T> & axis) {
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//angle = angle*(T)3.14159265358979323846/180; e' in radianti!
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T c = Cos(angle);
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T s = Sin(angle);
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T q = 1-c;
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Point3<T> t = axis;
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t.Normalize();
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element(0,0) = t[0]*t[0]*q + c;
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element(1,0) = t[0]*t[1]*q - t[2]*s;
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element(2,0) = t[0]*t[2]*q + t[1]*s;
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element(3,0) = 0;
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element(0,1) = t[1]*t[0]*q + t[2]*s;
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element(1,1) = t[1]*t[1]*q + c;
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element(2,1) = t[1]*t[2]*q - t[0]*s;
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element(3,1) = 0;
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element(0,2) = t[2]*t[0]*q -t[1]*s;
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element(1,2) = t[2]*t[1]*q +t[0]*s;
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element(2,2) = t[2]*t[2]*q +c;
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element(3,2) = 0;
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element(0,3) = 0;
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element(1,3) = 0;
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element(2,3) = 0;
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element(3,3) = 1;
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}
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template <class T> T Matrix44<T>::Determinant() const {
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LinearSolve<T> solve(*this);
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return solve.Determinant();
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}
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template <class T> Point4<T> operator*(const Matrix44<T> &m, const Point4<T> &p) {
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T w;
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Point4<T> s;
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s.x() = a[0][0]*p.x() + a[0][1]*p.y() + a[0][2]*p.z() + a[0][3];
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s.y() = a[1][0]*p.x() + a[1][1]*p.y() + a[1][2]*p.z() + a[1][3];
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s.z() = a[2][0]*p.x() + a[2][1]*p.y() + a[2][2]*p.z() + a[2][3];
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s.w() = a[3][0]*p.x() + a[3][1]*p.y() + a[3][2]*p.z() + a[3][3];
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if(s.w()!= 0) s /= s.w();
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return s;
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}
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template <class T> Point4<T> operator*(const Point4<T> &p, const Matrix44<T> &m) {
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T w;
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Point4<T> s;
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s.x() = a[0][0]*p.x() + a[0][1]*p.y() + a[0][2]*p.z() + a[0][3];
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s.y() = a[1][0]*p.x() + a[1][1]*p.y() + a[1][2]*p.z() + a[1][3];
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s.z() = a[2][0]*p.x() + a[2][1]*p.y() + a[2][2]*p.z() + a[2][3];
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s.w() = a[3][0]*p.x() + a[3][1]*p.y() + a[3][2]*p.z() + a[3][3];
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if(s.w() != 0) s /= s.w();
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return s;
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}
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template <class T> Matrix44<T> &Transpose(Matrix44<T> &m) {
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for(int i = 1; i < 4; i++)
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for(int j = 0; j < i; j++) {
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T t = element(i, j);
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element(i, j) = element(j, i);
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element(j, i) = t;
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}
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return *this;
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}
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template <class T> Matrix44<T> &Invert(Matrix44<T> &m) {
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LinearSolve<T> solve(m);
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for(int j = 0; j < 4; j++) { //Find inverse by columns.
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Point4<T> col(0, 0, 0, 0);
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col[j] = 1.0;
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col = solve.Solve(col);
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for(int i = 0; i < 4; i++)
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m.element(i, j) = col[i];
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}
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}
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/* LINEAR SOLVE IMPLEMENTATION */
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template <class T> LinearSolve<T>::LinearSolve(const Matrix44<T> &m): Matrix44<T>(m) {
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Decompose();
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}
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template <class T> T LinearSolve<T>::Determinant() const {
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T det = d;
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for(int j = 0; j < 4; j++)
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det *= element(j, j);
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return det;
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}
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/*replaces a matrix by its LU decomposition of a rowwise permutation.
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d is +or -1 depeneing of row permutation even or odd.*/
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#define TINY 1e-100
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template <class T> void LinearSolve<T>::Decompose() {
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d = 1; //no permutation still
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T scaling[4];
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//Saving the scvaling information per row
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for(int i = 0; i < 4; i++) {
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T largest = 0.0;
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for(int j = 0; j < 4; j++) {
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T t = fabs(element(i, j));
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if (t > largest) largest = t;
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}
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if (largest == 0.0) { //oooppps there is a zero row!
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return;
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}
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scaling[i] = 1.0 / largest;
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}
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int imax;
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for(int j = 0; j < 4; j++) {
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for(int i = 0; i < j; i++) {
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T sum = element(i,j);
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for(int k = 0; k < i; k++)
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sum -= element(i,k)*element(k,j);
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element(i,j) = sum;
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}
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T largest = 0.0;
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for(int i = j; i < 4; i++) {
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T sum = element(i,j);
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for(int k = 0; k < j; k++)
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sum -= element(i,k)*element(k,j);
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element(i,j) = sum;
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T t = scaling[i] * fabs(sum);
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if(t >= largest) {
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largest = t;
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imax = i;
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}
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}
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if (j != imax) {
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for (int k = 0; k < 4; k++) {
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T dum = element(imax,k);
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element(imax,k) = element(j,k);
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element(j,k) = dum;
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}
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d = -(d);
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scaling[imax] = scaling[j];
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}
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index[j]=imax;
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if (element(j,j) == 0.0) element(j,j) = TINY;
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if (j != 3) {
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T dum = 1.0 / (element(j,j));
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for (i = j+1; i < 4; i++)
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element(i,j) *= dum;
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}
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}
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}
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template <class T> Point4<T> LinearSolve<T>::Solve(Point4<T> &b) {
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Point4<T> x(b);
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int first = 0, ip;
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for(int i = 0; i < 4; i++) {
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ip = index[i];
|
||||
T sum = x[ip];
|
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x[ip] = x[i];
|
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if(first)
|
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for(int j = first; j <= i-1; j++)
|
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sum -= element(i,j) * x[j];
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else
|
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if (sum) first = i;
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}
|
||||
for (int i = 3; i >= 0; i--) {
|
||||
T sum = x[i];
|
||||
for (int j = i+1; j < 4; j++)
|
||||
sum -= element(i, j) * x[j];
|
||||
x[i] = sum / element(i, i);
|
||||
}
|
||||
return x;
|
||||
}
|
||||
|
||||
} //namespace
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
|
||||
/*#ifdef __GL_H__
|
||||
// Applicano la trasformazione intesa secondo la Apply
|
||||
void glMultMatrix(Matrix44<double> const & M) { glMultMatrixd(&(M.a[0][0]));}
|
||||
void glMultMatrix(Matrix44<float> const & M) { glMultMatrixf(&(M.a[0][0]));}
|
||||
void glLoadMatrix(Matrix44<double> const & M) { glLoadMatrixd(&(M.a[0][0]));}
|
||||
void glLoadMatrix(Matrix44<float> const & M) { glLoadMatrixf(&(M.a[0][0]));}
|
||||
#endif*/
|
||||
|
||||
|
||||
Loading…
Reference in New Issue