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* @date 10/11/2004 |
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* @version 1.0 |
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*/ |
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#ifndef MATH_SQUAREMATRIX_HPP |
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< |
#define MATH_SQUAREMATRIX_HPP |
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#ifndef MATH_SQUAREMATRIX3_HPP |
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#define MATH_SQUAREMATRIX3_HPP |
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|
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#include "Quaternion.hpp" |
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#include "SquareMatrix.hpp" |
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if (this == &m) |
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return *this; |
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SquareMatrix<Real, 3>::operator=(m); |
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return *this; |
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} |
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|
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/** |
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* @param w the first element |
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* @param x the second element |
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* @param y the third element |
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* @parma z the fourth element |
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* @param z the fourth element |
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*/ |
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void setupRotMat(Real w, Real x, Real y, Real z) { |
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Quaternion<Real> q(w, x, y, z); |
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return myEuler; |
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} |
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|
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/** Returns the determinant of this matrix. */ |
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Real determinant() const { |
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Real x,y,z; |
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|
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x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]); |
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y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]); |
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z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]); |
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|
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return(x + y + z); |
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} |
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|
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/** |
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* Sets the value of this matrix to the inversion of itself. |
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* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the |
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* implementation of inverse in SquareMatrix class |
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*/ |
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void inverse(); |
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SquareMatrix3<Real> inverse() { |
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SquareMatrix3<Real> m; |
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double det = determinant(); |
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if (fabs(det) <= oopse::epsilon) { |
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//"The method was called on a matrix with |determinant| <= 1e-6.", |
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//"This is a runtime or a programming error in your application."); |
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} |
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|
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void diagonalize(); |
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m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1]; |
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m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2]; |
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m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0]; |
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m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1]; |
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m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2]; |
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m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0]; |
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m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1]; |
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m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2]; |
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m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0]; |
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|
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m /= det; |
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return m; |
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} |
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|
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void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v) { |
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int i,j,k,maxI; |
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Real tmp, maxVal; |
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Vector3<Real> v_maxI, v_k, v_j; |
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|
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// diagonalize using Jacobi |
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jacobi(a, w, v); |
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|
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// if all the eigenvalues are the same, return identity matrix |
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if (w[0] == w[1] && w[0] == w[2] ){ |
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v = SquareMatrix3<Real>::identity(); |
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return |
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} |
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|
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// transpose temporarily, it makes it easier to sort the eigenvectors |
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v = v.tanspose(); |
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|
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// if two eigenvalues are the same, re-orthogonalize to optimally line |
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// up the eigenvectors with the x, y, and z axes |
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for (i = 0; i < 3; i++) { |
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if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same |
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// find maximum element of the independant eigenvector |
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maxVal = fabs(v(i, 0)); |
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maxI = 0; |
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for (j = 1; j < 3; j++) { |
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if (maxVal < (tmp = fabs(v(i, j)))){ |
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maxVal = tmp; |
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maxI = j; |
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} |
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} |
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|
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// swap the eigenvector into its proper position |
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if (maxI != i) { |
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tmp = w(maxI); |
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w(maxI) = w(i); |
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w(i) = tmp; |
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|
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v.swapRow(i, maxI); |
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} |
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// maximum element of eigenvector should be positive |
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if (v(maxI, maxI) < 0) { |
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v(maxI, 0) = -v(maxI, 0); |
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v(maxI, 1) = -v(maxI, 1); |
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v(maxI, 2) = -v(maxI, 2); |
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} |
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|
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// re-orthogonalize the other two eigenvectors |
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j = (maxI+1)%3; |
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k = (maxI+2)%3; |
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|
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v(j, 0) = 0.0; |
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v(j, 1) = 0.0; |
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v(j, 2) = 0.0; |
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v(j, j) = 1.0; |
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|
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/** @todo */ |
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v_maxI = v.getRow(maxI); |
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v_j = v.getRow(j); |
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v_k = cross(v_maxI, v_j); |
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v_k.normailze(); |
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v_j = cross(v_k, v_maxI); |
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v.setRow(j, v_j); |
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v.setRow(k, v_k); |
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|
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|
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// transpose vectors back to columns |
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v = v.transpose(); |
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return; |
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} |
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} |
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|
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// the three eigenvalues are different, just sort the eigenvectors |
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// to align them with the x, y, and z axes |
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|
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// find the vector with the largest x element, make that vector |
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// the first vector |
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maxVal = fabs(v(0, 0)); |
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maxI = 0; |
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for (i = 1; i < 3; i++) { |
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if (maxVal < (tmp = fabs(v(i, 0)))) { |
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maxVal = tmp; |
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maxI = i; |
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} |
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} |
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|
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// swap eigenvalue and eigenvector |
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if (maxI != 0) { |
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tmp = w(maxI); |
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w(maxI) = w(0); |
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w(0) = tmp; |
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v.swapRow(maxI, 0); |
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} |
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// do the same for the y element |
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if (fabs(v(1, 1)) < fabs(v(2, 1))) { |
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tmp = w(2); |
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w(2) = w(1); |
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w(1) = tmp; |
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v.swapRow(2, 1); |
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} |
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|
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// ensure that the sign of the eigenvectors is correct |
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for (i = 0; i < 2; i++) { |
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if (v(i, i) < 0) { |
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v(i, 0) = -v(i, 0); |
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v(i, 1) = -v(i, 1); |
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v(i, 2) = -v(i, 2); |
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} |
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} |
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|
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// set sign of final eigenvector to ensure that determinant is positive |
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if (determinant(v) < 0) { |
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v(2, 0) = -v(2, 0); |
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v(2, 1) = -v(2, 1); |
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v(2, 2) = -v(2, 2); |
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} |
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|
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// transpose the eigenvectors back again |
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v = v.transpose(); |
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return ; |
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} |
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}; |
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|
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< |
typedef template SquareMatrix3<double> Mat3x3d |
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< |
typedef template SquareMatrix3<double> RotMat3x3d; |
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> |
typedef SquareMatrix3<double> Mat3x3d; |
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typedef SquareMatrix3<double> RotMat3x3d; |
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|
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} //namespace oopse |
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#endif // MATH_SQUAREMATRIX_HPP |
