--- trunk/src/math/SquareMatrix3.hpp 2004/10/14 23:28:09 76 +++ trunk/src/math/SquareMatrix3.hpp 2004/10/20 18:07:08 123 @@ -29,10 +29,13 @@ * @date 10/11/2004 * @version 1.0 */ -#ifndef MATH_SQUAREMATRIX#_HPP -#define MATH_SQUAREMATRIX#_HPP + #ifndef MATH_SQUAREMATRIX3_HPP +#define MATH_SQUAREMATRIX3_HPP +#include "Quaternion.hpp" #include "SquareMatrix.hpp" +#include "Vector3.hpp" + namespace oopse { template @@ -47,18 +50,38 @@ namespace oopse { SquareMatrix3(const SquareMatrix& m) : SquareMatrix(m) { } + SquareMatrix3( const Vector3& eulerAngles) { + setupRotMat(eulerAngles); + } + + SquareMatrix3(Real phi, Real theta, Real psi) { + setupRotMat(phi, theta, psi); + } + + SquareMatrix3(const Quaternion& q) { + setupRotMat(q); + + } + + SquareMatrix3(Real w, Real x, Real y, Real z) { + setupRotMat(w, x, y, z); + } + /** copy assignment operator */ SquareMatrix3& operator =(const SquareMatrix& m) { if (this == &m) return *this; SquareMatrix::operator=(m); + return *this; } /** * Sets this matrix to a rotation matrix by three euler angles * @ param euler */ - void setupRotMat(const Vector3d& euler); + void setupRotMat(const Vector3& eulerAngles) { + setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]); + } /** * Sets this matrix to a rotation matrix by three euler angles @@ -66,50 +89,344 @@ namespace oopse { * @param theta * @psi theta */ - void setupRotMat(double phi, double theta, double psi); + void setupRotMat(Real phi, Real theta, Real psi) { + Real sphi, stheta, spsi; + Real cphi, ctheta, cpsi; + sphi = sin(phi); + stheta = sin(theta); + spsi = sin(psi); + cphi = cos(phi); + ctheta = cos(theta); + cpsi = cos(psi); + data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; + data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; + data_[0][2] = spsi * stheta; + + data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; + data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; + data_[1][2] = cpsi * stheta; + + data_[2][0] = stheta * sphi; + data_[2][1] = -stheta * cphi; + data_[2][2] = ctheta; + } + + /** * Sets this matrix to a rotation matrix by quaternion * @param quat */ - void setupRotMat(const Vector4d& quat); + void setupRotMat(const Quaternion& quat) { + setupRotMat(quat.w(), quat.x(), quat.y(), quat.z()); + } /** * Sets this matrix to a rotation matrix by quaternion - * @param q0 - * @param q1 - * @param q2 - * @parma q3 + * @param w the first element + * @param x the second element + * @param y the third element + * @param z the fourth element */ - void setupRotMat(double q0, double q1, double q2, double q4); + void setupRotMat(Real w, Real x, Real y, Real z) { + Quaternion q(w, x, y, z); + *this = q.toRotationMatrix3(); + } /** * Returns the quaternion from this rotation matrix * @return the quaternion from this rotation matrix * @exception invalid rotation matrix */ - Quaternion rotMatToQuat(); + Quaternion toQuaternion() { + Quaternion q; + Real t, s; + Real ad1, ad2, ad3; + t = data_[0][0] + data_[1][1] + data_[2][2] + 1.0; + if( t > 0.0 ){ + + s = 0.5 / sqrt( t ); + q[0] = 0.25 / s; + q[1] = (data_[1][2] - data_[2][1]) * s; + q[2] = (data_[2][0] - data_[0][2]) * s; + q[3] = (data_[0][1] - data_[1][0]) * s; + } else { + + ad1 = fabs( data_[0][0] ); + ad2 = fabs( data_[1][1] ); + ad3 = fabs( data_[2][2] ); + + if( ad1 >= ad2 && ad1 >= ad3 ){ + + s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] ); + q[0] = (data_[1][2] + data_[2][1]) / s; + q[1] = 0.5 / s; + q[2] = (data_[0][1] + data_[1][0]) / s; + q[3] = (data_[0][2] + data_[2][0]) / s; + } else if ( ad2 >= ad1 && ad2 >= ad3 ) { + s = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0; + q[0] = (data_[0][2] + data_[2][0]) / s; + q[1] = (data_[0][1] + data_[1][0]) / s; + q[2] = 0.5 / s; + q[3] = (data_[1][2] + data_[2][1]) / s; + } else { + + s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0; + q[0] = (data_[0][1] + data_[1][0]) / s; + q[1] = (data_[0][2] + data_[2][0]) / s; + q[2] = (data_[1][2] + data_[2][1]) / s; + q[3] = 0.5 / s; + } + } + + return q; + + } + /** * Returns the euler angles from this rotation matrix - * @return the quaternion from this rotation matrix + * @return the euler angles in a vector * @exception invalid rotation matrix + * We use so-called "x-convention", which is the most common definition. + * In this convention, the rotation given by Euler angles (phi, theta, psi), where the first + * rotation is by an angle phi about the z-axis, the second is by an angle + * theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the + * z-axis (again). */ - Vector3d rotMatToEuler(); + Vector3 toEulerAngles() { + Vector3 myEuler; + Real phi,theta,psi,eps; + Real ctheta,stheta; + + // set the tolerance for Euler angles and rotation elements + + theta = acos(std::min(1.0, std::max(-1.0,data_[2][2]))); + ctheta = data_[2][2]; + stheta = sqrt(1.0 - ctheta * ctheta); + + // when sin(theta) is close to 0, we need to consider singularity + // In this case, we can assign an arbitary value to phi (or psi), and then determine + // the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 + // in cases of singularity. + // we use atan2 instead of atan, since atan2 will give us -Pi to Pi. + // Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never + // change the sign of both of the parameters passed to atan2. + + if (fabs(stheta) <= oopse::epsilon){ + psi = 0.0; + phi = atan2(-data_[1][0], data_[0][0]); + } + // we only have one unique solution + else{ + phi = atan2(data_[2][0], -data_[2][1]); + psi = atan2(data_[0][2], data_[1][2]); + } + + //wrap phi and psi, make sure they are in the range from 0 to 2*Pi + if (phi < 0) + phi += M_PI; + + if (psi < 0) + psi += M_PI; + + myEuler[0] = phi; + myEuler[1] = theta; + myEuler[2] = psi; + + return myEuler; + } + /** Returns the determinant of this matrix. */ + Real determinant() const { + Real x,y,z; + + x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]); + y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]); + z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]); + + return(x + y + z); + } + /** * Sets the value of this matrix to the inversion of itself. * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the * implementation of inverse in SquareMatrix class */ - void inverse(); - - void diagonalize(); + SquareMatrix3 inverse() { + SquareMatrix3 m; + double det = determinant(); + if (fabs(det) <= oopse::epsilon) { + //"The method was called on a matrix with |determinant| <= 1e-6.", + //"This is a runtime or a programming error in your application."); + } - } + m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1]; + m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2]; + m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0]; + m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1]; + m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2]; + m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0]; + m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1]; + m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2]; + m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0]; + m /= det; + return m; + } + /** + * Extract the eigenvalues and eigenvectors from a 3x3 matrix. + * The eigenvectors (the columns of V) will be normalized. + * The eigenvectors are aligned optimally with the x, y, and z + * axes respectively. + * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is + * overwritten + * @param w will contain the eigenvalues of the matrix On return of this function + * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are + * normalized and mutually orthogonal. + * @warning a will be overwritten + */ + static void diagonalize(SquareMatrix3& a, Vector3& w, SquareMatrix3& v); }; +/*========================================================================= -} -#endif // MATH_SQUAREMATRIX#_HPP + Program: Visualization Toolkit + Module: $RCSfile: SquareMatrix3.hpp,v $ + + Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen + All rights reserved. + See Copyright.txt or http://www.kitware.com/Copyright.htm for details. + + This software is distributed WITHOUT ANY WARRANTY; without even + the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR + PURPOSE. See the above copyright notice for more information. + +=========================================================================*/ + template + void SquareMatrix3::diagonalize(SquareMatrix3& a, Vector3& w, + SquareMatrix3& v) { + int i,j,k,maxI; + Real tmp, maxVal; + Vector3 v_maxI, v_k, v_j; + + // diagonalize using Jacobi + jacobi(a, w, v); + // if all the eigenvalues are the same, return identity matrix + if (w[0] == w[1] && w[0] == w[2] ) { + v = SquareMatrix3::identity(); + return; + } + + // transpose temporarily, it makes it easier to sort the eigenvectors + v = v.transpose(); + + // if two eigenvalues are the same, re-orthogonalize to optimally line + // up the eigenvectors with the x, y, and z axes + for (i = 0; i < 3; i++) { + if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same + // find maximum element of the independant eigenvector + maxVal = fabs(v(i, 0)); + maxI = 0; + for (j = 1; j < 3; j++) { + if (maxVal < (tmp = fabs(v(i, j)))){ + maxVal = tmp; + maxI = j; + } + } + + // swap the eigenvector into its proper position + if (maxI != i) { + tmp = w(maxI); + w(maxI) = w(i); + w(i) = tmp; + + v.swapRow(i, maxI); + } + // maximum element of eigenvector should be positive + if (v(maxI, maxI) < 0) { + v(maxI, 0) = -v(maxI, 0); + v(maxI, 1) = -v(maxI, 1); + v(maxI, 2) = -v(maxI, 2); + } + + // re-orthogonalize the other two eigenvectors + j = (maxI+1)%3; + k = (maxI+2)%3; + + v(j, 0) = 0.0; + v(j, 1) = 0.0; + v(j, 2) = 0.0; + v(j, j) = 1.0; + + /** @todo */ + v_maxI = v.getRow(maxI); + v_j = v.getRow(j); + v_k = cross(v_maxI, v_j); + v_k.normalize(); + v_j = cross(v_k, v_maxI); + v.setRow(j, v_j); + v.setRow(k, v_k); + + + // transpose vectors back to columns + v = v.transpose(); + return; + } + } + + // the three eigenvalues are different, just sort the eigenvectors + // to align them with the x, y, and z axes + + // find the vector with the largest x element, make that vector + // the first vector + maxVal = fabs(v(0, 0)); + maxI = 0; + for (i = 1; i < 3; i++) { + if (maxVal < (tmp = fabs(v(i, 0)))) { + maxVal = tmp; + maxI = i; + } + } + + // swap eigenvalue and eigenvector + if (maxI != 0) { + tmp = w(maxI); + w(maxI) = w(0); + w(0) = tmp; + v.swapRow(maxI, 0); + } + // do the same for the y element + if (fabs(v(1, 1)) < fabs(v(2, 1))) { + tmp = w(2); + w(2) = w(1); + w(1) = tmp; + v.swapRow(2, 1); + } + + // ensure that the sign of the eigenvectors is correct + for (i = 0; i < 2; i++) { + if (v(i, i) < 0) { + v(i, 0) = -v(i, 0); + v(i, 1) = -v(i, 1); + v(i, 2) = -v(i, 2); + } + } + + // set sign of final eigenvector to ensure that determinant is positive + if (v.determinant() < 0) { + v(2, 0) = -v(2, 0); + v(2, 1) = -v(2, 1); + v(2, 2) = -v(2, 2); + } + + // transpose the eigenvectors back again + v = v.transpose(); + return ; + } + typedef SquareMatrix3 Mat3x3d; + typedef SquareMatrix3 RotMat3x3d; + +} //namespace oopse +#endif // MATH_SQUAREMATRIX_HPP +