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#include <cmath> |
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#include "Mat3x3d.hpp" |
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#include "Vector3d.hpp" |
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#include "Quaternion.hpp" |
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#include "Euler3.hpp" |
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|
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Mat3x3d::Mat3x3d(const Vector3d& v1, const Vector3d& v2, const Vector3d& v3){ |
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element[0][0] = v1.x; |
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element[0][1] = v1.y; |
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element[0][2] = v1.z; |
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|
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element[1][0] = v2.x; |
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element[1][1] = v2.y; |
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element[1][2] = v2.z; |
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|
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element[2][0] = v3.x; |
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element[2][1] = v3.y; |
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element[2][2] = v3.z; |
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} |
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Mat3x3d::Mat3x3d(const Quaternion& q){ |
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|
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double q0Sqr; |
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double q1Sqr; |
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double q2Sqr; |
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double q3Sqr; |
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|
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q0Sqr = q.x * q.x; |
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q1Sqr = q.y * q.y; |
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q2Sqr = q.z * q.z; |
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q3Sqr = q.w * q.w; |
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|
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|
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element[0][0]= q0Sqr + q1Sqr - q2Sqr - q3Sqr; |
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element[0][1] = 2.0 * ( q.y * q.z + q.x * q.w ); |
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element[0][2] = 2.0 * ( q.y * q.w - q.x * q.z ); |
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|
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element[1][0] = 2.0 * ( q.y * q.z - q.x * q.w ); |
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element[1][1] = q0Sqr - q1Sqr + q2Sqr - q3Sqr; |
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element[1][2] = 2.0 * ( q.z * q.w + q.x * q.y ); |
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|
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element[2][0] = 2.0 * ( q.y * q.w + q.x * q.z ); |
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element[2][1] = 2.0 * ( q.z * q.w - q.x * q.y ); |
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element[2][2] = q0Sqr - q1Sqr -q2Sqr +q3Sqr; |
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|
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} |
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|
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Mat3x3d::Mat3x3d(const Euler3& e){ |
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double sinTheta; |
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double sinPhi; |
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double sinPsi; |
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double cosTheta; |
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double cosPhi; |
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double cosPsi; |
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|
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sinTheta = sin(e.theta); |
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sinPhi = sin(e.phi); |
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sinPsi = sin(e.psi); |
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|
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cosTheta = cos(e.theta); |
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cosPhi = cos(e.phi); |
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cosPsi = cos(e.psi); |
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|
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element[0][0] = (cosPhi * cosPsi) - (sinPhi * cosTheta * sinPsi); |
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element[0][1] = (sinPhi * cosPsi) + (cosPhi * cosTheta * sinPsi); |
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element[0][2] = sinTheta * sinPsi; |
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|
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element[1][0] = -(cosPhi * sinPsi) - (sinPhi * cosTheta * cosPsi); |
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element[1][1] = -(sinPhi * sinPsi) + (cosPhi * cosTheta * cosPsi); |
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element[1][2] = sinTheta * cosPsi; |
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|
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element[2][0] = sinPhi * sinTheta; |
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element[2][1] = -cosPhi * sinTheta; |
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element[2][2] = cosTheta; |
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} |
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|
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Mat3x3d Mat3x3d::inverse() const{ |
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|
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Mat3x3d invMat; |
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|
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double determinant = det(); |
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|
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invMat.element[0][0] = element[1][1]*element[2][2] - element[1][2]*element[2][1]; |
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invMat.element[1][0] = element[1][2]*element[2][0] - element[1][0]*element[2][2]; |
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invMat.element[2][0] = element[1][0]*element[2][1] - element[1][1]*element[2][0]; |
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invMat.element[0][1] = element[2][1]*element[0][2] - element[2][2]*element[0][1]; |
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invMat.element[1][1] = element[2][2]*element[0][0] - element[2][0]*element[0][2]; |
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invMat.element[2][1] = element[2][0]*element[0][1] - element[2][1]*element[0][0]; |
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invMat.element[0][2] = element[0][1]*element[1][2] - element[0][2]*element[1][1]; |
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invMat.element[1][2] = element[0][2]*element[1][0] - element[0][0]*element[1][2]; |
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invMat.element[2][2] = element[0][0]*element[1][1] - element[0][1]*element[1][0]; |
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|
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invMat /= determinant; |
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|
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return(invMat); |
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} |
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|
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Mat3x3d Mat3x3d::transpose(void) const{ |
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Mat3x3d transposeMat; |
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|
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for(unsigned int i=0; i<3; i++) |
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for(unsigned int j=0; j<3; j++) |
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transposeMat.element[i][j] = element[j][i]; |
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|
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return(transposeMat); |
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|
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} |
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|
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double Mat3x3d::det() const{ |
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double x; |
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double y; |
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double z; |
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|
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x = element[0][0] * (element[1][1] * element[2][2] - element[1][2] * element[2][1]); |
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y = element[0][1] * (element[1][2] * element[2][0] - element[1][0] * element[2][2]); |
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z = element[0][2] * (element[1][0] * element[2][1] - element[1][1] * element[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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void Mat3x3d::diagonalize(Vector3d& v, Mat3x3d& m){ |
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diagonalize(v.vec, m.element); |
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} |
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|
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void Mat3x3d::diagonalize(Vector3d& v, double m[3][3]){ |
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diagonalize(v.vec, m); |
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} |
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|
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void Mat3x3d::diagonalize(double v[3], Mat3x3d& m){ |
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diagonalize(v, m.element); |
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} |
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|
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void Mat3x3d::diagonalize(double v[3], double m[3][3]){ |
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|
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} |
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|
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Quaternion Mat3x3d::toQuaternion(){ |
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Quaternion q; |
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double t, s; |
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double ad1, ad2, ad3; |
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|
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t = element[0][0] + element[1][1] + element[2][2] + 1.0; |
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if( t > 0.0 ){ |
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|
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s = 0.5 / sqrt( t ); |
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q.x = 0.25 / s; |
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q.y = (element[1][2] - element[2][1]) * s; |
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q.z = (element[2][0] - element[0][2]) * s; |
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q.w = (element[0][1] - element[1][0]) * s; |
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} |
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else{ |
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|
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ad1 = fabs( element[0][0] ); |
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ad2 = fabs( element[1][1] ); |
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ad3 = fabs( element[2][2] ); |
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|
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if( ad1 >= ad2 && ad1 >= ad3 ){ |
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s = 2.0 * sqrt( 1.0 + element[0][0] - element[1][1] - element[2][2] ); |
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q.x = (element[1][2] + element[2][1]) / s; |
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q.y = 0.5 / s; |
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q.z = (element[0][1] + element[1][0]) / s; |
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q.w = (element[0][2] + element[2][0]) / s; |
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} |
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else if( ad2 >= ad1 && ad2 >= ad3 ){ |
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s = sqrt( 1.0 + element[1][1] - element[0][0] - element[2][2] ) * 2.0; |
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q.x = (element[0][2] + element[2][0]) / s; |
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q.y = (element[0][1] + element[1][0]) / s; |
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q.z = 0.5 / s; |
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q.w = (element[1][2] + element[2][1]) / s; |
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} |
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else{ |
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s = sqrt( 1.0 + element[2][2] - element[0][0] - element[1][1] ) * 2.0; |
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q.x = (element[0][1] + element[1][0]) / s; |
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q.y = (element[0][2] + element[2][0]) / s; |
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q.z = (element[1][2] + element[2][1]) / s; |
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q.w = 0.5 / s; |
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} |
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} |
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return q; |
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} |
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|
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Euler3 Mat3x3d::toEuler(){ |
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// We use so-called "x-convention", which is the most common definition. |
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// In this convention, the rotation given by Euler angles (phi, theta, psi), where the first |
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// rotation is by an angle phi about the z-axis, the second is by an angle |
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// theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the |
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//z-axis (again). |
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|
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Euler3 e; |
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double cosTheta; |
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double sinTheta; |
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const double eps = 1.0e-8; |
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// set the tolerance for Euler angles and rotation elements |
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|
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e.theta = acos(min(1.0,max(-1.0, element[2][2]))); |
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cosTheta = element[2][2]; |
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sinTheta = sqrt(1.0 - cosTheta * cosTheta); |
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|
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// when sin(theta) is close to 0, we need to consider singularity |
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// In this case, we can assign an arbitary value to phi (or psi), and then determine |
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// the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 |
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// in cases of singularity. |
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// we use atan2 instead of atan, since atan2 will give us -Pi to Pi. |
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// Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never |
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// change the sign of both of the parameters passed to atan2. |
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|
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if (fabs(sinTheta) <= eps){ |
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e.psi = 0.0; |
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//e.phi = atan2(-Amat[Ayx], Amat[Axx]); |
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e.phi = atan2(-element[1][0], element[0][0]); |
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} |
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// we only have one unique solution |
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else{ |
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//e.phi = atan2(Amat[Azx], -Amat[Azy]); |
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//e.psi = atan2(Amat[Axz], Amat[Ayz]); |
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e.phi = atan2(element[2][0], -element[2][1]); |
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e.psi = atan2(element[0][2], -element[1][2]); |
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} |
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|
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//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
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//if (phi < 0) |
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// phi += M_PI; |
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|
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//if (psi < 0) |
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// psi += M_PI |
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|
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return e; |
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} |
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|
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|
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Vector3d operator*(const Mat3x3d& m, const Vector3d& v){ |
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Vector3d result; |
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|
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result.x = m.element[0][0] * v.x + m.element[0][1] * v.y + m.element[0][2]*v.z; |
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result.y = m.element[1][0] * v.x + m.element[1][1] * v.y + m.element[1][2]*v.z; |
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result.z = m.element[2][0] * v.x + m.element[2][1] * v.y + m.element[2][2]*v.z; |
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|
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return result; |
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} |
