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/*
Copyright 2008 Brain Research Institute, Melbourne, Australia
Written by J-Donald Tournier, 27/06/08.
This file is part of MRtrix.
MRtrix is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
MRtrix is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with MRtrix. If not, see <http://www.gnu.org/licenses/>.
04-07-2008 J-Donald Tournier <d.tournier@brain.org.au>
* test for rounding errors in Quaternion::from_matrix().
In certain cases, a negative number was passed to sqrt()
*/
#ifndef __quaternion_h__
#define __quaternion_h__
#include "mrtrix.h"
namespace MR {
namespace Math {
class Quaternion {
protected:
float x[4];
public:
Quaternion () { x[0] = 1.0; x[1] = x[2] = x[3] = 0.0; }
Quaternion (float t, float vx, float vy, float vz) { x[0] = t; x[1] = vx; x[2] = vy; x[3] = vz; }
Quaternion (float b, float c, float d) { x[0] = sqrt(1.0 - b*b - c*c - d*d); x[1] = b; x[2] = c; x[3] = d; }
Quaternion (float angle, float* axis)
{
x[0] = cos (angle/2.0); x[1] = axis[0]; x[2] = axis[1]; x[3] = axis[2];
float norm = sin (angle/2.0) / sqrt (x[1]*x[1] + x[2]*x[2] + x[3]*x[3]);
x[1] *= norm; x[2] *= norm; x[3] *= norm;
}
Quaternion (const float* matrix) { from_matrix (matrix); }
operator bool () const { return (!(gsl_isnan (x[0]) || gsl_isnan (x[1]) || gsl_isnan (x[2]) || gsl_isnan (x[3]))); }
bool operator! () const { return (gsl_isnan (x[0]) || gsl_isnan (x[1]) || gsl_isnan (x[2]) || gsl_isnan (x[3])); }
void invalidate () { x[0] = x[1] = x[2] = x[3] = GSL_NAN; }
void normalise ()
{
float n = 1.0 / sqrt (x[0]*x[0] + x[1]*x[1] + x[2]*x[2] + x[3]*x[3]);
x[0] *= n; x[1] *= n; x[2] *= n; x[3] *= n;
}
void from_matrix (const float* matrix);
void to_matrix (float* matrix);
const float& operator[] (int index) const { return (x[index]); }
float& operator[] (int index) { return (x[index]); }
bool operator== (const Quaternion& y) const { return (memcmp (x, y.x, 4*sizeof(float)) == 0); }
bool operator!= (const Quaternion& y) const { return (memcmp (x, y.x, 4*sizeof(float))); }
Quaternion operator* (const Quaternion& y) const;
const Quaternion& operator*= (const Quaternion& y) { *this = (*this) * y; return (*this); }
};
std::ostream& operator<< (std::ostream& stream, const Quaternion& q);
inline Quaternion Quaternion::operator* (const Quaternion& y) const
{
Quaternion q (
x[0]*y[0] - x[1]*y[1] - x[2]*y[2] - x[3]*y[3],
x[0]*y[1] + x[1]*y[0] + x[2]*y[3] - x[3]*y[2],
x[0]*y[2] - x[1]*y[3] + x[2]*y[0] + x[3]*y[1],
x[0]*y[3] + x[1]*y[2] - x[2]*y[1] + x[3]*y[0] );
q.normalise();
return (q);
}
inline void Quaternion::from_matrix (const float* matrix)
{
x[0] = 1.0 + matrix[0] + matrix[4] + matrix[8];
x[0] = x[0] > 0.0 ? 0.5 * sqrt (x[0]) : 0.0;
if (fabs (x[0]) < 0.1) {
x[1] = 1.0 + matrix[0] - matrix[4] - matrix[8];
x[1] = x[1] > 0.0 ? 0.5 * sqrt (x[1]) : 0.0;
if (fabs (x[1]) < 0.1) {
x[2] = 1.0 - matrix[0] + matrix[4] - matrix[8];
x[2] = x[2] > 0.0 ? 0.5 * sqrt (x[2]) : 0.0;
if (fabs (x[2]) < 0.1) {
x[3] = 0.5 * sqrt (1.0 - matrix[0] - matrix[4] + matrix[8]);
x[0] = (matrix[3] - matrix[1]) / (4.0 * x[3]);
x[1] = (matrix[2] + matrix[6]) / (4.0 * x[3]);
x[2] = (matrix[7] + matrix[5]) / (4.0 * x[3]);
}
else {
x[0] = (matrix[2] - matrix[6]) / (4.0 * x[2]);
x[1] = (matrix[3] + matrix[1]) / (4.0 * x[2]);
x[3] = (matrix[7] + matrix[5]) / (4.0 * x[2]);
}
}
else {
x[0] = (matrix[7] - matrix[5]) / (4.0 * x[1]);
x[2] = (matrix[3] + matrix[1]) / (4.0 * x[1]);
x[3] = (matrix[2] + matrix[6]) / (4.0 * x[1]);
}
}
else {
x[1] = (matrix[7] - matrix[5]) / (4.0 * x[0]);
x[2] = (matrix[2] - matrix[6]) / (4.0 * x[0]);
x[3] = (matrix[3] - matrix[1]) / (4.0 * x[0]);
}
normalise();
}
inline void Quaternion::to_matrix (float* matrix)
{
matrix[0] = x[0]*x[0] + x[1]*x[1] - x[2]*x[2] - x[3]*x[3];
matrix[1] = 2.0*x[1]*x[2] - 2.0*x[0]*x[3];
matrix[2] = 2.0*x[1]*x[3] + 2.0*x[0]*x[2];
matrix[3] = 2.0*x[1]*x[2] + 2.0*x[0]*x[3];
matrix[4] = x[0]*x[0] + x[2]*x[2] - x[1]*x[1] - x[3]*x[3];
matrix[5] = 2.0*x[2]*x[3] - 2.0*x[0]*x[1];
matrix[6] = 2.0*x[1]*x[3] - 2.0*x[0]*x[2];
matrix[7] = 2.0*x[2]*x[3] + 2*x[0]*x[1];
matrix[8] = x[0]*x[0] + x[3]*x[3] - x[2]*x[2] - x[1]*x[1];
}
inline std::ostream& operator<< (std::ostream& stream, const Quaternion& q)
{
stream << "[ " << q[0] << " " << q[1] << "i " << q[2] << "j " << q[3] << "k ]";
return (stream);
}
}
}
#endif
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