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root/OpenMD/branches/development/src/math/Quaternion.hpp

Comparing:
trunk/src/math/Quaternion.hpp (file contents), Revision 507 by gezelter, Fri Apr 15 22:04:00 2005 UTC vs.
branches/development/src/math/Quaternion.hpp (file contents), Revision 1850 by gezelter, Wed Feb 20 15:39:39 2013 UTC

#	Line 6 | Line 6
6		* redistribute this software in source and binary code form, provided
7		* that the following conditions are met:
8		*
9	<	* 1. Acknowledgement of the program authors must be made in any
10	<	*    publication of scientific results based in part on use of the
11	<	*    program.  An acceptable form of acknowledgement is citation of
12	<	*    the article in which the program was described (Matthew
13	<	*    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	<	*    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	<	*    Parallel Simulation Engine for Molecular Dynamics,"
16	<	*    J. Comput. Chem. 26, pp. 252-271 (2005))
17	<	*
18	<	* 2. Redistributions of source code must retain the above copyright
9	>	* 1. Redistributions of source code must retain the above copyright
10		*    notice, this list of conditions and the following disclaimer.
11		*
12	<	* 3. Redistributions in binary form must reproduce the above copyright
12	>	* 2. Redistributions in binary form must reproduce the above copyright
13		*    notice, this list of conditions and the following disclaimer in the
14		*    documentation and/or other materials provided with the
15		*    distribution.
#	Line 37 | Line 28
28		* arising out of the use of or inability to use software, even if the
29		* University of Notre Dame has been advised of the possibility of
30		* such damages.
31	+	*
32	+	* SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
33	+	* research, please cite the appropriate papers when you publish your
34	+	* work.  Good starting points are:
35	+	*
36	+	* [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37	+	* [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38	+	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
39	+	* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	+	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41		*/
42
43		/**
#	Line 48 | Line 49
49
50		#ifndef MATH_QUATERNION_HPP
51		#define MATH_QUATERNION_HPP
52	+	#include "config.h"
53	+	#include <cmath>
54
55	<	#include "math/Vector.hpp"
55	>	#include "math/Vector3.hpp"
56		#include "math/SquareMatrix.hpp"
57	+	#define ISZERO(a,eps) ( (a)>-(eps) && (a)<(eps) )
58	+	const RealType tiny=1.0e-6;
59
60	<	namespace oopse{
60	>	namespace OpenMD{
61
62		/**
63		* @class Quaternion Quaternion.hpp "math/Quaternion.hpp"
64		* Quaternion is a sort of a higher-level complex number.
65		* It is defined as Q = w + x*i + y*j + z*k,
66	<	* where w, x, y, and z are numbers of type T (e.g. double), and
66	>	* where w, x, y, and z are numbers of type T (e.g. RealType), and
67		* i*i = -1; j*j = -1; k*k = -1;
68		* i*j = k; j*k = i; k*i = j;
69		*/
70		template<typename Real>
71		class Quaternion : public Vector<Real, 4> {
72	+
73		public:
74		Quaternion() : Vector<Real, 4>() {}
75
#	Line 78 | Line 84 | namespace oopse{
84		/** Constructs and initializes a Quaternion from a  Vector<Real,4> */
85		Quaternion(const Vector<Real,4>& v)
86		: Vector<Real, 4>(v){
87	<	}
87	>	}
88
89		/** copy assignment */
90		Quaternion& operator =(const Vector<Real, 4>& v){
91		if (this == & v)
92		return *this;
93	<
93	>
94		Vector<Real, 4>::operator=(v);
95	<
95	>
96		return *this;
97		}
98	<
98	>
99		/**
100		* Returns the value of the first element of this quaternion.
101		* @return the value of the first element of this quaternion
#	Line 242 | Line 248 | namespace oopse{
248		* Returns the conjugate quaternion of this quaternion
249		* @return the conjugate quaternion of this quaternion
250		*/
251	<	Quaternion<Real> conjugate() {
251	>	Quaternion<Real> conjugate() const {
252		return Quaternion<Real>(w(), -x(), -y(), -z());
253	+	}
254	+
255	+
256	+	/**
257	+	return rotation angle from -PI to PI
258	+	*/
259	+	inline Real get_rotation_angle() const{
260	+	if( w() < (Real)0.0 )
261	+	return 2.0*atan2(-sqrt( x()*x() + y()*y() + z()*z() ), -w() );
262	+	else
263	+	return 2.0*atan2( sqrt( x()*x() + y()*y() + z()*z() ),  w() );
264	+	}
265	+
266	+	/**
267	+	create a unit quaternion from axis angle representation
268	+	*/
269	+	Quaternion<Real> fromAxisAngle(const Vector3<Real>& axis,
270	+	const Real& angle){
271	+	Vector3<Real> v(axis);
272	+	v.normalize();
273	+	Real half_angle = angle*0.5;
274	+	Real sin_a = sin(half_angle);
275	+	*this = Quaternion<Real>(cos(half_angle),
276	+	v.x()*sin_a,
277	+	v.y()*sin_a,
278	+	v.z()*sin_a);
279	+	return *this;
280	+	}
281	+
282	+	/**
283	+	convert a quaternion to axis angle representation,
284	+	preserve the axis direction and angle from -PI to +PI
285	+	*/
286	+	void toAxisAngle(Vector3<Real>& axis, Real& angle)const {
287	+	Real vl = sqrt( x()*x() + y()*y() + z()*z() );
288	+	if( vl > tiny ) {
289	+	Real ivl = 1.0/vl;
290	+	axis.x() = x() * ivl;
291	+	axis.y() = y() * ivl;
292	+	axis.z() = z() * ivl;
293	+
294	+	if( w() < 0 )
295	+	angle = 2.0*atan2(-vl, -w()); //-PI,0
296	+	else
297	+	angle = 2.0*atan2( vl,  w()); //0,PI
298	+	} else {
299	+	axis = Vector3<Real>(0.0,0.0,0.0);
300	+	angle = 0.0;
301	+	}
302	+	}
303	+
304	+	/**
305	+	shortest arc quaternion rotate one vector to another by shortest path.
306	+	create rotation from -> to, for any length vectors.
307	+	*/
308	+	Quaternion<Real> fromShortestArc(const Vector3d& from,
309	+	const Vector3d& to ) {
310	+
311	+	Vector3d c( cross(from,to) );
312	+	*this = Quaternion<Real>(dot(from,to),
313	+	c.x(),
314	+	c.y(),
315	+	c.z());
316	+
317	+	this->normalize();    // if "from" or "to" not unit, normalize quat
318	+	w() += 1.0f;            // reducing angle to halfangle
319	+	if( w() <= 1e-6 ) {     // angle close to PI
320	+	if( ( from.z()*from.z() ) > ( from.x()*from.x() ) ) {
321	+	this->data_[0] =  w();
322	+	this->data_[1] =  0.0;       //cross(from , Vector3d(1,0,0))
323	+	this->data_[2] =  from.z();
324	+	this->data_[3] = -from.y();
325	+	} else {
326	+	this->data_[0] =  w();
327	+	this->data_[1] =  from.y();  //cross(from, Vector3d(0,0,1))
328	+	this->data_[2] = -from.x();
329	+	this->data_[3] =  0.0;
330	+	}
331	+	}
332	+	this->normalize();
333	+	}
334	+
335	+	Real ComputeTwist(const Quaternion& q) {
336	+	return  (Real)2.0 * atan2(q.z(), q.w());
337	+	}
338	+
339	+	void RemoveTwist(Quaternion& q) {
340	+	Real t = ComputeTwist(q);
341	+	Quaternion rt = fromAxisAngle(V3Z, t);
342	+
343	+	q *= rt.inverse();
344	+	}
345	+
346	+	void getTwistSwingAxisAngle(Real& twistAngle, Real& swingAngle,
347	+	Vector3<Real>& swingAxis) {
348	+
349	+	twistAngle = (Real)2.0 * atan2(z(), w());
350	+	Quaternion rt, rs;
351	+	rt.fromAxisAngle(V3Z, twistAngle);
352	+	rs = *this * rt.inverse();
353	+
354	+	Real vl = sqrt( rs.x()*rs.x() + rs.y()*rs.y() + rs.z()*rs.z() );
355	+	if( vl > tiny ) {
356	+	Real ivl = 1.0 / vl;
357	+	swingAxis.x() = rs.x() * ivl;
358	+	swingAxis.y() = rs.y() * ivl;
359	+	swingAxis.z() = rs.z() * ivl;
360	+
361	+	if( rs.w() < 0.0 )
362	+	swingAngle = 2.0*atan2(-vl, -rs.w()); //-PI,0
363	+	else
364	+	swingAngle = 2.0*atan2( vl,  rs.w()); //0,PI
365	+	} else {
366	+	swingAxis = Vector3<Real>(1.0,0.0,0.0);
367	+	swingAngle = 0.0;
368	+	}
369	+	}
370	+
371	+
372	+	Vector3<Real> rotate(const Vector3<Real>& v) {
373	+
374	+	Quaternion<Real> q(v.x() * w() + v.z() * y() - v.y() * z(),
375	+	v.y() * w() + v.x() * z() - v.z() * x(),
376	+	v.z() * w() + v.y() * x() - v.x() * y(),
377	+	v.x() * x() + v.y() * y() + v.z() * z());
378	+
379	+	return Vector3<Real>(w()*q.x() + x()*q.w() + y()*q.z() - z()*q.y(),
380	+	w()*q.y() + y()*q.w() + z()*q.x() - x()*q.z(),
381	+	w()*q.z() + z()*q.w() + x()*q.y() - y()*q.x())*
382	+	( 1.0/this->lengthSquare() );
383	+	}
384	+
385	+	Quaternion<Real>& align (const Vector3<Real>& V1,
386	+	const Vector3<Real>& V2) {
387	+
388	+	// If V1 and V2 are not parallel, the axis of rotation is the unit-length
389	+	// vector U = Cross(V1,V2)/Length(Cross(V1,V2)).  The angle of rotation,
390	+	// A, is the angle between V1 and V2.  The quaternion for the rotation is
391	+	// q = cos(A/2) + sin(A/2)*(ux*i+uy*j+uz*k) where U = (ux,uy,uz).
392	+	//
393	+	// (1) Rather than extract A = acos(Dot(V1,V2)), multiply by 1/2, then
394	+	//     compute sin(A/2) and cos(A/2), we reduce the computational costs
395	+	//     by computing the bisector B = (V1+V2)/Length(V1+V2), so cos(A/2) =
396	+	//     Dot(V1,B).
397	+	//
398	+	// (2) The rotation axis is U = Cross(V1,B)/Length(Cross(V1,B)), but
399	+	//     Length(Cross(V1,B)) = Length(V1)*Length(B)*sin(A/2) = sin(A/2), in
400	+	//     which case sin(A/2)*(ux*i+uy*j+uz*k) = (cx*i+cy*j+cz*k) where
401	+	//     C = Cross(V1,B).
402	+	//
403	+	// If V1 = V2, then B = V1, cos(A/2) = 1, and U = (0,0,0).  If V1 = -V2,
404	+	// then B = 0.  This can happen even if V1 is approximately -V2 using
405	+	// floating point arithmetic, since Vector3::Normalize checks for
406	+	// closeness to zero and returns the zero vector accordingly.  The test
407	+	// for exactly zero is usually not recommend for floating point
408	+	// arithmetic, but the implementation of Vector3::Normalize guarantees
409	+	// the comparison is robust.  In this case, the A = pi and any axis
410	+	// perpendicular to V1 may be used as the rotation axis.
411	+
412	+	Vector3<Real> Bisector = V1 + V2;
413	+	Bisector.normalize();
414	+
415	+	Real CosHalfAngle = dot(V1,Bisector);
416	+
417	+	this->data_[0] = CosHalfAngle;
418	+
419	+	if (CosHalfAngle != (Real)0.0) {
420	+	Vector3<Real> Cross = cross(V1, Bisector);
421	+	this->data_[1] = Cross.x();
422	+	this->data_[2] = Cross.y();
423	+	this->data_[3] = Cross.z();
424	+	} else {
425	+	Real InvLength;
426	+	if (fabs(V1[0]) >= fabs(V1[1])) {
427	+	// V1.x or V1.z is the largest magnitude component
428	+	InvLength = (Real)1.0/sqrt(V1[0]*V1[0] + V1[2]*V1[2]);
429	+
430	+	this->data_[1] = -V1[2]*InvLength;
431	+	this->data_[2] = (Real)0.0;
432	+	this->data_[3] = +V1[0]*InvLength;
433	+	} else {
434	+	// V1.y or V1.z is the largest magnitude component
435	+	InvLength = (Real)1.0 / sqrt(V1[1]*V1[1] + V1[2]*V1[2]);
436	+
437	+	this->data_[1] = (Real)0.0;
438	+	this->data_[2] = +V1[2]*InvLength;
439	+	this->data_[3] = -V1[1]*InvLength;
440	+	}
441	+	}
442	+	return *this;
443		}
444
445	+	void toTwistSwing ( Real& tw, Real& sx, Real& sy ) {
446	+
447	+	// First test if the swing is in the singularity:
448	+
449	+	if ( ISZERO(z(),tiny) && ISZERO(w(),tiny) ) { sx=sy=M_PI; tw=0; return; }
450	+
451	+	// Decompose into twist-swing by solving the equation:
452	+	//
453	+	//                       Qtwist(t*2) * Qswing(s*2) = q
454	+	//
455	+	// note: (x,y) is the normalized swing axis (x*x+y*y=1)
456	+	//
457	+	//          ( Ct 0 0 St ) * ( Cs xSs ySs 0 ) = ( qw qx qy qz )
458	+	//  ( CtCs  xSsCt-yStSs  xStSs+ySsCt  StCs ) = ( qw qx qy qz )      (1)
459	+	// From (1): CtCs / StCs = qw/qz => Ct/St = qw/qz => tan(t) = qz/qw (2)
460	+	//
461	+	// The swing rotation/2 s comes from:
462	+	//
463	+	// From (1): (CtCs)^2 + (StCs)^2 = qw^2 + qz^2 =>
464	+	//                                       Cs = sqrt ( qw^2 + qz^2 ) (3)
465	+	//
466	+	// From (1): (xSsCt-yStSs)^2 + (xStSs+ySsCt)^2 = qx^2 + qy^2 =>
467	+	//                                       Ss = sqrt ( qx^2 + qy^2 ) (4)
468	+	// From (1):  |SsCt -StSs| |x| = |qx|
469	+	//            |StSs +SsCt| |y|   |qy|                              (5)
470	+
471	+	Real qw, qx, qy, qz;
472	+
473	+	if ( w()<0 ) {
474	+	qw=-w();
475	+	qx=-x();
476	+	qy=-y();
477	+	qz=-z();
478	+	} else {
479	+	qw=w();
480	+	qx=x();
481	+	qy=y();
482	+	qz=z();
483	+	}
484	+
485	+	Real t = atan2 ( qz, qw ); // from (2)
486	+	Real s = atan2( sqrt(qx*qx+qy*qy), sqrt(qz*qz+qw*qw) ); // from (3)
487	+	// and (4)
488	+
489	+	Real x=0.0, y=0.0, sins=sin(s);
490	+
491	+	if ( !ISZERO(sins,tiny) ) {
492	+	Real sint = sin(t);
493	+	Real cost = cos(t);
494	+
495	+	// by solving the linear system in (5):
496	+	y = (-qx*sint + qy*cost)/sins;
497	+	x = ( qx*cost + qy*sint)/sins;
498	+	}
499	+
500	+	tw = (Real)2.0*t;
501	+	sx = (Real)2.0*x*s;
502	+	sy = (Real)2.0*y*s;
503	+	}
504	+
505	+	void toSwingTwist(Real& sx, Real& sy, Real& tw ) {
506	+
507	+	// Decompose q into swing-twist using a similar development as
508	+	// in function toTwistSwing
509	+
510	+	if ( ISZERO(z(),tiny) && ISZERO(w(),tiny) ) { sx=sy=M_PI; tw=0; }
511	+
512	+	Real qw, qx, qy, qz;
513	+	if ( w() < 0 ){
514	+	qw=-w();
515	+	qx=-x();
516	+	qy=-y();
517	+	qz=-z();
518	+	} else {
519	+	qw=w();
520	+	qx=x();
521	+	qy=y();
522	+	qz=z();
523	+	}
524	+
525	+	// Get the twist t:
526	+	Real t = 2.0 * atan2(qz,qw);
527	+
528	+	Real bet = atan2( sqrt(qx*qx+qy*qy), sqrt(qz*qz+qw*qw) );
529	+	Real gam = t/2.0;
530	+	Real sinc = ISZERO(bet,tiny)? 1.0 : sin(bet)/bet;
531	+	Real singam = sin(gam);
532	+	Real cosgam = cos(gam);
533	+
534	+	sx = Real( (2.0/sinc) * (cosgam*qx - singam*qy) );
535	+	sy = Real( (2.0/sinc) * (singam*qx + cosgam*qy) );
536	+	tw = Real( t );
537	+	}
538	+
539	+
540	+
541		/**
542		* Returns the corresponding rotation matrix (3x3)
543		* @return a 3x3 rotation matrix
544		*/
545		SquareMatrix<Real, 3> toRotationMatrix3() {
546		SquareMatrix<Real, 3> rotMat3;
547	<
547	>
548		Real w2;
549		Real x2;
550		Real y2;
#	Line 355 | Line 647 | namespace oopse{
647		return equal(lhs[0] ,rhs[0]) && equal(lhs[1] , rhs[1]) && equal(lhs[2], rhs[2]) && equal(lhs[3], rhs[3]);
648		}
649
650	<	typedef Quaternion<double> Quat4d;
650	>	typedef Quaternion<RealType> Quat4d;
651		}
652		#endif //MATH_QUATERNION_HPP

Comparing:
trunk/src/math/Quaternion.hpp (property svn:keywords), Revision 507 by gezelter, Fri Apr 15 22:04:00 2005 UTC vs.
branches/development/src/math/Quaternion.hpp (property svn:keywords), Revision 1850 by gezelter, Wed Feb 20 15:39:39 2013 UTC

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