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cqrlib.c
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cqrlib.c
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/*
* cqrlib.c
*
*
* Created by Herbert J. Bernstein on 2/15/09.
* Copyright 2009 Herbert J. Bernstein. All rights reserved.
*
* Revised, 8 July 2009 for CQR_FAR macro -- HJB
*/
/* Work supported in part by NIH NIGMS under grant 1R15GM078077-01 and DOE
under grant ER63601-1021466-0009501. Any opinions, findings, and
conclusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the funding agencies.
*/
/**********************************************************************
* *
* YOU MAY REDISTRIBUTE THE CQRlib API UNDER THE TERMS OF THE LGPL *
* *
**********************************************************************/
/************************* LGPL NOTICES *******************************
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Lesser General Public *
* License as published by the Free Software Foundation; either *
* version 2.1 of the License, or (at your option) any later version. *
* *
* This library 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 *
* Lesser General Public License for more details. *
* *
* You should have received a copy of the GNU Lesser General Public *
* License along with this library; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301 USA *
* *
**********************************************************************/
/* A utility library for quaternion arithmetic and
quaternion rotation math. See
"Quaternions and spatial rotation", Wikipedia
http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation
K. Shoemake, "Quaternions", Department of Computer Science,
University of Pennsylvania, Philadelphia, PA 19104,
ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/quatut.ps.Z
K. Shoemake, "Animating rotation with quaternion curves",
ACM SIGGRAPH Computer Graphics, Vol 19, No. 3, pp 245--254,
1985.
*/
#ifdef __cplusplus
extern "C" {
#endif
#ifdef _MSC_VER
#define USE_LOCAL_HEADERS
#endif
#ifndef USE_LOCAL_HEADERS
#include <cqrlib.h>
#else
#include "cqrlib.h"
#endif
/* CQRCreateQuaternion -- create a quaternion = w +ix+jy+kz */
int CQRCreateQuaternion(CQRQuaternionHandle CQR_FAR * quaternion, double w, double x, double y, double z) {
*quaternion = (CQRQuaternionHandle)CQR_MALLOC(sizeof(CQRQuaternion));
if (!*quaternion) return CQR_NO_MEMORY;
(*quaternion)->w = w;
(*quaternion)->x = x;
(*quaternion)->y = y;
(*quaternion)->z = z;
return CQR_SUCCESS;
}
/* CQRCreateEmptyQuaternion -- create a quaternion = 0 +i0+j0+k0 */
int CQRCreateEmptyQuaternion(CQRQuaternionHandle CQR_FAR * quaternion) {
*quaternion = (CQRQuaternionHandle)CQR_MALLOC(sizeof(CQRQuaternion));
if (!*quaternion) return CQR_NO_MEMORY;
(*quaternion)->w = 0;
(*quaternion)->x = 0;
(*quaternion)->y = 0;
(*quaternion)->z = 0;
return CQR_SUCCESS;
}
/* CQRFreeQuaternion -- free a quaternion */
int CQRFreeQuaternion(CQRQuaternionHandle CQR_FAR * quaternion) {
if (!quaternion) return CQR_BAD_ARGUMENT;
CQR_FREE(*quaternion);
*quaternion = NULL;
return CQR_SUCCESS;
}
/* CQRSetQuaternion -- create an existing quaternion = w +ix+jy+kz */
int CQRSetQuaternion( CQRQuaternionHandle quaternion, double w, double x, double y, double z) {
if (!quaternion) return CQR_BAD_ARGUMENT;
quaternion->w = w;
quaternion->x = x;
quaternion->y = y;
quaternion->z = z;
return CQR_SUCCESS;
}
/* CQRGetQuaternionW -- get the w component of a quaternion */
int CQRGetQuaternionW( double CQR_FAR * qw, CQRQuaternionHandle q ) {
if (!qw || ! q) return CQR_BAD_ARGUMENT;
*qw = q->w;
return CQR_SUCCESS;
}
/* CQRGetQuaternionX -- get the x component of a quaternion */
int CQRGetQuaternionX( double CQR_FAR * qx, CQRQuaternionHandle q ) {
if (!qx || ! q) return CQR_BAD_ARGUMENT;
*qx = q->x;
return CQR_SUCCESS;
}
/* CQRGetQuaternionY -- get the y component of a quaternion */
int CQRGetQuaternionY( double CQR_FAR * qy, CQRQuaternionHandle q ) {
if (!qy || ! q) return CQR_BAD_ARGUMENT;
*qy = q->y;
return CQR_SUCCESS;
}
/* CQRGetQuaternionZ -- get the z component of a quaternion */
int CQRGetQuaternionZ( double CQR_FAR * qz, CQRQuaternionHandle q ) {
if (!qz || ! q) return CQR_BAD_ARGUMENT;
*qz = q->z;
return CQR_SUCCESS;
}
/* CQRGetQuaternionIm -- get the imaginary component of a quaternion */
int CQRGetQuaternionIm( CQRQuaternionHandle quaternion, CQRQuaternionHandle q ) {
if (!quaternion || ! q) return CQR_BAD_ARGUMENT;
quaternion->w = 0.;
quaternion->x = q->x;
quaternion->y = q->y;
quaternion->z = q->z;
return CQR_SUCCESS;
}
/* CQRGetQuaternionAxis -- get the axis for the polar representation of a quaternion */
int CQRGetQuaternionAxis( CQRQuaternionHandle quaternion, CQRQuaternionHandle q ) {
double anorm;
if (!quaternion || ! q) return CQR_BAD_ARGUMENT;
anorm = sqrt((q->x)*(q->x)+(q->y)*(q->y)+(q->z)*(q->z));
if (anorm < DBL_MIN) {
quaternion->w = 0.;
quaternion->x = 0.;
quaternion->y = 0.;
quaternion->z = 0.;
} else {
quaternion->w = 0.;
quaternion->x = q->x/anorm;
quaternion->y = q->y/anorm;
quaternion->z = q->z/anorm;
}
return CQR_SUCCESS;
}
/* CQRGetQuaternionAngle -- get the angular component of the polar representation
of aquaternion */
int CQRGetQuaternionAngle( double CQR_FAR * angle, CQRQuaternionHandle q ) {
double cosangle, sinangle;
double radius, anorm;
if (!angle || ! q) return CQR_BAD_ARGUMENT;
radius = sqrt( (q->w)*(q->w) + (q->x)*(q->x) + (q->y)*(q->y) + (q->z)*(q->z) );
anorm = sqrt( (q->x)*(q->x) + (q->y)*(q->y) + (q->z)*(q->z) );
if ( anorm <= DBL_MIN) {
return CQR_SUCCESS;
}
cosangle = (q->w)/radius;
sinangle = anorm/radius;
*angle = atan2(sinangle,cosangle);
return CQR_SUCCESS;
}
/* CQRLog -- get the natural logarithm of a quaternion */
int CQRLog( CQRQuaternionHandle quaternion, CQRQuaternionHandle q ) {
CQRQuaternion axis;
double angle;
double ipnormsq;
double PI;
if (!quaternion || ! q) return CQR_BAD_ARGUMENT;
CQRGetQuaternionAxis(&axis,q);
CQRGetQuaternionAngle(&angle,q);
if (q->w < 0.) {
ipnormsq = (q->x)*(q->x) + (q->y)*(q->y) + (q->z)*(q->z);
if (ipnormsq <= DBL_MIN ) {
PI = atan2(1.,1.)*4.;
CQRMSet(axis,0.,1.,0.,0.);
angle = PI;
}
}
quaternion->w = log(sqrt((q->w)*(q->w) + (q->x)*(q->x) + (q->y)*(q->y) + (q->z)*(q->z) ));
quaternion->x = axis.x*angle;
quaternion->y = axis.y*angle;
quaternion->z = axis.z*angle;
return CQR_SUCCESS;
}
/* CQRExp -- get the exponential (exp) of a quaternion */
int CQRExp( CQRQuaternionHandle quaternion, CQRQuaternionHandle q ) {
CQRQuaternion impart = {0,0,0,0};
double angle;
double rat;
if (!quaternion || ! q) return CQR_BAD_ARGUMENT;
CQRGetQuaternionIm(&impart,q);
CQRMNorm(angle,impart);
if (angle <= DBL_MIN) {
quaternion->w = cos(angle)*exp(q->w);
quaternion->x = 0.;
quaternion->y = 0.;
quaternion->z = 0.;
} else {
rat = exp(q->w)*sin(angle)/angle;
quaternion->w = cos(angle)*exp(q->w);
quaternion->x = rat*q->x;
quaternion->y = rat*q->y;
quaternion->z = rat*q->z;
}
return CQR_SUCCESS;
}
/* CQRQuaternionPower -- take a quaternion to a quaternion power */
int CQRQuaternionPower( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, CQRQuaternionHandle p) {
CQRQuaternion qlog,qlogtimesp;
CQRLog(&qlog,q);
CQRMMultiply(qlogtimesp,qlog,*p);
CQRExp(quaternion,&qlogtimesp);
return CQR_SUCCESS;
}
/* CQRDoublePower -- take a quarernion to a double power */
int CQRDoublePower( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, double p) {
CQRQuaternion qlog,qlogtimesp;
CQRLog(&qlog,q);
CQRMScalarMultiply(qlogtimesp,qlog,p);
CQRExp(quaternion,&qlogtimesp);
return CQR_SUCCESS;
}
/* CQRIntegerPower -- take a quaternion to an integer power */
int CQRIntegerPower( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, int p) {
CQRQuaternion qtemp, qsq, qprod;
unsigned int ptemp;
CQRMSet(*quaternion,1.0,0.,0.,0.);
if ( p == 0 ) return CQR_SUCCESS;
else if ( p > 0 ) {
CQRMCopy(qtemp,*q);
ptemp = p;
} else {
CQRMInverse(qtemp,*q);
ptemp = -p;
}
while(ptemp) {
if ((ptemp&1)!= 0) {
CQRMMultiply(qprod,*quaternion,qtemp);
CQRMCopy(*quaternion,qprod);
}
ptemp >>= 1;
if (ptemp==0) break;
CQRMMultiply(qsq,qtemp,qtemp);
CQRMCopy(qtemp,qsq)
}
return CQR_SUCCESS;
}
/* CQRIntegerRoot -- take the given integer root of a quaternion, returning
the indicated mth choice from among multiple roots.
For reals the cycle runs through first the i-based
roots, then the j-based roots and then the k-based roots,
out of the infinite number of possible roots of reals. */
int CQRIntegerRoot( CQRQuaternionHandle quaternion, CQRQuaternionHandle q, int r, int m) {
double PI;
CQRQuaternion qlog,qlogoverr,qaxis;
double recip, qaxisnormsq;
int cycle;
PI = 4.*atan2(1.,1.);
if (r == 0) return CQR_BAD_ARGUMENT;
recip = 1./((double)r);
CQRLog(&qlog,q);
if (m != 0) {
CQRGetQuaternionAxis(&qaxis,q);
CQRMNormsq(qaxisnormsq,qaxis);
if (qaxisnormsq <= DBL_MIN) {
cycle = (m/r)%3;
switch (cycle) {
case 1:
CQRMSet(qaxis,0.,0.,1.,0.);
break;
case 2:
CQRMSet(qaxis,0.,0.,0.,1.);
break;
default:
CQRMSet(qaxis,0.,1.,0.,0.);
break;
}
}
CQRMScalarMultiply(qaxis,qaxis,2.*PI*((double)m));
CQRMAdd(qlog,qlog,qaxis);
}
CQRMScalarMultiply(qlogoverr,qlog,recip);
CQRExp(quaternion,&qlogoverr);
return CQR_SUCCESS;
}
/* CQRAdd -- add a quaternion (q1) to a quaternion (q2) */
int CQRAdd (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
if (!quaternion || !q1 || !q2 ) return CQR_BAD_ARGUMENT;
CQRMAdd(*quaternion,*q1,*q2);
return CQR_SUCCESS;
}
/* CQRSubtract -- subtract a quaternion (q2) from a quaternion (q1) */
int CQRSubtract (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
if (!quaternion || !q1 || !q2 ) return CQR_BAD_ARGUMENT;
CQRMSubtract(*quaternion,*q1,*q2);
return CQR_SUCCESS;
}
/* CQRMultiply -- multiply a quaternion (q1) by quaternion (q2) */
int CQRMultiply (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
if (!quaternion || !q1 || !q2 ) return CQR_BAD_ARGUMENT;
CQRMMultiply(*quaternion,*q1,*q2);
return CQR_SUCCESS;
}
/* CQRDot -- dot product of quaternion (q1) by quaternion (q2) as 4-vectors */
int CQRDot (double CQR_FAR * dotprod, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
if (!dotprod || !q1 || !q2 ) return CQR_BAD_ARGUMENT;
*dotprod = q1->w*q2->w + q1->x*q2->x + q1->y*q2->y +q1->z*q2->z;
return CQR_SUCCESS;
}
/* CQRDivide -- divide a quaternion (q1) by quaternion (q2) */
int CQRDivide (CQRQuaternionHandle quaternion, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
double norm2sq;
CQRQuaternion q;
if (!quaternion || !q1 || !q2 ) return CQR_BAD_ARGUMENT;
norm2sq = q2->w*q2->w+q2->x*q2->x+q2->y*q2->y+q2->z*q2->z;
if (norm2sq==0.) return CQR_BAD_ARGUMENT;
q.w = q1->z*q2->z + q1->y*q2->y + q1->x*q2->x + q1->w*q2->w;
q.x = -q1->y*q2->z + q1->z*q2->y - q1->w*q2->x + q1->x*q2->w;
q.y = q1->x*q2->z - q1->w*q2->y - q1->z*q2->x + q1->y*q2->w;
q.z = -q1->w*q2->z - q1->x*q2->y + q1->y*q2->x + q1->z*q2->w;
quaternion->w=q.w/norm2sq;
quaternion->x=q.x/norm2sq;
quaternion->y=q.y/norm2sq;
quaternion->z=q.z/norm2sq;
return CQR_SUCCESS;
}
/* CQRScalarMultiply -- multiply a quaternion (q) by scalar (s) */
int CQRScalarMultiply (CQRQuaternionHandle quaternion, CQRQuaternionHandle q, double s ) {
if (!quaternion || !q ) return CQR_BAD_ARGUMENT;
CQRMScalarMultiply(*quaternion,*q,s);
return CQR_SUCCESS;
}
/* CQREqual -- return 0 if quaternion q1 == q2 */
int CQREqual (CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
if ( !q1 || !q2 ) return CQR_BAD_ARGUMENT;
return ((q1->w==q2->w)&&(q1->x==q2->x)&&(q1->y==q2->y)&&(q1->z==q2->z))?CQR_SUCCESS:CQR_FAILED;
}
/* CQRConjugate -- Form the conjugate of a quaternion qconj */
int CQRConjugate (CQRQuaternionHandle qconjugate, CQRQuaternionHandle quaternion) {
if (!quaternion || !qconjugate ) return CQR_BAD_ARGUMENT;
CQRMConjugate(*qconjugate,*quaternion);
return CQR_SUCCESS;
}
/* CQRNormsq -- Form the normsquared of a quaternion */
int CQRNormsq (double CQR_FAR * normsq, CQRQuaternionHandle quaternion ) {
if (!quaternion || !normsq ) return CQR_BAD_ARGUMENT;
CQRMNormsq(*normsq,*quaternion);
return CQR_SUCCESS;
}
/* CQRNorm -- Form the norm of a quaternion */
int CQRNorm (double CQR_FAR * norm, CQRQuaternionHandle quaternion ) {
if (!quaternion || !norm ) return CQR_BAD_ARGUMENT;
CQRMNorm(*norm,*quaternion);
return CQR_SUCCESS;
}
/* CQRDistsq -- Form the distance squared between two quaternions */
int CQRDistsq (double CQR_FAR * distsq, CQRQuaternionHandle q1, CQRQuaternionHandle q2 ) {
if (!q1 || !q2 || !distsq ) return CQR_BAD_ARGUMENT;
CQRMDistsq(*distsq,*q1,*q2);
return CQR_SUCCESS;
}
/* CQRDist -- Form the distance between two quaternions */
int CQRDist (double CQR_FAR * dist, CQRQuaternionHandle q1, CQRQuaternionHandle q2) {
if (!q1 || !q2 || !dist ) return CQR_BAD_ARGUMENT;
CQRMDist(*dist,*q1,*q2);
return CQR_SUCCESS;
}
/* CQRInverse -- Form the inverse of a quaternion */
int CQRInverse (CQRQuaternionHandle inversequaternion, CQRQuaternionHandle quaternion ) {
double normsq;
if (!quaternion || !inversequaternion ) return CQR_BAD_ARGUMENT;
CQRMConjugate(*inversequaternion,*quaternion);
CQRMNormsq(normsq,*quaternion);
if (normsq > 0.) {
CQRMScalarMultiply(*inversequaternion,*inversequaternion,1./normsq);
return CQR_SUCCESS;
} else return CQR_BAD_ARGUMENT;
}
/* CQRRotateByQuaternion -- Rotate a vector by a Quaternion, w = qvq* */
int CQRRotateByQuaternion(double CQR_FAR * w, CQRQuaternionHandle rotquaternion, double CQR_FAR * v) {
CQRQuaternion vquat, wquat, qconj;
if (!w || !rotquaternion || !v ) return CQR_BAD_ARGUMENT;
CQRMSet(vquat,0,v[0],v[1],v[2]);
CQRMMultiply(wquat,*rotquaternion,vquat);
CQRMConjugate(qconj,*rotquaternion);
CQRMMultiply(vquat,wquat,qconj);
w[0] = vquat.x;
w[1] = vquat.y;
w[2] = vquat.z;
return CQR_SUCCESS;
}
/* CQRAxis2Quaternion -- Form the quaternion for a rotation around axis v by angle theta */
int CQRAxis2Quaternion (CQRQuaternionHandle rotquaternion, double CQR_FAR * v, double theta) {
double normsq, norm;
if (!rotquaternion || !v ) return CQR_BAD_ARGUMENT;
normsq = v[0]*v[0] + v[1]*v[1] + v[2]*v[2];
if (normsq == 0.) return CQR_BAD_ARGUMENT;
if (normsq == 1.) {
CQRMSet(*rotquaternion,cos(theta/2),sin(theta/2)*v[0],sin(theta/2)*v[1],sin(theta/2)*v[2]);
} else {
norm = sqrt(normsq);
CQRMSet(*rotquaternion,cos(theta/2),sin(theta/2)*v[0]/norm,sin(theta/2)*v[1]/norm,sin(theta/2)*v[2]/norm);
}
return CQR_SUCCESS;
}
/* CQRMatrix2Quaternion -- Form the quaternion from a 3x3 rotation matrix R */
int CQRMatrix2Quaternion (CQRQuaternionHandle rotquaternion, double R[3][3]) {
double trace, recip, fourxsq, fourysq, fourzsq;
trace = R[0][0] + R[1][1] + R[2][2];
if (trace > -.75) {
rotquaternion->w = sqrt((1.+trace))/2.;
recip = .25/rotquaternion->w;
rotquaternion->z = (R[1][0]-R[0][1])*recip;
rotquaternion->y = (R[0][2]-R[2][0])*recip;
rotquaternion->x = (R[2][1]-R[1][2])*recip;
return CQR_SUCCESS;
}
fourxsq = 1.+ R[0][0] - R[1][1] - R[2][2];
if (fourxsq >= .25) {
rotquaternion->x = sqrt(fourxsq)/2.;
recip = .25/rotquaternion->x;
rotquaternion->y = (R[1][0]+R[0][1])*recip;
rotquaternion->z = (R[0][2]+R[2][0])*recip;
rotquaternion->w = (R[2][1]-R[1][2])*recip;
return CQR_SUCCESS;
}
fourysq = 1.+ R[1][1] - R[0][0] - R[2][2];
if (fourysq >= .25) {
rotquaternion->y = sqrt(fourysq)/2.;
recip = .25/rotquaternion->y;
rotquaternion->x = (R[1][0]+R[0][1])*recip;
rotquaternion->w = (R[0][2]-R[2][0])*recip;
rotquaternion->z = (R[2][1]+R[1][2])*recip;
return CQR_SUCCESS;
}
fourzsq = 1.+ R[2][2] - R[0][0] - R[1][1];
if (fourzsq >= .25) {
rotquaternion->z = sqrt(fourzsq)/2.;
recip = .25/rotquaternion->z;
rotquaternion->w = (R[1][0]-R[0][1])*recip;
rotquaternion->x = (R[0][2]+R[2][0])*recip;
rotquaternion->y = (R[2][1]+R[1][2])*recip;
return CQR_SUCCESS;
}
return CQR_BAD_ARGUMENT;
}
/* CQRQuaternion2Matrix -- Form the 3x3 rotation matrix from a quaternion */
int CQRQuaternion2Matrix (double R[3][3], CQRQuaternionHandle rotquaternion) {
double twoxy, twoyz, twoxz, twowx, twowy, twowz;
double ww, xx, yy, zz;
if (!R || !rotquaternion) return CQR_BAD_ARGUMENT;
ww = (rotquaternion->w)*(rotquaternion->w);
xx = (rotquaternion->x)*(rotquaternion->x);
yy = (rotquaternion->y)*(rotquaternion->y);
zz = (rotquaternion->z)*(rotquaternion->z);
R[0][0] = ww + xx - yy - zz;
R[1][1] = ww - xx + yy - zz;
R[2][2] = ww - xx - yy + zz;
twoxy = 2.*(rotquaternion->x)*(rotquaternion->y);
twoyz = 2.*(rotquaternion->y)*(rotquaternion->z);
twoxz = 2.*(rotquaternion->x)*(rotquaternion->z);
twowx = 2.*(rotquaternion->w)*(rotquaternion->x);
twowy = 2.*(rotquaternion->w)*(rotquaternion->y);
twowz = 2.*(rotquaternion->w)*(rotquaternion->z);
R[0][1] = twoxy - twowz;
R[0][2] = twoxz + twowy;
R[1][0] = twoxy + twowz;
R[1][2] = twoyz - twowx;
R[2][0] = twoxz - twowy;
R[2][1] = twoyz + twowx;
return CQR_SUCCESS;
}
/* CQRQuaternion2Angles -- Convert a Quaternion into Euler Angles for Rz(Ry(Rx))) convention */
int CQRQuaternion2Angles (double CQR_FAR * RotX, double CQR_FAR * RotY, double CQR_FAR * RotZ, CQRQuaternionHandle rotquaternion) {
double SRX, SRY, SRZ, TRX, TRY, TRZ;
double NSum;
double TSum;
double RMX0, RMX1, RMY0, RMY1, RMZ0, RMZ1, RMZ2;
double PI;
PI = 4.*atan2(1.,1.);
if (!rotquaternion || !RotX || !RotY || !RotZ) return CQR_BAD_ARGUMENT;
RMX0 = rotquaternion->w*rotquaternion->w + rotquaternion->x*rotquaternion->x
- rotquaternion->y*rotquaternion->y - rotquaternion->z*rotquaternion->z;
RMX1 = 2.*(rotquaternion->x*rotquaternion->y-rotquaternion->w*rotquaternion->z);
RMY0 = 2.*(rotquaternion->x*rotquaternion->y+rotquaternion->w*rotquaternion->z);
RMY1 = rotquaternion->w*rotquaternion->w - rotquaternion->x*rotquaternion->x
+ rotquaternion->y*rotquaternion->y - rotquaternion->z*rotquaternion->z;
RMZ0 = 2.*(rotquaternion->x*rotquaternion->z-rotquaternion->w*rotquaternion->y);
RMZ1 = 2.*(rotquaternion->w*rotquaternion->x+rotquaternion->y*rotquaternion->z);
RMZ2 = rotquaternion->w*rotquaternion->w - rotquaternion->x*rotquaternion->x
- rotquaternion->y*rotquaternion->y + rotquaternion->z*rotquaternion->z;
if (RMZ0 < 1. ) {
if (RMZ0 > -1.) {
SRY = asin(-RMZ0);
} else {
SRY = .5*PI;
}
} else {
SRY = -.5*PI;
}
if (RMZ0 > .9999995) {
SRX = atan2(-RMX1,RMY1);
SRZ = 0;
} else {
if (RMZ0 < -.9999995 ) {
SRX = atan2(RMX1,RMY1);
SRZ = 0;
} else {
SRX = atan2(RMZ1,RMZ2);
SRZ = atan2(RMY0,RMX0);
}
}
TRX = PI+SRX;
if ( TRX > 2.*PI ) TRX -= 2.*PI;
TRY = PI+SRY;
if ( TRY > 2.*PI ) TRY -= 2.*PI;
TRZ = PI+SRZ;
if ( TRZ > 2.*PI ) TRZ -= 2.*PI;
NSum = 0;
TSum = 0;
NSum += fabs(cos(SRX)-cos(*RotX)) + fabs(sin(SRX)-sin(*RotX))
+ fabs(cos(SRY)-cos(*RotY)) + fabs(sin(SRY)-sin(*RotY))
+ fabs(cos(SRZ)-cos(*RotZ)) + fabs(sin(SRZ)-sin(*RotZ));
TSum += fabs(cos(TRX)-cos(*RotX)) + fabs(sin(TRX)-sin(*RotX))
+ fabs(cos(TRY)-cos(*RotY)) + fabs(sin(TRY)-sin(*RotY))
+ fabs(cos(TRZ)-cos(*RotZ)) + fabs(sin(TRZ)-sin(*RotZ));
if (NSum < TSum) {
*RotX = SRX; *RotY = SRY; *RotZ = SRZ;
} else {
*RotX = TRX; *RotY = TRY; *RotZ = TRZ;
}
return CQR_SUCCESS;
}
/* CQRAngles2Quaternion -- Convert Euler Angles for Rz(Ry(Rx))) convention into a quaternion */
int CQRAngles2Quaternion (CQRQuaternionHandle rotquaternion, double RotX, double RotY, double RotZ ) {
double cx, cy, cz, sx, sy, sz;
if (!rotquaternion) return CQR_BAD_ARGUMENT;
cx = cos(RotX/2);
sx = sin(RotX/2);
cy = cos(RotY/2);
sy = sin(RotY/2);
cz = cos(RotZ/2);
sz = sin(RotZ/2);
rotquaternion->w = cx*cy*cz + sx*sy*sz;
rotquaternion->x = sx*cy*cz - cx*sy*sz;
rotquaternion->y = cx*sy*cz + sx*cy*sz;
rotquaternion->z = cx*cy*sz - sx*sy*cz;
return CQR_SUCCESS;
}
/* Represent a 3-vector as a quaternion with w=0 */
int CQRPoint2Quaternion( CQRQuaternionHandle quaternion, double v[3] )
{
quaternion->w = 0.;
quaternion->x = v[0];
quaternion->y = v[1];
quaternion->z = v[2];
return CQR_SUCCESS;
}
/* SLERP -- Spherical Linear Interpolation
Take two quaternions and two weights and combine them
following a great circle on the unit quaternion 4-D sphere
and linear interpolation between the radii
This version keeps a quaternion separate from the negative
of the same quaternion and is not appropriate for
quaternions representing rotations. Use CQRHLERP
to apply SLERP to quaternions representing rotations
*/
int CQRSLERP (CQRQuaternionHandle quaternion, const CQRQuaternionHandle q1, const CQRQuaternionHandle q2,
const double w1, const double w2)
{
CQRQuaternion s1;
CQRQuaternion s2;
CQRQuaternion st1;
CQRQuaternion st2;
CQRQuaternion sout;
CQRQuaternion sout2;
double normsq, norm1sq, norm2sq;
double r1,r2, cosomega,sinomega, omega;
double t, t1, t2;
if (!quaternion || !q1 || !q2 ) return CQR_BAD_ARGUMENT;
CQRMNormsq(norm1sq,*q1);
CQRMNormsq(norm2sq,*q2);
t = w1/(w1+w2);
if (norm1sq <= DBL_MIN) {
CQRMScalarMultiply(*quaternion,*q2,(1-t));
return CQR_SUCCESS;
}
if (norm2sq <= DBL_MIN) {
CQRMScalarMultiply(*quaternion,*q1,t);
return CQR_SUCCESS;
}
if (fabs(norm1sq-1.)<= DBL_MIN) {
r1 = 1.;
CQRMCopy(s1,*q1);
} else {
r1 = sqrt(norm1sq);
CQRMScalarMultiply(s1,*q1,(1/r1));
}
if (fabs(norm2sq-1.)<= DBL_MIN) {
r2 = 1.;
CQRMCopy(s2,*q2);
} else {
r2 = sqrt(norm1sq);
CQRMScalarMultiply(s2,*q2,(1/r2));
}
CQRMDot(cosomega,s1,s2);
if (cosomega>=1. || cosomega<=-1.) {
sinomega = 0.;
} else {
sinomega=sqrt(1.-cosomega*cosomega);
}
omega=atan2(sinomega,cosomega);
if (sinomega <= 0.05) {
t1=t*(1-t*t*omega*omega/6.);
t2=(1-t)*(1.-(1-t)*(1-t)*omega*omega/6.);
CQRMScalarMultiply(st1,s1,t1);
CQRMScalarMultiply(st2,s2,t2);
if (cosomega >=0.) {
CQRMAdd(sout,st1,st2);
} else {
if (sinomega <= 0.00001) {
sout.w = -st1.x+st2.x;
sout.x = st1.w-st2.w;
sout.y = st1.z-st2.z;
sout.z = -st1.y+st2.y;
} else {
CQRMAdd(sout,s1,s2);
}
CQRMNormsq(normsq,sout);
CQRMScalarMultiply(sout,sout,1/sqrt(normsq));
if (t >= 0.5) {
CQRSLERP(&sout2,&sout,&s1,2-2.*t,2.*t-1.);
CQRMCopy(sout,sout2);
}else {
CQRSLERP(&sout2,&sout,&s2,2.*t,1.-2.*t-1.);
CQRMCopy(sout,sout2);
}
}
CQRMNormsq(normsq,sout);
if (normsq <= DBL_MIN) {
CQRMSet(*quaternion,0.,0.,0.,0.);
} else {
CQRMScalarMultiply(*quaternion,sout,(t*r1+(1-t)*r2)/sqrt(normsq));
}
return CQR_SUCCESS;
}
t1 = sin(t*omega);
t2 = sin((1-t)*omega);
CQRMScalarMultiply(st1,s1,t1);
CQRMScalarMultiply(st2,s2,t2);
CQRMAdd(sout,st1,st2);
CQRMNormsq(normsq,sout);
CQRMScalarMultiply(*quaternion,sout,(r1*t+r2*(1-t))/sqrt(normsq));
return CQR_SUCCESS;
}
/* HLERP -- Hemispherical Linear Interpolation
Take two quaternions and two weights and combine them
following a great circle on the unit quaternion 4-D sphere
and linear interpolation between the radii
This is the hemispherical version, for use with quaternions