317 lines
8.4 KiB
C++
317 lines
8.4 KiB
C++
/*************************************************************************
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* *
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* Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
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* All rights reserved. Email: russ@q12.org Web: www.q12.org *
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* *
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* This library is free software; you can redistribute it and/or *
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* modify it under the terms of EITHER: *
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* (1) The GNU Lesser General Public License as published by the Free *
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* Software Foundation; either version 2.1 of the License, or (at *
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* your option) any later version. The text of the GNU Lesser *
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* General Public License is included with this library in the *
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* file LICENSE.TXT. *
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* (2) The BSD-style license that is included with this library in *
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* the file LICENSE-BSD.TXT. *
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* *
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* This library is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
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* LICENSE.TXT and LICENSE-BSD.TXT for more details. *
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* *
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*************************************************************************/
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/*
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quaternions have the format: (s,vx,vy,vz) where (vx,vy,vz) is the
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"rotation axis" and s is the "rotation angle".
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*/
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#include <ode/rotation.h>
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#include <ode/odemath.h>
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#define _R(i,j) R[(i)*4+(j)]
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#define SET_3x3_IDENTITY \
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_R(0,0) = REAL(1.0); \
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_R(0,1) = REAL(0.0); \
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_R(0,2) = REAL(0.0); \
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_R(0,3) = REAL(0.0); \
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_R(1,0) = REAL(0.0); \
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_R(1,1) = REAL(1.0); \
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_R(1,2) = REAL(0.0); \
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_R(1,3) = REAL(0.0); \
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_R(2,0) = REAL(0.0); \
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_R(2,1) = REAL(0.0); \
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_R(2,2) = REAL(1.0); \
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_R(2,3) = REAL(0.0);
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void dRSetIdentity (dMatrix3 R)
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{
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dAASSERT (R);
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SET_3x3_IDENTITY;
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}
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void dRFromAxisAndAngle (dMatrix3 R, dReal ax, dReal ay, dReal az,
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dReal angle)
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{
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dAASSERT (R);
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dQuaternion q;
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dQFromAxisAndAngle (q,ax,ay,az,angle);
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dQtoR (q,R);
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}
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void dRFromEulerAngles (dMatrix3 R, dReal phi, dReal theta, dReal psi)
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{
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dReal sphi,cphi,stheta,ctheta,spsi,cpsi;
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dAASSERT (R);
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sphi = dSin(phi);
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cphi = dCos(phi);
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stheta = dSin(theta);
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ctheta = dCos(theta);
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spsi = dSin(psi);
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cpsi = dCos(psi);
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_R(0,0) = cpsi*ctheta;
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_R(0,1) = spsi*ctheta;
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_R(0,2) =-stheta;
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_R(0,3) = REAL(0.0);
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_R(1,0) = cpsi*stheta*sphi - spsi*cphi;
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_R(1,1) = spsi*stheta*sphi + cpsi*cphi;
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_R(1,2) = ctheta*sphi;
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_R(1,3) = REAL(0.0);
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_R(2,0) = cpsi*stheta*cphi + spsi*sphi;
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_R(2,1) = spsi*stheta*cphi - cpsi*sphi;
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_R(2,2) = ctheta*cphi;
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_R(2,3) = REAL(0.0);
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}
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void dRFrom2Axes (dMatrix3 R, dReal ax, dReal ay, dReal az,
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dReal bx, dReal by, dReal bz)
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{
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dReal l,k;
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dAASSERT (R);
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l = dSqrt (ax*ax + ay*ay + az*az);
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if (l <= REAL(0.0)) {
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dDEBUGMSG ("zero length vector");
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return;
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}
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l = dRecip(l);
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ax *= l;
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ay *= l;
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az *= l;
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k = ax*bx + ay*by + az*bz;
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bx -= k*ax;
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by -= k*ay;
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bz -= k*az;
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l = dSqrt (bx*bx + by*by + bz*bz);
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if (l <= REAL(0.0)) {
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dDEBUGMSG ("zero length vector");
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return;
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}
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l = dRecip(l);
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bx *= l;
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by *= l;
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bz *= l;
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_R(0,0) = ax;
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_R(1,0) = ay;
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_R(2,0) = az;
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_R(0,1) = bx;
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_R(1,1) = by;
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_R(2,1) = bz;
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_R(0,2) = - by*az + ay*bz;
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_R(1,2) = - bz*ax + az*bx;
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_R(2,2) = - bx*ay + ax*by;
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_R(0,3) = REAL(0.0);
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_R(1,3) = REAL(0.0);
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_R(2,3) = REAL(0.0);
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}
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void dRFromZAxis (dMatrix3 R, dReal ax, dReal ay, dReal az)
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{
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dVector3 n,p,q;
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n[0] = ax;
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n[1] = ay;
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n[2] = az;
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dNormalize3 (n);
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dPlaneSpace (n,p,q);
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_R(0,0) = p[0];
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_R(1,0) = p[1];
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_R(2,0) = p[2];
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_R(0,1) = q[0];
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_R(1,1) = q[1];
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_R(2,1) = q[2];
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_R(0,2) = n[0];
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_R(1,2) = n[1];
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_R(2,2) = n[2];
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_R(0,3) = REAL(0.0);
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_R(1,3) = REAL(0.0);
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_R(2,3) = REAL(0.0);
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}
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void dQSetIdentity (dQuaternion q)
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{
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dAASSERT (q);
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q[0] = 1;
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q[1] = 0;
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q[2] = 0;
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q[3] = 0;
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}
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void dQFromAxisAndAngle (dQuaternion q, dReal ax, dReal ay, dReal az,
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dReal angle)
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{
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dAASSERT (q);
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dReal l = ax*ax + ay*ay + az*az;
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if (l > REAL(0.0)) {
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angle *= REAL(0.5);
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q[0] = dCos (angle);
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l = dSin(angle) * dRecipSqrt(l);
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q[1] = ax*l;
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q[2] = ay*l;
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q[3] = az*l;
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}
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else {
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q[0] = 1;
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q[1] = 0;
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q[2] = 0;
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q[3] = 0;
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}
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}
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void dQMultiply0 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
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{
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dAASSERT (qa && qb && qc);
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qa[0] = qb[0]*qc[0] - qb[1]*qc[1] - qb[2]*qc[2] - qb[3]*qc[3];
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qa[1] = qb[0]*qc[1] + qb[1]*qc[0] + qb[2]*qc[3] - qb[3]*qc[2];
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qa[2] = qb[0]*qc[2] + qb[2]*qc[0] + qb[3]*qc[1] - qb[1]*qc[3];
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qa[3] = qb[0]*qc[3] + qb[3]*qc[0] + qb[1]*qc[2] - qb[2]*qc[1];
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}
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void dQMultiply1 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
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{
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dAASSERT (qa && qb && qc);
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qa[0] = qb[0]*qc[0] + qb[1]*qc[1] + qb[2]*qc[2] + qb[3]*qc[3];
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qa[1] = qb[0]*qc[1] - qb[1]*qc[0] - qb[2]*qc[3] + qb[3]*qc[2];
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qa[2] = qb[0]*qc[2] - qb[2]*qc[0] - qb[3]*qc[1] + qb[1]*qc[3];
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qa[3] = qb[0]*qc[3] - qb[3]*qc[0] - qb[1]*qc[2] + qb[2]*qc[1];
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}
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void dQMultiply2 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
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{
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dAASSERT (qa && qb && qc);
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qa[0] = qb[0]*qc[0] + qb[1]*qc[1] + qb[2]*qc[2] + qb[3]*qc[3];
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qa[1] = -qb[0]*qc[1] + qb[1]*qc[0] - qb[2]*qc[3] + qb[3]*qc[2];
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qa[2] = -qb[0]*qc[2] + qb[2]*qc[0] - qb[3]*qc[1] + qb[1]*qc[3];
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qa[3] = -qb[0]*qc[3] + qb[3]*qc[0] - qb[1]*qc[2] + qb[2]*qc[1];
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}
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void dQMultiply3 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
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{
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dAASSERT (qa && qb && qc);
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qa[0] = qb[0]*qc[0] - qb[1]*qc[1] - qb[2]*qc[2] - qb[3]*qc[3];
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qa[1] = -qb[0]*qc[1] - qb[1]*qc[0] + qb[2]*qc[3] - qb[3]*qc[2];
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qa[2] = -qb[0]*qc[2] - qb[2]*qc[0] + qb[3]*qc[1] - qb[1]*qc[3];
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qa[3] = -qb[0]*qc[3] - qb[3]*qc[0] + qb[1]*qc[2] - qb[2]*qc[1];
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}
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// dRfromQ(), dQfromR() and dDQfromW() are derived from equations in "An Introduction
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// to Physically Based Modeling: Rigid Body Simulation - 1: Unconstrained
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// Rigid Body Dynamics" by David Baraff, Robotics Institute, Carnegie Mellon
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// University, 1997.
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void dRfromQ (dMatrix3 R, const dQuaternion q)
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{
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dAASSERT (q && R);
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// q = (s,vx,vy,vz)
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dReal qq1 = 2*q[1]*q[1];
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dReal qq2 = 2*q[2]*q[2];
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dReal qq3 = 2*q[3]*q[3];
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_R(0,0) = 1 - qq2 - qq3;
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_R(0,1) = 2*(q[1]*q[2] - q[0]*q[3]);
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_R(0,2) = 2*(q[1]*q[3] + q[0]*q[2]);
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_R(0,3) = REAL(0.0);
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_R(1,0) = 2*(q[1]*q[2] + q[0]*q[3]);
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_R(1,1) = 1 - qq1 - qq3;
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_R(1,2) = 2*(q[2]*q[3] - q[0]*q[1]);
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_R(1,3) = REAL(0.0);
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_R(2,0) = 2*(q[1]*q[3] - q[0]*q[2]);
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_R(2,1) = 2*(q[2]*q[3] + q[0]*q[1]);
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_R(2,2) = 1 - qq1 - qq2;
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_R(2,3) = REAL(0.0);
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}
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void dQfromR (dQuaternion q, const dMatrix3 R)
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{
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dAASSERT (q && R);
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dReal tr,s;
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tr = _R(0,0) + _R(1,1) + _R(2,2);
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if (tr >= 0) {
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s = dSqrt (tr + 1);
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q[0] = REAL(0.5) * s;
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s = REAL(0.5) * dRecip(s);
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q[1] = (_R(2,1) - _R(1,2)) * s;
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q[2] = (_R(0,2) - _R(2,0)) * s;
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q[3] = (_R(1,0) - _R(0,1)) * s;
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}
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else {
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// find the largest diagonal element and jump to the appropriate case
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if (_R(1,1) > _R(0,0)) {
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if (_R(2,2) > _R(1,1)) goto case_2;
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goto case_1;
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}
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if (_R(2,2) > _R(0,0)) goto case_2;
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goto case_0;
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case_0:
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s = dSqrt((_R(0,0) - (_R(1,1) + _R(2,2))) + 1);
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q[1] = REAL(0.5) * s;
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s = REAL(0.5) * dRecip(s);
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q[2] = (_R(0,1) + _R(1,0)) * s;
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q[3] = (_R(2,0) + _R(0,2)) * s;
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q[0] = (_R(2,1) - _R(1,2)) * s;
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return;
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case_1:
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s = dSqrt((_R(1,1) - (_R(2,2) + _R(0,0))) + 1);
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q[2] = REAL(0.5) * s;
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s = REAL(0.5) * dRecip(s);
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q[3] = (_R(1,2) + _R(2,1)) * s;
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q[1] = (_R(0,1) + _R(1,0)) * s;
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q[0] = (_R(0,2) - _R(2,0)) * s;
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return;
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case_2:
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s = dSqrt((_R(2,2) - (_R(0,0) + _R(1,1))) + 1);
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q[3] = REAL(0.5) * s;
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s = REAL(0.5) * dRecip(s);
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q[1] = (_R(2,0) + _R(0,2)) * s;
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q[2] = (_R(1,2) + _R(2,1)) * s;
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q[0] = (_R(1,0) - _R(0,1)) * s;
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return;
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}
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}
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void dDQfromW (dReal dq[4], const dVector3 w, const dQuaternion q)
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{
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dAASSERT (w && q && dq);
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dq[0] = REAL(0.5)*(- w[0]*q[1] - w[1]*q[2] - w[2]*q[3]);
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dq[1] = REAL(0.5)*( w[0]*q[0] + w[1]*q[3] - w[2]*q[2]);
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dq[2] = REAL(0.5)*(- w[0]*q[3] + w[1]*q[0] + w[2]*q[1]);
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dq[3] = REAL(0.5)*( w[0]*q[2] - w[1]*q[1] + w[2]*q[0]);
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}
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