--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ode/src/rotation.cpp Tue Feb 02 01:00:49 2010 +0200
@@ -0,0 +1,308 @@
+/*************************************************************************
+ * *
+ * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
+ * All rights reserved. Email: russ@q12.org Web: www.q12.org *
+ * *
+ * This library is free software; you can redistribute it and/or *
+ * modify it under the terms of EITHER: *
+ * (1) 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. The text of the GNU Lesser *
+ * General Public License is included with this library in the *
+ * file LICENSE.TXT. *
+ * (2) The BSD-style license that is included with this library in *
+ * the file LICENSE-BSD.TXT. *
+ * *
+ * 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 files *
+ * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
+ * *
+ *************************************************************************/
+
+/*
+
+quaternions have the format: (s,vx,vy,vz) where (vx,vy,vz) is the
+"rotation axis" and s is the "rotation angle".
+
+*/
+
+#include <ode/rotation.h>
+#include <ode/odemath.h>
+
+#include <ode/lookup_tables.h>
+
+
+#define _R(i,j) R[(i)*4+(j)]
+
+#define SET_3x3_IDENTITY \
+ _R(0,0) = REAL(1.0); \
+ _R(0,1) = REAL(0.0); \
+ _R(0,2) = REAL(0.0); \
+ _R(0,3) = REAL(0.0); \
+ _R(1,0) = REAL(0.0); \
+ _R(1,1) = REAL(1.0); \
+ _R(1,2) = REAL(0.0); \
+ _R(1,3) = REAL(0.0); \
+ _R(2,0) = REAL(0.0); \
+ _R(2,1) = REAL(0.0); \
+ _R(2,2) = REAL(1.0); \
+ _R(2,3) = REAL(0.0);
+
+
+EXPORT_C void dRSetIdentity (dMatrix3 R)
+{
+ SET_3x3_IDENTITY;
+}
+
+
+EXPORT_C void dRFromAxisAndAngle (dMatrix3 R, dReal ax, dReal ay, dReal az,
+ dReal angle)
+{
+ dQuaternion q;
+ dQFromAxisAndAngle (q,ax,ay,az,angle);
+ dQtoR (q,R);
+}
+
+
+EXPORT_C void dRFromEulerAngles (dMatrix3 R, dReal phi, dReal theta, dReal psi)
+{
+ dReal sphi,cphi,stheta,ctheta,spsi,cpsi;
+
+ sphi = dSin(phi);
+ cphi = dCos(phi);
+ stheta = dSin(theta);
+ ctheta = dCos(theta);
+ spsi = dSin(psi);
+ cpsi = dCos(psi);
+ _R(0,0) = dMUL(cpsi,ctheta);
+ _R(0,1) = dMUL(spsi,ctheta);
+ _R(0,2) =-stheta;
+ _R(0,3) = REAL(0.0);
+ _R(1,0) = dMUL(cpsi,dMUL(stheta,sphi)) - dMUL(spsi,cphi);
+ _R(1,1) = dMUL(spsi,dMUL(stheta,sphi)) + dMUL(cpsi,cphi);
+ _R(1,2) = dMUL(ctheta,sphi);
+ _R(1,3) = REAL(0.0);
+ _R(2,0) = dMUL(cpsi,dMUL(stheta,cphi)) + dMUL(spsi,sphi);
+ _R(2,1) = dMUL(spsi,dMUL(stheta,cphi)) - dMUL(cpsi,sphi);
+ _R(2,2) = dMUL(ctheta,cphi);
+ _R(2,3) = REAL(0.0);
+}
+
+
+EXPORT_C void dRFrom2Axes (dMatrix3 R, dReal ax, dReal ay, dReal az,
+ dReal bx, dReal by, dReal bz)
+{
+ dReal l,k;
+
+ l = dSqrt (dMUL(ax,ax) + dMUL(ay,ay) + dMUL(az,az));
+ if (l <= REAL(0.0)) {
+ return;
+ }
+ l = dRecip(l);
+ ax = dMUL(ax,l);
+ ay = dMUL(ay,l);
+ az = dMUL(az,l);
+ k = dMUL(ax,bx) + dMUL(ay,by) + dMUL(az,bz);
+ bx -= dMUL(k,ax);
+ by -= dMUL(k,ay);
+ bz -= dMUL(k,az);
+ l = dSqrt (dMUL(bx,bx) + dMUL(by,by) + dMUL(bz,bz));
+ if (l <= REAL(0.0)) {
+ return;
+ }
+ l = dRecip(l);
+ bx = dMUL(bx,l);
+ by = dMUL(by,l);
+ bz = dMUL(bz,l);
+ _R(0,0) = ax;
+ _R(1,0) = ay;
+ _R(2,0) = az;
+ _R(0,1) = bx;
+ _R(1,1) = by;
+ _R(2,1) = bz;
+ _R(0,2) = - dMUL(by,az) + dMUL(ay,bz);
+ _R(1,2) = - dMUL(bz,ax) + dMUL(az,bx);
+ _R(2,2) = - dMUL(bx,ay) + dMUL(ax,by);
+ _R(0,3) = REAL(0.0);
+ _R(1,3) = REAL(0.0);
+ _R(2,3) = REAL(0.0);
+}
+
+
+EXPORT_C void dRFromZAxis (dMatrix3 R, dReal ax, dReal ay, dReal az)
+{
+ dVector3 n,p,q;
+ n[0] = ax;
+ n[1] = ay;
+ n[2] = az;
+ dNormalize3 (n);
+ dPlaneSpace (n,p,q);
+ _R(0,0) = p[0];
+ _R(1,0) = p[1];
+ _R(2,0) = p[2];
+ _R(0,1) = q[0];
+ _R(1,1) = q[1];
+ _R(2,1) = q[2];
+ _R(0,2) = n[0];
+ _R(1,2) = n[1];
+ _R(2,2) = n[2];
+ _R(0,3) = REAL(0.0);
+ _R(1,3) = REAL(0.0);
+ _R(2,3) = REAL(0.0);
+}
+
+
+EXPORT_C void dQSetIdentity (dQuaternion q)
+{
+ q[0] = REAL(1.0);
+ q[1] = 0;
+ q[2] = 0;
+ q[3] = 0;
+}
+
+
+EXPORT_C void dQFromAxisAndAngle (dQuaternion q, dReal ax, dReal ay, dReal az,
+ dReal angle)
+{
+ dReal l = dMUL(ax,ax) + dMUL(ay,ay) + dMUL(az,az);
+ if (l > REAL(0.0)) {
+ angle = dMUL(angle,REAL(0.5));
+ q[0] = dCos (angle);
+ l = dMUL(dReal(dSin(angle)),dRecipSqrt(l));
+ q[1] = dMUL(ax,l);
+ q[2] = dMUL(ay,l);
+ q[3] = dMUL(az,l);
+ }
+ else {
+ q[0] = REAL(1.0);
+ q[1] = 0;
+ q[2] = 0;
+ q[3] = 0;
+ }
+}
+
+
+EXPORT_C void dQMultiply0 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
+{
+ qa[0] = dMUL(qb[0],qc[0]) - dMUL(qb[1],qc[1]) - dMUL(qb[2],qc[2]) - dMUL(qb[3],qc[3]);
+ qa[1] = dMUL(qb[0],qc[1]) + dMUL(qb[1],qc[0]) + dMUL(qb[2],qc[3]) - dMUL(qb[3],qc[2]);
+ qa[2] = dMUL(qb[0],qc[2]) + dMUL(qb[2],qc[0]) + dMUL(qb[3],qc[1]) - dMUL(qb[1],qc[3]);
+ qa[3] = dMUL(qb[0],qc[3]) + dMUL(qb[3],qc[0]) + dMUL(qb[1],qc[2]) - dMUL(qb[2],qc[1]);
+}
+
+
+EXPORT_C void dQMultiply1 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
+{
+ qa[0] = dMUL(qb[0],qc[0]) + dMUL(qb[1],qc[1]) + dMUL(qb[2],qc[2]) + dMUL(qb[3],qc[3]);
+ qa[1] = dMUL(qb[0],qc[1]) - dMUL(qb[1],qc[0]) - dMUL(qb[2],qc[3]) + dMUL(qb[3],qc[2]);
+ qa[2] = dMUL(qb[0],qc[2]) - dMUL(qb[2],qc[0]) - dMUL(qb[3],qc[1]) + dMUL(qb[1],qc[3]);
+ qa[3] = dMUL(qb[0],qc[3]) - dMUL(qb[3],qc[0]) - dMUL(qb[1],qc[2]) + dMUL(qb[2],qc[1]);
+}
+
+
+EXPORT_C void dQMultiply2 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
+{
+ qa[0] = dMUL(qb[0],qc[0]) + dMUL(qb[1],qc[1]) + dMUL(qb[2],qc[2]) + dMUL(qb[3],qc[3]);
+ qa[1] = -dMUL(qb[0],qc[1]) + dMUL(qb[1],qc[0]) - dMUL(qb[2],qc[3]) + dMUL(qb[3],qc[2]);
+ qa[2] = -dMUL(qb[0],qc[2]) + dMUL(qb[2],qc[0]) - dMUL(qb[3],qc[1]) + dMUL(qb[1],qc[3]);
+ qa[3] = -dMUL(qb[0],qc[3]) + dMUL(qb[3],qc[0]) - dMUL(qb[1],qc[2]) + dMUL(qb[2],qc[1]);
+}
+
+
+EXPORT_C void dQMultiply3 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc)
+{
+ qa[0] = dMUL(qb[0],qc[0]) - dMUL(qb[1],qc[1]) - dMUL(qb[2],qc[2]) - dMUL(qb[3],qc[3]);
+ qa[1] = -dMUL(qb[0],qc[1]) - dMUL(qb[1],qc[0]) + dMUL(qb[2],qc[3]) - dMUL(qb[3],qc[2]);
+ qa[2] = -dMUL(qb[0],qc[2]) - dMUL(qb[2],qc[0]) + dMUL(qb[3],qc[1]) - dMUL(qb[1],qc[3]);
+ qa[3] = -dMUL(qb[0],qc[3]) - dMUL(qb[3],qc[0]) + dMUL(qb[1],qc[2]) - dMUL(qb[2],qc[1]);
+}
+
+
+// dRfromQ(), dQfromR() and dDQfromW() are derived from equations in "An Introduction
+// to Physically Based Modeling: Rigid Body Simulation - 1: Unconstrained
+// Rigid Body Dynamics" by David Baraff, Robotics Institute, Carnegie Mellon
+// University, 1997.
+
+EXPORT_C void dRfromQ (dMatrix3 R, const dQuaternion q)
+{
+
+ // q = (s,vx,vy,vz)
+ dReal qq1 = 2*dMUL(q[1],q[1]);
+ dReal qq2 = 2*dMUL(q[2],q[2]);
+ dReal qq3 = 2*dMUL(q[3],q[3]);
+ _R(0,0) = REAL(1.0) - qq2 - qq3;
+ _R(0,1) = 2*(dMUL(q[1],q[2]) - dMUL(q[0],q[3]));
+ _R(0,2) = 2*(dMUL(q[1],q[3]) + dMUL(q[0],q[2]));
+ _R(0,3) = REAL(0.0);
+ _R(1,0) = 2*(dMUL(q[1],q[2]) + dMUL(q[0],q[3]));
+ _R(1,1) = REAL(1.0) - qq1 - qq3;
+ _R(1,2) = 2*(dMUL(q[2],q[3]) - dMUL(q[0],q[1]));
+ _R(1,3) = REAL(0.0);
+ _R(2,0) = 2*(dMUL(q[1],q[3]) - dMUL(q[0],q[2]));
+ _R(2,1) = 2*(dMUL(q[2],q[3]) + dMUL(q[0],q[1]));
+ _R(2,2) = REAL(1.0) - qq1 - qq2;
+ _R(2,3) = REAL(0.0);
+}
+
+
+EXPORT_C void dQfromR (dQuaternion q, const dMatrix3 R)
+{
+
+ dReal tr,s;
+ tr = _R(0,0) + _R(1,1) + _R(2,2);
+ if (tr >= 0) {
+ s = dSqrt (tr + REAL(1.0));
+ q[0] = dMUL(REAL(0.5),s);
+ s = dMUL(REAL(0.5),dRecip(s));
+ q[1] = dMUL((_R(2,1) - _R(1,2)),s);
+ q[2] = dMUL((_R(0,2) - _R(2,0)),s);
+ q[3] = dMUL((_R(1,0) - _R(0,1)),s);
+ }
+ else {
+ // find the largest diagonal element and jump to the appropriate case
+ if (_R(1,1) > _R(0,0)) {
+ if (_R(2,2) > _R(1,1)) goto case_2;
+ goto case_1;
+ }
+ if (_R(2,2) > _R(0,0)) goto case_2;
+ goto case_0;
+
+ case_0:
+ s = dSqrt((_R(0,0) - (_R(1,1) + _R(2,2))) + REAL(1.0));
+ q[1] = dMUL(REAL(0.5),s);
+ s = dMUL(REAL(0.5),dRecip(s));
+ q[2] = dMUL((_R(0,1) + _R(1,0)),s);
+ q[3] = dMUL((_R(2,0) + _R(0,2)),s);
+ q[0] = dMUL((_R(2,1) - _R(1,2)),s);
+ return;
+
+ case_1:
+ s = dSqrt((_R(1,1) - (_R(2,2) + _R(0,0))) + REAL(1.0));
+ q[2] = dMUL(REAL(0.5),s);
+ s = dMUL(REAL(0.5),dRecip(s));
+ q[3] = dMUL((_R(1,2) + _R(2,1)),s);
+ q[1] = dMUL((_R(0,1) + _R(1,0)),s);
+ q[0] = dMUL((_R(0,2) - _R(2,0)),s);
+ return;
+
+ case_2:
+ s = dSqrt((_R(2,2) - (_R(0,0) + _R(1,1))) + REAL(1.0));
+ q[3] = dMUL(REAL(0.5),s);
+ s = dMUL(REAL(0.5),dRecip(s));
+ q[1] = dMUL((_R(2,0) + _R(0,2)),s);
+ q[2] = dMUL((_R(1,2) + _R(2,1)),s);
+ q[0] = dMUL((_R(1,0) - _R(0,1)),s);
+ return;
+ }
+}
+
+
+EXPORT_C void dDQfromW (dReal dq[4], const dVector3 w, const dQuaternion q)
+{
+
+ dq[0] = dMUL(REAL(0.5),(- dMUL(w[0],q[1]) - dMUL(w[1],q[2]) - dMUL(w[2],q[3])));
+ dq[1] = dMUL(REAL(0.5),( dMUL(w[0],q[0]) + dMUL(w[1],q[3]) - dMUL(w[2],q[2])));
+ dq[2] = dMUL(REAL(0.5),(- dMUL(w[0],q[3]) + dMUL(w[1],q[0]) + dMUL(w[2],q[1])));
+ dq[3] = dMUL(REAL(0.5),( dMUL(w[0],q[2]) - dMUL(w[1],q[1]) + dMUL(w[2],q[0])));
+}