/************************************************************************* * * * 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.hpp" #include "odemath.h" #define dDEBUGMSG(e) #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); void dRSetIdentity (dMatrix3 R) { dAASSERT (R); SET_3x3_IDENTITY; } void dRFromAxisAndAngle (dMatrix3 R, dReal ax, dReal ay, dReal az, dReal angle) { dAASSERT (R); dQuaternion q; dQFromAxisAndAngle (q,ax,ay,az,angle); dQtoR (q,R); } void dRFromEulerAngles (dMatrix3 R, dReal phi, dReal theta, dReal psi) { dReal sphi,cphi,stheta,ctheta,spsi,cpsi; dAASSERT (R); sphi = dSin(phi); cphi = dCos(phi); stheta = dSin(theta); ctheta = dCos(theta); spsi = dSin(psi); cpsi = dCos(psi); _R(0,0) = cpsi*ctheta; _R(0,1) = spsi*ctheta; _R(0,2) =-stheta; _R(0,3) = REAL(0.0); _R(1,0) = cpsi*stheta*sphi - spsi*cphi; _R(1,1) = spsi*stheta*sphi + cpsi*cphi; _R(1,2) = ctheta*sphi; _R(1,3) = REAL(0.0); _R(2,0) = cpsi*stheta*cphi + spsi*sphi; _R(2,1) = spsi*stheta*cphi - cpsi*sphi; _R(2,2) = ctheta*cphi; _R(2,3) = REAL(0.0); } void dRFrom2Axes (dMatrix3 R, dReal ax, dReal ay, dReal az, dReal bx, dReal by, dReal bz) { dReal l,k; dAASSERT (R); l = dSqrt (ax*ax + ay*ay + az*az); if (l <= REAL(0.0)) { dDEBUGMSG ("zero length vector"); return; } l = dRecip(l); ax *= l; ay *= l; az *= l; k = ax*bx + ay*by + az*bz; bx -= k*ax; by -= k*ay; bz -= k*az; l = dSqrt (bx*bx + by*by + bz*bz); if (l <= REAL(0.0)) { dDEBUGMSG ("zero length vector"); return; } l = dRecip(l); bx *= l; by *= l; 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) = - by*az + ay*bz; _R(1,2) = - bz*ax + az*bx; _R(2,2) = - bx*ay + ax*by; _R(0,3) = REAL(0.0); _R(1,3) = REAL(0.0); _R(2,3) = REAL(0.0); } 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); } void dQSetIdentity (dQuaternion q) { dAASSERT (q); q[0] = 1; q[1] = 0; q[2] = 0; q[3] = 0; } void dQFromAxisAndAngle (dQuaternion q, dReal ax, dReal ay, dReal az, dReal angle) { dAASSERT (q); dReal l = ax*ax + ay*ay + az*az; if (l > REAL(0.0)) { angle *= REAL(0.5); q[0] = dCos (angle); l = dSin(angle) * dRecipSqrt(l); q[1] = ax*l; q[2] = ay*l; q[3] = az*l; } else { q[0] = 1; q[1] = 0; q[2] = 0; q[3] = 0; } } void dQMultiply0 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc) { dAASSERT (qa && qb && qc); qa[0] = qb[0]*qc[0] - qb[1]*qc[1] - qb[2]*qc[2] - qb[3]*qc[3]; qa[1] = qb[0]*qc[1] + qb[1]*qc[0] + qb[2]*qc[3] - qb[3]*qc[2]; qa[2] = qb[0]*qc[2] + qb[2]*qc[0] + qb[3]*qc[1] - qb[1]*qc[3]; qa[3] = qb[0]*qc[3] + qb[3]*qc[0] + qb[1]*qc[2] - qb[2]*qc[1]; } void dQMultiply1 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc) { dAASSERT (qa && qb && qc); qa[0] = qb[0]*qc[0] + qb[1]*qc[1] + qb[2]*qc[2] + qb[3]*qc[3]; qa[1] = qb[0]*qc[1] - qb[1]*qc[0] - qb[2]*qc[3] + qb[3]*qc[2]; qa[2] = qb[0]*qc[2] - qb[2]*qc[0] - qb[3]*qc[1] + qb[1]*qc[3]; qa[3] = qb[0]*qc[3] - qb[3]*qc[0] - qb[1]*qc[2] + qb[2]*qc[1]; } void dQMultiply2 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc) { dAASSERT (qa && qb && qc); qa[0] = qb[0]*qc[0] + qb[1]*qc[1] + qb[2]*qc[2] + qb[3]*qc[3]; qa[1] = -qb[0]*qc[1] + qb[1]*qc[0] - qb[2]*qc[3] + qb[3]*qc[2]; qa[2] = -qb[0]*qc[2] + qb[2]*qc[0] - qb[3]*qc[1] + qb[1]*qc[3]; qa[3] = -qb[0]*qc[3] + qb[3]*qc[0] - qb[1]*qc[2] + qb[2]*qc[1]; } void dQMultiply3 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc) { dAASSERT (qa && qb && qc); qa[0] = qb[0]*qc[0] - qb[1]*qc[1] - qb[2]*qc[2] - qb[3]*qc[3]; qa[1] = -qb[0]*qc[1] - qb[1]*qc[0] + qb[2]*qc[3] - qb[3]*qc[2]; qa[2] = -qb[0]*qc[2] - qb[2]*qc[0] + qb[3]*qc[1] - qb[1]*qc[3]; qa[3] = -qb[0]*qc[3] - qb[3]*qc[0] + qb[1]*qc[2] - 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. void dRfromQ (dMatrix3 R, const dQuaternion q) { dAASSERT (q && R); // q = (s,vx,vy,vz) dReal qq1 = 2*q[1]*q[1]; dReal qq2 = 2*q[2]*q[2]; dReal qq3 = 2*q[3]*q[3]; _R(0,0) = 1 - qq2 - qq3; _R(0,1) = 2*(q[1]*q[2] - q[0]*q[3]); _R(0,2) = 2*(q[1]*q[3] + q[0]*q[2]); _R(0,3) = REAL(0.0); _R(1,0) = 2*(q[1]*q[2] + q[0]*q[3]); _R(1,1) = 1 - qq1 - qq3; _R(1,2) = 2*(q[2]*q[3] - q[0]*q[1]); _R(1,3) = REAL(0.0); _R(2,0) = 2*(q[1]*q[3] - q[0]*q[2]); _R(2,1) = 2*(q[2]*q[3] + q[0]*q[1]); _R(2,2) = 1 - qq1 - qq2; _R(2,3) = REAL(0.0); } void dQfromR (dQuaternion q, const dMatrix3 R) { dAASSERT (q && R); dReal tr,s; tr = _R(0,0) + _R(1,1) + _R(2,2); if (tr >= 0) { s = dSqrt (tr + 1); q[0] = REAL(0.5) * s; s = REAL(0.5) * dRecip(s); q[1] = (_R(2,1) - _R(1,2)) * s; q[2] = (_R(0,2) - _R(2,0)) * s; q[3] = (_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))) + 1); q[1] = REAL(0.5) * s; s = REAL(0.5) * dRecip(s); q[2] = (_R(0,1) + _R(1,0)) * s; q[3] = (_R(2,0) + _R(0,2)) * s; q[0] = (_R(2,1) - _R(1,2)) * s; return; case_1: s = dSqrt((_R(1,1) - (_R(2,2) + _R(0,0))) + 1); q[2] = REAL(0.5) * s; s = REAL(0.5) * dRecip(s); q[3] = (_R(1,2) + _R(2,1)) * s; q[1] = (_R(0,1) + _R(1,0)) * s; q[0] = (_R(0,2) - _R(2,0)) * s; return; case_2: s = dSqrt((_R(2,2) - (_R(0,0) + _R(1,1))) + 1); q[3] = REAL(0.5) * s; s = REAL(0.5) * dRecip(s); q[1] = (_R(2,0) + _R(0,2)) * s; q[2] = (_R(1,2) + _R(2,1)) * s; q[0] = (_R(1,0) - _R(0,1)) * s; return; } } void dDQfromW (dReal dq[4], const dVector3 w, const dQuaternion q) { dAASSERT (w && q && dq); dq[0] = REAL(0.5)*(- w[0]*q[1] - w[1]*q[2] - w[2]*q[3]); dq[1] = REAL(0.5)*( w[0]*q[0] + w[1]*q[3] - w[2]*q[2]); dq[2] = REAL(0.5)*(- w[0]*q[3] + w[1]*q[0] + w[2]*q[1]); dq[3] = REAL(0.5)*( w[0]*q[2] - w[1]*q[1] + w[2]*q[0]); }