/*************************************************************************
* *
* 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>
#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(1,0) = cpsi*stheta*sphi - spsi*cphi;
_R(1,1) = spsi*stheta*sphi + cpsi*cphi;
_R(1,2) = ctheta*sphi;
_R(2,0) = cpsi*stheta*cphi + spsi*sphi;
_R(2,1) = spsi*stheta*cphi - cpsi*sphi;
_R(2,2) = ctheta*cphi;
}
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;
}
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];
}
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(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(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;
}
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]);
}
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