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+/*************************************************************************
+ *                                                                       *
+ * 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.                     *
+ *                                                                       *
+ *************************************************************************/
+
+/*
+
+some useful collision utility stuff.
+
+*/
+
+#ifndef _ODE_COLLISION_UTIL_H_
+#define _ODE_COLLISION_UTIL_H_
+
+#include <ode/common.h>
+#include <ode/contact.h>
+#include <ode/odemath.h>
+#include <ode/rotation.h>
+
+
+// given a pointer `p' to a dContactGeom, return the dContactGeom at
+// p + skip bytes.
+#define CONTACT(p,skip) ((dContactGeom*) (((char*)p) + (skip)))
+
+#if 1
+#include "collision_kernel.h"
+// Fetches a contact
+inline dContactGeom* SAFECONTACT(int Flags, dContactGeom* Contacts, int Index, int Stride){
+        dIASSERT(Index >= 0 && Index < (Flags & NUMC_MASK));
+        return ((dContactGeom*)(((char*)Contacts) + (Index * Stride)));
+}
+#endif
+
+
+// if the spheres (p1,r1) and (p2,r2) collide, set the contact `c' and
+// return 1, else return 0.
+
+int dCollideSpheres (dVector3 p1, dReal r1,
+                     dVector3 p2, dReal r2, dContactGeom *c);
+
+
+// given two lines
+//    qa = pa + alpha* ua
+//    qb = pb + beta * ub
+// where pa,pb are two points, ua,ub are two unit length vectors, and alpha,
+// beta go from [-inf,inf], return alpha and beta such that qa and qb are
+// as close as possible
+
+void dLineClosestApproach (const dVector3 pa, const dVector3 ua,
+                           const dVector3 pb, const dVector3 ub,
+                           dReal *alpha, dReal *beta);
+
+
+// given a line segment p1-p2 and a box (center 'c', rotation 'R', side length
+// vector 'side'), compute the points of closest approach between the box
+// and the line. return these points in 'lret' (the point on the line) and
+// 'bret' (the point on the box). if the line actually penetrates the box
+// then the solution is not unique, but only one solution will be returned.
+// in this case the solution points will coincide.
+
+void dClosestLineBoxPoints (const dVector3 p1, const dVector3 p2,
+                            const dVector3 c, const dMatrix3 R,
+                            const dVector3 side,
+                            dVector3 lret, dVector3 bret);
+
+// 20 Apr 2004
+// Start code by Nguyen Binh
+int dClipEdgeToPlane(dVector3 &vEpnt0, dVector3 &vEpnt1, const dVector4& plPlane);
+// clip polygon with plane and generate new polygon points
+void dClipPolyToPlane(const dVector3 avArrayIn[], const int ctIn, dVector3 avArrayOut[], int &ctOut, const dVector4 &plPlane );
+
+void dClipPolyToCircle(const dVector3 avArrayIn[], const int ctIn, dVector3 avArrayOut[], int &ctOut, const dVector4 &plPlane ,dReal fRadius);
+
+// Some vector math
+inline void dVector3Subtract(const dVector3& a,const dVector3& b,dVector3& c)
+{
+        c[0] = a[0] - b[0];
+        c[1] = a[1] - b[1];
+        c[2] = a[2] - b[2];
+}
+
+// Some vector math
+inline void dVector3Scale(dVector3& a,dReal nScale)
+{
+        a[0] *= nScale ;
+        a[1] *= nScale ;
+        a[2] *= nScale ;
+}
+
+inline void dVector3Add(const dVector3& a,const dVector3& b,dVector3& c)
+{
+        c[0] = a[0] + b[0];
+        c[1] = a[1] + b[1];
+        c[2] = a[2] + b[2];
+}
+
+inline void dVector3Copy(const dVector3& a,dVector3& c)
+{
+        c[0] = a[0];
+        c[1] = a[1];
+        c[2] = a[2];
+}
+
+inline void dVector3Cross(const dVector3& a,const dVector3& b,dVector3& c)
+{
+        dCROSS(c,=,a,b);
+}
+
+inline dReal dVector3Length(const dVector3& a)
+{
+        return dSqrt(a[0]*a[0]+a[1]*a[1]+a[2]*a[2]);
+}
+
+inline dReal dVector3Dot(const dVector3& a,const dVector3& b)
+{
+        return dDOT(a,b);
+}
+
+inline void dVector3Inv(dVector3& a)
+{
+        a[0] = -a[0];
+        a[1] = -a[1];
+        a[2] = -a[2];
+}
+
+inline dReal dVector3Length2(const dVector3& a)
+{
+        return (a[0]*a[0]+a[1]*a[1]+a[2]*a[2]);
+}
+
+inline void dMat3GetCol(const dMatrix3& m,const int col, dVector3& v)
+{
+        v[0] = m[col + 0];
+        v[1] = m[col + 4];
+        v[2] = m[col + 8];
+}
+
+inline void dVector3CrossMat3Col(const dMatrix3& m,const int col,const dVector3& v,dVector3& r)
+{
+        r[0] =  v[1] * m[2*4 + col] - v[2] * m[1*4 + col]; 
+        r[1] =  v[2] * m[0*4 + col] - v[0] * m[2*4 + col]; 
+        r[2] =  v[0] * m[1*4 + col] - v[1] * m[0*4 + col];
+}
+
+inline void dMat3ColCrossVector3(const dMatrix3& m,const int col,const dVector3& v,dVector3& r)
+{
+        r[0] =   v[2] * m[1*4 + col] - v[1] * m[2*4 + col]; 
+        r[1] =   v[0] * m[2*4 + col] - v[2] * m[0*4 + col]; 
+        r[2] =   v[1] * m[0*4 + col] - v[0] * m[1*4 + col];
+}
+
+inline void dMultiplyMat3Vec3(const dMatrix3& m,const dVector3& v, dVector3& r)
+{
+        dMULTIPLY0_331(r,m,v);
+}
+
+inline dReal dPointPlaneDistance(const dVector3& point,const dVector4& plane)
+{
+        return (plane[0]*point[0] + plane[1]*point[1] + plane[2]*point[2] + plane[3]);
+}
+
+inline void dConstructPlane(const dVector3& normal,const dReal& distance, dVector4& plane)
+{
+        plane[0] = normal[0];
+        plane[1] = normal[1];
+        plane[2] = normal[2];
+        plane[3] = distance;
+}
+
+inline void dMatrix3Copy(const dReal* source,dMatrix3& dest)
+{
+        dest[0] =       source[0];
+        dest[1] =       source[1];
+        dest[2] =       source[2];
+
+        dest[4] =       source[4];
+        dest[5] =       source[5];
+        dest[6] =       source[6];
+
+        dest[8] =       source[8];
+        dest[9] =       source[9];
+        dest[10]=       source[10];
+}
+
+inline dReal dMatrix3Det( const dMatrix3& mat )
+{
+        dReal det;
+
+        det = mat[0] * ( mat[5]*mat[10] - mat[9]*mat[6] )
+                - mat[1] * ( mat[4]*mat[10] - mat[8]*mat[6] )
+                + mat[2] * ( mat[4]*mat[9]  - mat[8]*mat[5] );
+
+        return( det );
+}
+
+
+inline void dMatrix3Inv( const dMatrix3& ma, dMatrix3& dst )
+{
+        dReal det = dMatrix3Det( ma );
+
+        if ( dFabs( det ) < REAL(0.0005) )
+        {
+                dRSetIdentity( dst );
+                return;
+        }
+
+        dst[0] =    ma[5]*ma[10] - ma[6]*ma[9]   / det;
+        dst[1] = -( ma[1]*ma[10] - ma[9]*ma[2] ) / det;
+        dst[2] =    ma[1]*ma[6]  - ma[5]*ma[2]   / det;
+
+        dst[4] = -( ma[4]*ma[10] - ma[6]*ma[8] ) / det;
+        dst[5] =    ma[0]*ma[10] - ma[8]*ma[2]   / det;
+        dst[6] = -( ma[0]*ma[6] - ma[4]*ma[2] ) / det;
+
+        dst[8] =    ma[4]*ma[9] - ma[8]*ma[5]   / det;
+        dst[9] = -( ma[0]*ma[9] - ma[8]*ma[1] ) / det;
+        dst[10] =    ma[0]*ma[5] - ma[1]*ma[4]   / det;
+}
+
+inline void dQuatTransform(const dQuaternion& quat,const dVector3& source,dVector3& dest)
+{
+
+        // Nguyen Binh : this code seem to be the fastest.
+        dReal x0 =      source[0] * quat[0] + source[2] * quat[2] - source[1] * quat[3];
+        dReal x1 =      source[1] * quat[0] + source[0] * quat[3] - source[2] * quat[1];
+        dReal x2 =      source[2] * quat[0] + source[1] * quat[1] - source[0] * quat[2];
+        dReal x3 =      source[0] * quat[1] + source[1] * quat[2] + source[2] * quat[3];
+
+        dest[0]  =      quat[0] * x0 + quat[1] * x3 + quat[2] * x2 - quat[3] * x1;
+        dest[1]  =      quat[0] * x1 + quat[2] * x3 + quat[3] * x0 - quat[1] * x2;
+        dest[2]  =      quat[0] * x2 + quat[3] * x3 + quat[1] * x1 - quat[2] * x0;
+
+        /*
+        // nVidia SDK implementation
+        dVector3 uv, uuv; 
+        dVector3 qvec;
+        qvec[0] = quat[1];
+        qvec[1] = quat[2];
+        qvec[2] = quat[3];
+
+        dVector3Cross(qvec,source,uv);
+        dVector3Cross(qvec,uv,uuv);
+
+        dVector3Scale(uv,REAL(2.0)*quat[0]);
+        dVector3Scale(uuv,REAL(2.0));
+
+        dest[0] = source[0] + uv[0] + uuv[0];
+        dest[1] = source[1] + uv[1] + uuv[1];
+        dest[2] = source[2] + uv[2] + uuv[2];   
+        */
+}
+
+inline void dQuatInvTransform(const dQuaternion& quat,const dVector3& source,dVector3& dest)
+{
+
+        dReal norm = quat[0]*quat[0] + quat[1]*quat[1] + quat[2]*quat[2] + quat[3]*quat[3];
+
+        if (norm > REAL(0.0))
+        {
+                dQuaternion invQuat;
+                invQuat[0] =  quat[0] / norm;
+                invQuat[1] = -quat[1] / norm;
+                invQuat[2] = -quat[2] / norm;
+                invQuat[3] = -quat[3] / norm;   
+                
+                dQuatTransform(invQuat,source,dest);
+
+        }
+        else
+        {
+                // Singular -> return identity
+                dVector3Copy(source,dest);
+        }
+}
+
+inline void dGetEulerAngleFromRot(const dMatrix3& mRot,dReal& rX,dReal& rY,dReal& rZ)
+{
+        rY = asin(mRot[0 * 4 + 2]);
+        if (rY < M_PI /2)
+        {
+                if (rY > -M_PI /2)
+                {
+                        rX = atan2(-mRot[1*4 + 2], mRot[2*4 + 2]);
+                        rZ = atan2(-mRot[0*4 + 1], mRot[0*4 + 0]);
+                }
+                else
+                {
+                        // not unique
+                        rX = -atan2(mRot[1*4 + 0], mRot[1*4 + 1]);
+                        rZ = REAL(0.0);
+                }
+        }
+        else
+        {
+                // not unique
+                rX = atan2(mRot[1*4 + 0], mRot[1*4 + 1]);
+                rZ = REAL(0.0);
+        }
+}
+
+inline void dQuatInv(const dQuaternion& source, dQuaternion& dest)
+{
+        dReal norm = source[0]*source[0] + source[1]*source[1] + source[2]*source[2] + source[3]*source[3];
+
+        if (norm > 0.0f)
+        {
+                dest[0] = source[0] / norm;
+                dest[1] = -source[1] / norm;
+                dest[2] = -source[2] / norm;
+                dest[3] = -source[3] / norm;    
+        }
+        else
+        {
+                // Singular -> return identity
+                dest[0] = REAL(1.0);
+                dest[1] = REAL(0.0);
+                dest[2] = REAL(0.0);
+                dest[3] = REAL(0.0);
+        }
+}
+
+
+#endif