332 lines
13 KiB
C++
332 lines
13 KiB
C++
/*
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Copyright (c) 2003-2015 Erwin Coumans, Jakub Stepien
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This software is provided 'as-is', without any express or implied warranty.
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In no event will the authors be held liable for any damages arising from the use of this software.
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Permission is granted to anyone to use this software for any purpose,
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including commercial applications, and to alter it and redistribute it freely,
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subject to the following restrictions:
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1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
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2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
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3. This notice may not be removed or altered from any source distribution.
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*/
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///These spatial algebra classes are used for btMultiBody,
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///see BulletDynamics/Featherstone
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#ifndef BT_SPATIAL_ALGEBRA_H
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#define BT_SPATIAL_ALGEBRA_H
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#include "btMatrix3x3.h"
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struct btSpatialForceVector
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{
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btVector3 m_topVec, m_bottomVec;
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//
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btSpatialForceVector() { setZero(); }
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btSpatialForceVector(const btVector3 &angular, const btVector3 &linear) : m_topVec(linear), m_bottomVec(angular) {}
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btSpatialForceVector(const btScalar &ax, const btScalar &ay, const btScalar &az, const btScalar &lx, const btScalar &ly, const btScalar &lz)
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{
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setValue(ax, ay, az, lx, ly, lz);
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}
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//
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void setVector(const btVector3 &angular, const btVector3 &linear) { m_topVec = linear; m_bottomVec = angular; }
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void setValue(const btScalar &ax, const btScalar &ay, const btScalar &az, const btScalar &lx, const btScalar &ly, const btScalar &lz)
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{
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m_bottomVec.setValue(ax, ay, az); m_topVec.setValue(lx, ly, lz);
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}
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//
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void addVector(const btVector3 &angular, const btVector3 &linear) { m_topVec += linear; m_bottomVec += angular; }
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void addValue(const btScalar &ax, const btScalar &ay, const btScalar &az, const btScalar &lx, const btScalar &ly, const btScalar &lz)
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{
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m_bottomVec[0] += ax; m_bottomVec[1] += ay; m_bottomVec[2] += az;
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m_topVec[0] += lx; m_topVec[1] += ly; m_topVec[2] += lz;
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}
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//
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const btVector3 & getLinear() const { return m_topVec; }
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const btVector3 & getAngular() const { return m_bottomVec; }
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//
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void setLinear(const btVector3 &linear) { m_topVec = linear; }
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void setAngular(const btVector3 &angular) { m_bottomVec = angular; }
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//
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void addAngular(const btVector3 &angular) { m_bottomVec += angular; }
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void addLinear(const btVector3 &linear) { m_topVec += linear; }
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//
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void setZero() { m_topVec.setZero(); m_bottomVec.setZero(); }
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//
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btSpatialForceVector & operator += (const btSpatialForceVector &vec) { m_topVec += vec.m_topVec; m_bottomVec += vec.m_bottomVec; return *this; }
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btSpatialForceVector & operator -= (const btSpatialForceVector &vec) { m_topVec -= vec.m_topVec; m_bottomVec -= vec.m_bottomVec; return *this; }
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btSpatialForceVector operator - (const btSpatialForceVector &vec) const { return btSpatialForceVector(m_bottomVec - vec.m_bottomVec, m_topVec - vec.m_topVec); }
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btSpatialForceVector operator + (const btSpatialForceVector &vec) const { return btSpatialForceVector(m_bottomVec + vec.m_bottomVec, m_topVec + vec.m_topVec); }
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btSpatialForceVector operator - () const { return btSpatialForceVector(-m_bottomVec, -m_topVec); }
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btSpatialForceVector operator * (const btScalar &s) const { return btSpatialForceVector(s * m_bottomVec, s * m_topVec); }
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//btSpatialForceVector & operator = (const btSpatialForceVector &vec) { m_topVec = vec.m_topVec; m_bottomVec = vec.m_bottomVec; return *this; }
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};
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struct btSpatialMotionVector
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{
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btVector3 m_topVec, m_bottomVec;
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//
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btSpatialMotionVector() { setZero(); }
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btSpatialMotionVector(const btVector3 &angular, const btVector3 &linear) : m_topVec(angular), m_bottomVec(linear) {}
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//
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void setVector(const btVector3 &angular, const btVector3 &linear) { m_topVec = angular; m_bottomVec = linear; }
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void setValue(const btScalar &ax, const btScalar &ay, const btScalar &az, const btScalar &lx, const btScalar &ly, const btScalar &lz)
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{
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m_topVec.setValue(ax, ay, az); m_bottomVec.setValue(lx, ly, lz);
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}
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//
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void addVector(const btVector3 &angular, const btVector3 &linear) { m_topVec += linear; m_bottomVec += angular; }
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void addValue(const btScalar &ax, const btScalar &ay, const btScalar &az, const btScalar &lx, const btScalar &ly, const btScalar &lz)
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{
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m_topVec[0] += ax; m_topVec[1] += ay; m_topVec[2] += az;
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m_bottomVec[0] += lx; m_bottomVec[1] += ly; m_bottomVec[2] += lz;
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}
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//
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const btVector3 & getAngular() const { return m_topVec; }
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const btVector3 & getLinear() const { return m_bottomVec; }
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//
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void setAngular(const btVector3 &angular) { m_topVec = angular; }
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void setLinear(const btVector3 &linear) { m_bottomVec = linear; }
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//
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void addAngular(const btVector3 &angular) { m_topVec += angular; }
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void addLinear(const btVector3 &linear) { m_bottomVec += linear; }
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//
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void setZero() { m_topVec.setZero(); m_bottomVec.setZero(); }
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//
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btScalar dot(const btSpatialForceVector &b) const
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{
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return m_bottomVec.dot(b.m_topVec) + m_topVec.dot(b.m_bottomVec);
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}
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//
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template<typename SpatialVectorType>
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void cross(const SpatialVectorType &b, SpatialVectorType &out) const
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{
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out.m_topVec = m_topVec.cross(b.m_topVec);
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out.m_bottomVec = m_bottomVec.cross(b.m_topVec) + m_topVec.cross(b.m_bottomVec);
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}
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template<typename SpatialVectorType>
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SpatialVectorType cross(const SpatialVectorType &b) const
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{
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SpatialVectorType out;
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out.m_topVec = m_topVec.cross(b.m_topVec);
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out.m_bottomVec = m_bottomVec.cross(b.m_topVec) + m_topVec.cross(b.m_bottomVec);
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return out;
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}
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//
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btSpatialMotionVector & operator += (const btSpatialMotionVector &vec) { m_topVec += vec.m_topVec; m_bottomVec += vec.m_bottomVec; return *this; }
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btSpatialMotionVector & operator -= (const btSpatialMotionVector &vec) { m_topVec -= vec.m_topVec; m_bottomVec -= vec.m_bottomVec; return *this; }
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btSpatialMotionVector & operator *= (const btScalar &s) { m_topVec *= s; m_bottomVec *= s; return *this; }
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btSpatialMotionVector operator - (const btSpatialMotionVector &vec) const { return btSpatialMotionVector(m_topVec - vec.m_topVec, m_bottomVec - vec.m_bottomVec); }
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btSpatialMotionVector operator + (const btSpatialMotionVector &vec) const { return btSpatialMotionVector(m_topVec + vec.m_topVec, m_bottomVec + vec.m_bottomVec); }
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btSpatialMotionVector operator - () const { return btSpatialMotionVector(-m_topVec, -m_bottomVec); }
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btSpatialMotionVector operator * (const btScalar &s) const { return btSpatialMotionVector(s * m_topVec, s * m_bottomVec); }
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};
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struct btSymmetricSpatialDyad
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{
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btMatrix3x3 m_topLeftMat, m_topRightMat, m_bottomLeftMat;
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//
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btSymmetricSpatialDyad() { setIdentity(); }
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btSymmetricSpatialDyad(const btMatrix3x3 &topLeftMat, const btMatrix3x3 &topRightMat, const btMatrix3x3 &bottomLeftMat) { setMatrix(topLeftMat, topRightMat, bottomLeftMat); }
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//
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void setMatrix(const btMatrix3x3 &topLeftMat, const btMatrix3x3 &topRightMat, const btMatrix3x3 &bottomLeftMat)
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{
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m_topLeftMat = topLeftMat;
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m_topRightMat = topRightMat;
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m_bottomLeftMat = bottomLeftMat;
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}
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//
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void addMatrix(const btMatrix3x3 &topLeftMat, const btMatrix3x3 &topRightMat, const btMatrix3x3 &bottomLeftMat)
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{
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m_topLeftMat += topLeftMat;
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m_topRightMat += topRightMat;
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m_bottomLeftMat += bottomLeftMat;
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}
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//
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void setIdentity() { m_topLeftMat.setIdentity(); m_topRightMat.setIdentity(); m_bottomLeftMat.setIdentity(); }
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//
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btSymmetricSpatialDyad & operator -= (const btSymmetricSpatialDyad &mat)
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{
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m_topLeftMat -= mat.m_topLeftMat;
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m_topRightMat -= mat.m_topRightMat;
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m_bottomLeftMat -= mat.m_bottomLeftMat;
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return *this;
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}
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//
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btSpatialForceVector operator * (const btSpatialMotionVector &vec)
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{
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return btSpatialForceVector(m_bottomLeftMat * vec.m_topVec + m_topLeftMat.transpose() * vec.m_bottomVec, m_topLeftMat * vec.m_topVec + m_topRightMat * vec.m_bottomVec);
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}
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};
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struct btSpatialTransformationMatrix
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{
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btMatrix3x3 m_rotMat; //btMatrix3x3 m_trnCrossMat;
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btVector3 m_trnVec;
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//
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enum eOutputOperation
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{
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None = 0,
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Add = 1,
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Subtract = 2
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};
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//
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template<typename SpatialVectorType>
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void transform( const SpatialVectorType &inVec,
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SpatialVectorType &outVec,
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eOutputOperation outOp = None)
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{
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if(outOp == None)
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{
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outVec.m_topVec = m_rotMat * inVec.m_topVec;
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outVec.m_bottomVec = -m_trnVec.cross(outVec.m_topVec) + m_rotMat * inVec.m_bottomVec;
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}
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else if(outOp == Add)
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{
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outVec.m_topVec += m_rotMat * inVec.m_topVec;
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outVec.m_bottomVec += -m_trnVec.cross(outVec.m_topVec) + m_rotMat * inVec.m_bottomVec;
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}
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else if(outOp == Subtract)
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{
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outVec.m_topVec -= m_rotMat * inVec.m_topVec;
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outVec.m_bottomVec -= -m_trnVec.cross(outVec.m_topVec) + m_rotMat * inVec.m_bottomVec;
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}
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}
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template<typename SpatialVectorType>
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void transformRotationOnly( const SpatialVectorType &inVec,
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SpatialVectorType &outVec,
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eOutputOperation outOp = None)
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{
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if(outOp == None)
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{
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outVec.m_topVec = m_rotMat * inVec.m_topVec;
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outVec.m_bottomVec = m_rotMat * inVec.m_bottomVec;
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}
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else if(outOp == Add)
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{
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outVec.m_topVec += m_rotMat * inVec.m_topVec;
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outVec.m_bottomVec += m_rotMat * inVec.m_bottomVec;
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}
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else if(outOp == Subtract)
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{
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outVec.m_topVec -= m_rotMat * inVec.m_topVec;
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outVec.m_bottomVec -= m_rotMat * inVec.m_bottomVec;
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}
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}
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template<typename SpatialVectorType>
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void transformInverse( const SpatialVectorType &inVec,
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SpatialVectorType &outVec,
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eOutputOperation outOp = None)
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{
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if(outOp == None)
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{
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outVec.m_topVec = m_rotMat.transpose() * inVec.m_topVec;
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outVec.m_bottomVec = m_rotMat.transpose() * (inVec.m_bottomVec + m_trnVec.cross(inVec.m_topVec));
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}
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else if(outOp == Add)
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{
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outVec.m_topVec += m_rotMat.transpose() * inVec.m_topVec;
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outVec.m_bottomVec += m_rotMat.transpose() * (inVec.m_bottomVec + m_trnVec.cross(inVec.m_topVec));
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}
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else if(outOp == Subtract)
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{
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outVec.m_topVec -= m_rotMat.transpose() * inVec.m_topVec;
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outVec.m_bottomVec -= m_rotMat.transpose() * (inVec.m_bottomVec + m_trnVec.cross(inVec.m_topVec));
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}
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}
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template<typename SpatialVectorType>
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void transformInverseRotationOnly( const SpatialVectorType &inVec,
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SpatialVectorType &outVec,
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eOutputOperation outOp = None)
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{
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if(outOp == None)
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{
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outVec.m_topVec = m_rotMat.transpose() * inVec.m_topVec;
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outVec.m_bottomVec = m_rotMat.transpose() * inVec.m_bottomVec;
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}
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else if(outOp == Add)
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{
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outVec.m_topVec += m_rotMat.transpose() * inVec.m_topVec;
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outVec.m_bottomVec += m_rotMat.transpose() * inVec.m_bottomVec;
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}
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else if(outOp == Subtract)
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{
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outVec.m_topVec -= m_rotMat.transpose() * inVec.m_topVec;
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outVec.m_bottomVec -= m_rotMat.transpose() * inVec.m_bottomVec;
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}
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}
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void transformInverse( const btSymmetricSpatialDyad &inMat,
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btSymmetricSpatialDyad &outMat,
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eOutputOperation outOp = None)
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{
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const btMatrix3x3 r_cross( 0, -m_trnVec[2], m_trnVec[1],
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m_trnVec[2], 0, -m_trnVec[0],
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-m_trnVec[1], m_trnVec[0], 0);
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if(outOp == None)
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{
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outMat.m_topLeftMat = m_rotMat.transpose() * ( inMat.m_topLeftMat - inMat.m_topRightMat * r_cross ) * m_rotMat;
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outMat.m_topRightMat = m_rotMat.transpose() * inMat.m_topRightMat * m_rotMat;
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outMat.m_bottomLeftMat = m_rotMat.transpose() * (r_cross * (inMat.m_topLeftMat - inMat.m_topRightMat * r_cross) + inMat.m_bottomLeftMat - inMat.m_topLeftMat.transpose() * r_cross) * m_rotMat;
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}
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else if(outOp == Add)
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{
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outMat.m_topLeftMat += m_rotMat.transpose() * ( inMat.m_topLeftMat - inMat.m_topRightMat * r_cross ) * m_rotMat;
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outMat.m_topRightMat += m_rotMat.transpose() * inMat.m_topRightMat * m_rotMat;
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outMat.m_bottomLeftMat += m_rotMat.transpose() * (r_cross * (inMat.m_topLeftMat - inMat.m_topRightMat * r_cross) + inMat.m_bottomLeftMat - inMat.m_topLeftMat.transpose() * r_cross) * m_rotMat;
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}
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else if(outOp == Subtract)
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{
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outMat.m_topLeftMat -= m_rotMat.transpose() * ( inMat.m_topLeftMat - inMat.m_topRightMat * r_cross ) * m_rotMat;
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outMat.m_topRightMat -= m_rotMat.transpose() * inMat.m_topRightMat * m_rotMat;
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outMat.m_bottomLeftMat -= m_rotMat.transpose() * (r_cross * (inMat.m_topLeftMat - inMat.m_topRightMat * r_cross) + inMat.m_bottomLeftMat - inMat.m_topLeftMat.transpose() * r_cross) * m_rotMat;
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}
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}
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template<typename SpatialVectorType>
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SpatialVectorType operator * (const SpatialVectorType &vec)
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{
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SpatialVectorType out;
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transform(vec, out);
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return out;
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}
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};
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template<typename SpatialVectorType>
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void symmetricSpatialOuterProduct(const SpatialVectorType &a, const SpatialVectorType &b, btSymmetricSpatialDyad &out)
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{
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//output op maybe?
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out.m_topLeftMat = outerProduct(a.m_topVec, b.m_bottomVec);
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out.m_topRightMat = outerProduct(a.m_topVec, b.m_topVec);
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out.m_topLeftMat = outerProduct(a.m_bottomVec, b.m_bottomVec);
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//maybe simple a*spatTranspose(a) would be nicer?
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}
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template<typename SpatialVectorType>
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btSymmetricSpatialDyad symmetricSpatialOuterProduct(const SpatialVectorType &a, const SpatialVectorType &b)
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{
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btSymmetricSpatialDyad out;
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out.m_topLeftMat = outerProduct(a.m_topVec, b.m_bottomVec);
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out.m_topRightMat = outerProduct(a.m_topVec, b.m_topVec);
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out.m_bottomLeftMat = outerProduct(a.m_bottomVec, b.m_bottomVec);
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return out;
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//maybe simple a*spatTranspose(a) would be nicer?
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}
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#endif //BT_SPATIAL_ALGEBRA_H
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