SpatialAlgebra.h

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#ifndef SimTK_SIMMATRIX_SPATIAL_ALGEBRA_H_
#define SimTK_SIMMATRIX_SPATIAL_ALGEBRA_H_

/* -------------------------------------------------------------------------- *
 *                      SimTK Core: SimTK Simmatrix(tm)                       *
 * -------------------------------------------------------------------------- *
 * This is part of the SimTK Core biosimulation toolkit originating from      *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org.               *
 *                                                                            *
 * Portions copyright (c) 2005-7 Stanford University and the Authors.         *
 * Authors: Michael Sherman                                                   *
 * Contributors:                                                              *
 *                                                                            *
 * Permission is hereby granted, free of charge, to any person obtaining a    *
 * copy of this software and associated documentation files (the "Software"), *
 * to deal in the Software without restriction, including without limitation  *
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,   *
 * and/or sell copies of the Software, and to permit persons to whom the      *
 * Software is furnished to do so, subject to the following conditions:       *
 *                                                                            *
 * The above copyright notice and this permission notice shall be included in *
 * all copies or substantial portions of the Software.                        *
 *                                                                            *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,   *
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL    *
 * THE AUTHORS, CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,    *
 * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR      *
 * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE  *
 * USE OR OTHER DEALINGS IN THE SOFTWARE.                                     *
 * -------------------------------------------------------------------------- */

#include "SimTKcommon/SmallMatrix.h"

#include <iostream>

namespace SimTK {

// Spatial vectors are used for (orientation,translation) quantities.
// These include
//      spatial velocity     = (angularVelocity,linearVelocity)
//      spatial acceleration = (angularAcceleration,linearAcceleration)
//      generalized forces   = (torque,force)
// Spatial configuration has to be handled differently though since
// orientation is not a vector quantity. (We use "Transform" for this concept
// which includes an orientation matrix and a translation vector.)
typedef Vec<2,   Vec3>  SpatialVec;
typedef Row<2,   Row3>  SpatialRow;
typedef Mat<2,2, Mat33> SpatialMat;

// support for efficient matrix multiplication involving the special phi
// matrix

using namespace SimTK;

class PhiMatrixTranspose;


inline static Vec3 
unitVec(const Vec3& v) { 
    Real tmpNorm = v.norm();
    if (tmpNorm < 1e-15) tmpNorm = 1e-15;

    Vec3 ret = v/tmpNorm;

    return ret;
}

class PhiMatrix {
public:
    typedef PhiMatrixTranspose TransposeType;

    PhiMatrix() { setToNaN(); }
    PhiMatrix(const Vec3& l) : l_(l) {}

    void setToZero() { l_ = 0.; }
    void setToNaN()  { l_.setToNaN(); }

    const Vec3& l() const { return l_; }
private:
    Vec3 l_;
};

class PhiMatrixTranspose {
public:
  PhiMatrixTranspose(const PhiMatrix& phi) : phi(phi) {}
  const Vec3& l() const {return phi.l();}
private:
  const PhiMatrix& phi;
};

inline PhiMatrixTranspose
transpose(const PhiMatrix& phi)
{
    PhiMatrixTranspose ret(phi);
    return ret;
}

inline PhiMatrixTranspose
operator~(const PhiMatrix& phi) {return transpose(phi);}

inline SpatialVec
operator*(const PhiMatrix&  phi,
          const SpatialVec& v)
{
    return SpatialVec(v[0] + phi.l() % v[1],
                      v[1]);
}

inline SpatialMat
operator*(const PhiMatrix&  phi,
          const SpatialMat& m)
{
    const Mat33 x = crossMat(phi.l());
    return SpatialMat( m(0,0) + x*m(1,0), m(0,1) + x*m(1,1),
                           m(1,0)       ,     m(1,1));
}

inline SpatialVec
operator*(const PhiMatrixTranspose& phiT,
          const SpatialVec&         v)
{
    return SpatialVec(v[0],
                      v[1] + v[0] % phiT.l());
}


inline SpatialMat
operator*(const SpatialMat::THerm&  m,
          const PhiMatrixTranspose& phiT)
{
    const Mat33 x = crossMat(phiT.l());
    return SpatialMat( m(0,0) - m(0,1) * x, m(0,1),
                       m(1,0) - m(1,1) * x, m(1,1) );
}

inline SpatialMat
operator*(const SpatialMat&         m,
          const PhiMatrixTranspose& phiT)
{
    const Mat33 x = crossMat(phiT.l());
    return SpatialMat( m(0,0) - m(0,1) * x, m(0,1),
                       m(1,0) - m(1,1) * x, m(1,1) );
}

inline bool
operator==(const PhiMatrix& p1, const PhiMatrix& p2)
{
    return p1.l() == p2.l();
}

inline bool
operator==(const PhiMatrixTranspose& p1, const PhiMatrixTranspose& p2)
{
    return p1.l() == p2.l();
}
} // namespace SimTK

#endif // SimTK_SIMMATRIX_SPATIAL_ALGEBRA_H_