Geodesic.h

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#ifndef SimTK_SIMMATH_GEODESIC_H_
#define SimTK_SIMMATH_GEODESIC_H_

/* -------------------------------------------------------------------------- *
 *                       Simbody(tm): SimTKmath                               *
 * -------------------------------------------------------------------------- *
 * This is part of the SimTK 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/home/simbody.  *
 *                                                                            *
 * Portions copyright (c) 2012 Stanford University and the Authors.           *
 * Authors: Ian Stavness, Michael Sherman                                     *
 * Contributors:                                                              *
 *                                                                            *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may    *
 * not use this file except in compliance with the License. You may obtain a  *
 * copy of the License at http://www.apache.org/licenses/LICENSE-2.0.         *
 *                                                                            *
 * Unless required by applicable law or agreed to in writing, software        *
 * distributed under the License is distributed on an "AS IS" BASIS,          *
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   *
 * See the License for the specific language governing permissions and        *
 * limitations under the License.                                             *
 * -------------------------------------------------------------------------- */

//==============================================================================
//                           GEODESIC CLASS
//==============================================================================


#include "SimTKcommon.h"
#include "simmath/internal/common.h"

namespace SimTK {

class SimTK_SIMMATH_EXPORT Geodesic {
public:
    Geodesic() {clear();}

    int getNumPoints() const {return (int)frenetFrames.size(); }

    const Array_<Transform>& getFrenetFrames() const {return frenetFrames;}
    Array_<Transform>&       updFrenetFrames() {return frenetFrames;}
    void addFrenetFrame(const Transform& Kf) {frenetFrames.push_back(Kf);}

    Array_<Real>& updArcLengths() {return arcLengths;}
    const Array_<Real>& getArcLengths() const {return arcLengths;}
    void addArcLength(Real s) {arcLengths.push_back(s);}

    Array_<Real>& updCurvatures() {return curvature;}
    const Array_<Real>& getCurvatures() const {return curvature;}
    void addCurvature(Real kappa) {curvature.push_back(kappa);}

    Array_<Vec2>& updDirectionalSensitivityPtoQ() 
    {   return directionalSensitivityPtoQ; }
    const Array_<Vec2>& getDirectionalSensitivityPtoQ() const 
    {   return directionalSensitivityPtoQ; }
    void addDirectionalSensitivityPtoQ(const Vec2& jP) {
        directionalSensitivityPtoQ.push_back(jP);
    }

    Array_<Vec2>& updDirectionalSensitivityQtoP() 
    {   return directionalSensitivityQtoP; }
    const Array_<Vec2>& getDirectionalSensitivityQtoP() const 
    {   return directionalSensitivityQtoP; }
    void addDirectionalSensitivityQtoP(const Vec2& jQ) {
        directionalSensitivityQtoP.push_back(jQ);
    }

    Array_<Vec2>& updPositionalSensitivityPtoQ() 
    {   return positionalSensitivityPtoQ; }
    const Array_<Vec2>& getPositionalSensitivityPtoQ() const 
    {   return positionalSensitivityPtoQ; }
    void addPositionalSensitivityPtoQ(const Vec2& jtP) {
        positionalSensitivityPtoQ.push_back(jtP);
    }

    Array_<Vec2>& updPositionalSensitivityQtoP() 
    {   return positionalSensitivityQtoP; }
    const Array_<Vec2>& getPositionalSensitivityQtoP() const 
    {   return positionalSensitivityQtoP; }
    void addPositionalSensitivityQtoP(const Vec2& jtQ) {
        positionalSensitivityQtoP.push_back(jtQ);
    }

    void setTorsionAtP(Real tauP) {torsionAtP = tauP;}
    void setTorsionAtQ(Real tauQ) {torsionAtQ = tauQ;}
    void setBinormalCurvatureAtP(Real muP) {binormalCurvatureAtP = muP;}
    void setBinormalCurvatureAtQ(Real muQ) {binormalCurvatureAtQ = muQ;}

    Real getLength() const {return arcLengths.empty() ? 0 : arcLengths.back();}

    Real calcLengthDot(const Vec3& xdotP, const Vec3& xdotQ) const 
    {   return ~xdotQ*getTangentQ() - ~xdotP*getTangentP(); }

    const Vec3& getPointP() const {return frenetFrames.front().p();}
    const Vec3& getPointQ() const {return frenetFrames.back().p();}

    const UnitVec3& getNormalP() const {return frenetFrames.front().z();}
    const UnitVec3& getNormalQ() const {return frenetFrames.back().z();}

    const UnitVec3& getTangentP() const {return frenetFrames.front().y();}
    const UnitVec3& getTangentQ() const {return frenetFrames.back().y();}

    const UnitVec3& getBinormalP() const {return frenetFrames.front().x();}
    const UnitVec3& getBinormalQ() const {return frenetFrames.back().x();}

    Real getCurvatureP() const {return curvature.front();}
    Real getCurvatureQ() const {return curvature.back();}

    Real getTorsionP() const {return torsionAtP;}
    Real getTorsionQ() const {return torsionAtQ;}

    Real getBinormalCurvatureP() const {return binormalCurvatureAtP;}
    Real getBinormalCurvatureQ() const {return binormalCurvatureAtQ;}

    Real getJacobiP() const {return directionalSensitivityQtoP.front()[0];}
    Real getJacobiQ() const {return directionalSensitivityPtoQ.back()[0];}

    // Note sign change here -- we calculated this by integrating backwards
    // so the arc length we used had the opposite sign from the true arc
    // length parameter.
    Real getJacobiPDot() const {return -directionalSensitivityQtoP.front()[1];}
    Real getJacobiQDot() const {return directionalSensitivityPtoQ.back()[1];}

    // XXX testing
    Real getJacobiTransP() const {return positionalSensitivityQtoP.front()[0];}
    Real getJacobiTransQ() const {return positionalSensitivityPtoQ.back()[0];}
    Real getJacobiTransPDot() const {return -positionalSensitivityQtoP.front()[1];}
    Real getJacobiTransQDot() const {return positionalSensitivityPtoQ.back()[1];}

    void clear() {
        arcLengths.clear();
        frenetFrames.clear(); 
        directionalSensitivityPtoQ.clear(); 
        directionalSensitivityQtoP.clear(); 
        positionalSensitivityPtoQ.clear(); 
        positionalSensitivityQtoP.clear(); 
        curvature.clear();
        torsionAtP = torsionAtQ = NaN;
        binormalCurvatureAtP = binormalCurvatureAtQ = NaN;
        convexFlag = shortestFlag = false;
        initialStepSizeHint = achievedAccuracy = NaN;
    }

    void setIsConvex(bool isConvex) {convexFlag = isConvex;}
    void setIsShortest(bool isShortest) {shortestFlag = isShortest;}
    void setInitialStepSizeHint(Real sz) {initialStepSizeHint=sz;} 
    void setAchievedAccuracy(Real acc) {achievedAccuracy=acc;} 

    bool isConvex() const {return convexFlag;}
    bool isShortest() const {return shortestFlag;}
    Real getInitialStepSizeHint() const {return initialStepSizeHint;}
    Real getAchievedAccuracy() const {return achievedAccuracy;}

    void dump(std::ostream& o) const;

private:
    // All these arrays are the same length when the geodesic is complete.
    Array_<Real>      arcLengths; // arc length coord corresponding to point
    Array_<Transform> frenetFrames; // see above for more info
    Array_<Vec2>      directionalSensitivityPtoQ; // jQ and jQdot
    Array_<Vec2>      directionalSensitivityQtoP; // jP and -jPdot
    Array_<Vec2>      positionalSensitivityPtoQ; // jtQ and jtQdot
    Array_<Vec2>      positionalSensitivityQtoP; // jtP and -jtPdot
    Array_<Real>      curvature; // normal curvature kappa in tangent direction
    // These are only calculated at the end points.
    Real              torsionAtP, torsionAtQ; // torsion tau (only at ends) 
    Real              binormalCurvatureAtP, binormalCurvatureAtQ;

    // This flag is set true if curvature[i]>=0 for all i.
    bool convexFlag; // is this geodesic over a convex surface?

    bool shortestFlag; // XXX is this geodesic the shortest one of the surface?
    Real initialStepSizeHint; // the initial step size to be tried when integrating this geodesic
    Real achievedAccuracy; // the accuracy to which this geodesic curve has been calculated
};


class GeodesicDecorator : public DecorationGenerator {
public:
    GeodesicDecorator(const Geodesic& geod, const Vec3& color) :
            m_geod(geod), m_color(color) { }

    virtual void generateDecorations(const State& state,
            Array_<DecorativeGeometry>& geometry) override {
//        m_system.realize(state, Stage::Position);

        // draw connected line segments from pts
        const Array_<Transform>& Kfs = m_geod.getFrenetFrames();
        Vec3 prevPt;
        for (int i = 0; i < (int) Kfs.size(); ++i) {
            Vec3 cur = Kfs[i].p();
            if (i > 0) {
                geometry.push_back(
                        DecorativeLine(prevPt, cur)
                        .setColor(m_color)
                        .setLineThickness(3));
            }
            prevPt = cur;

            geometry.push_back(DecorativeFrame(Real(.2)).setTransform(Kfs[i]));
        }
    }

private:
    const Geodesic& m_geod;
    const Vec3& m_color;
};




class GeodesicOptions {
    // XXX stub
};


} // namespace SimTK

#endif // SimTK_SIMMATH_GEODESIC_H_