h2isometry.h

#ifndef H2ISOMETRY_H
#define H2ISOMETRY_H

#include "tools.h"
#include "sl2cmatrix.h"
#include "h2point.h"
#include "h2geodesic.h"
#include "h2polygon.h"

class H2Isometry
{
    friend H2Isometry operator *(const H2Isometry & f1, const H2Isometry & f2);
    friend H2Point operator *(const H2Isometry & f, const H2Point & p);
    friend H2Point operator *(const H2Point & p, const H2Isometry & f);
    friend H2Polygon operator *(const H2Isometry &f, const H2Polygon &P);
    friend H2Geodesic operator *(const H2Isometry & f, const H2Geodesic & L);
    friend H2GeodesicArc operator *(const H2Isometry & f, const H2GeodesicArc & L);
    friend bool almostEqual(const H2Isometry & f1, const H2Isometry & f2);
    friend std::ostream & operator<<(std::ostream & out, const H2Isometry &f);
    friend class FenchelNielsenConstructor;
    friend class PantsTree;
    friend class PantsTreeNode;

public:
    H2Isometry();
    H2Isometry(uint i);
    H2Isometry(const SL2RMatrix &A);

    static bool almostEqual(const H2Isometry & f1, const H2Isometry & f2);
    void getDiskCoordinates(Complex &u, Complex &a) const;

    SL2CMatrix getSU11Matrix() const;
    SL2RMatrix getSL2RMatrix() const;

    void setIdentity();
    void setSU11Matrix(const SL2CMatrix & A);
    void setSL2Rmatrix(const SL2RMatrix & A);
    void setDiskCoordinates(const Complex & u, const Complex & a);

    void setByNormalizingPairOnLeftHandSide(const H2Isometry &f1, const H2Isometry &f1left);
    void setByNormalizingPairOnRightHandSide(const H2Isometry &f1, const H2Isometry &f1left);

    bool isHyperbolic() const;
    bool isElliptic() const;
    bool isParabolic() const;

    bool axis(H2Geodesic &L) const;

    Complex hitComplexInDiskModel(const Complex & z);

    H2Isometry inverse() const;
    double traceSquared() const;
    double translationLength() const;
    double error() const;

    static H2Isometry findConjugatorForGluing(const H2Isometry & f1, const H2Isometry & f1left,
                                     const H2Isometry & f2, const H2Isometry &f2left, double twistNormalized);

    void setByMappingPointToOrigin(const H2Point & p);
    void setTranslationAxisAndLength(const H2Geodesic & axis, double length);
    void setByMappingPointInDiskModelNormalized(const Complex & zIn, const Complex & zOut);
    void setByMappingGeodesic(const H2Geodesic & L1, const H2Geodesic & L2);

private:
    Complex u,a;

    void setTranslationLengthNormalized(double length);

    void setVerticalTranslation(double t);
    void setVerticalTranslation(double t1, double t2);
    void setVerticalTranslation(double t1, double t2, double t3);

    void setByMappingToVerticalUp(const H2Geodesic & L);
    void setByMappingToVerticalDown(const H2Geodesic & L);

    void fixedPointsInDiskModel(CP1Point &c1, CP1Point &c2) const;

    static double geodesicNormalizer(const H2Geodesic & L);
};

#endif // H2ISOMETRY_H