Ellipse.h

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/*
 * LSST Data Management System
 * Copyright 2014-2015 AURA/LSST.
 *
 * This product includes software developed by the
 * LSST Project (http://www.lsst.org/).
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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
 * GNU General Public License for more details.
 *
 * You should have received a copy of the LSST License Statement and
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 * see <https://www.lsstcorp.org/LegalNotices/>.
 */

#ifndef LSST_SPHGEOM_ELLIPSE_H_
#define LSST_SPHGEOM_ELLIPSE_H_


#include <iosfwd>

#include "Circle.h"
#include "Matrix3d.h"
#include "Region.h"
#include "UnitVector3d.h"


namespace lsst {
namespace sphgeom {

class Ellipse : public Region {
public:
    static constexpr uint8_t TYPE_CODE = 'e';

    static Ellipse empty() { return Ellipse(); }

    static Ellipse full() { return Ellipse().complement(); }

    Ellipse() :
        _S(1.0),
        _a(-2.0),
        _b(-2.0),
        _gamma(0.0),
        _tana(std::numeric_limits<double>::infinity()),
        _tanb(std::numeric_limits<double>::infinity())
    {}

    explicit Ellipse(Circle const & c) {
        *this = Ellipse(c.getCenter(), c.getCenter(), c.getOpeningAngle());
    }

    explicit Ellipse(UnitVector3d const & v, Angle alpha = Angle(0.0)) {
        *this = Ellipse(v, v, alpha);
    }

    Ellipse(UnitVector3d const & f1, UnitVector3d const & f2, Angle alpha);

    Ellipse(UnitVector3d const & center,
            Angle alpha,
            Angle beta,
            Angle orientation);

    bool operator==(Ellipse const & e) const {
        return _S == e._S && _a == e._a && _b == e._b;
    }

    bool operator!=(Ellipse const & e) const { return !(*this == e); }

    bool isEmpty() const { return Angle(0.5 * PI) + _a < _gamma; }

    bool isFull() const { return Angle(0.5 * PI) - _a <= _gamma; }

    bool isGreatCircle() const { return _a.asRadians() == 0.0; }

    bool isCircle() const { return _a == _b; }

    Matrix3d const & getTransformMatrix() const { return _S; }

    UnitVector3d getCenter() const {
        return UnitVector3d::fromNormalized(_S(2,0), _S(2,1), _S(2,2));
    }

    UnitVector3d getF1() const {
        UnitVector3d n = UnitVector3d::fromNormalized(_S(1,0), _S(1,1), _S(1,2));
        return getCenter().rotatedAround(n, -_gamma);
    }

    UnitVector3d getF2() const {
        UnitVector3d n = UnitVector3d::fromNormalized(_S(1,0), _S(1,1), _S(1,2));
        return getCenter().rotatedAround(n, _gamma);
    }

    Angle getAlpha() const { return Angle(0.5 * PI) + _a; }

    Angle getBeta() const { return Angle(0.5 * PI) + _b; }

    Angle getGamma() const { return _gamma; }

    Ellipse & complement() {
        _S = Matrix3d(-_S(0,0), -_S(0,1), -_S(0,2),
                       _S(1,0),  _S(1,1),  _S(1,2),
                      -_S(2,0), -_S(2,1), -_S(2,2));
        _a = -_a;
        _b = -_b;
        return *this;
    }

    Ellipse complemented() const { return Ellipse(*this).complement(); }

    // Region interface
    std::unique_ptr<Region> clone() const override {
        return std::unique_ptr<Ellipse>(new Ellipse(*this));
    }

    Box getBoundingBox() const override;
    Box3d getBoundingBox3d() const override;
    Circle getBoundingCircle() const override;

    bool contains(UnitVector3d const &v) const override;

    Relationship relate(Region const & r) const override {
        // Dispatch on the type of r.
        return invert(r.relate(*this));
    }

    Relationship relate(Box const &) const override;
    Relationship relate(Circle const &) const override;
    Relationship relate(ConvexPolygon const &) const override;
    Relationship relate(Ellipse const &) const override;

    std::vector<uint8_t> encode() const override;

    static std::unique_ptr<Ellipse> decode(std::vector<uint8_t> const & s) {
        return decode(s.data(), s.size());
    }
    static std::unique_ptr<Ellipse> decode(uint8_t const * buffer, size_t n);

private:
    static constexpr size_t ENCODED_SIZE = 113;

    Matrix3d _S;
    Angle _a; // α - π/2
    Angle _b; // β - π/2
    Angle _gamma; // Half the angle between the ellipse foci
    double _tana; // |tan a| = |cot α|
    double _tanb; // |tan b| = |cot β|
};

std::ostream & operator<<(std::ostream &, Ellipse const &);

}} // namespace lsst::sphgeom

#endif // LSST_SPHGEOM_ELLIPSE_H_