nh-rep/code/pre_processing/ParametricSample/Mathematics/Arc2.h

// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2021
// Distributed under the Boost Software License, Version 1.0.
// https://www.boost.org/LICENSE_1_0.txt
// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// Version: 4.0.2019.08.13

#pragma once

#include <Mathematics/Vector2.h>

// The circle containing the arc is represented as |X-C| = R where C is the
// center and R is the radius.  The arc is defined by two points end0 and
// end1 on the circle so that end1 is obtained from end0 by traversing
// counterclockwise.  The application is responsible for ensuring that end0
// and end1 are on the circle and that they are properly ordered.

namespace gte
{
    template <typename Real>
    class Arc2
    {
    public:
        // Construction and destruction.  The default constructor sets the
        // center to (0,0), radius to 1, end0 to (1,0), and end1 to (0,1).
        Arc2()
            :
            center(Vector2<Real>::Zero()),
            radius((Real)1)
        {
            end[0] = Vector2<Real>::Unit(0);
            end[1] = Vector2<Real>::Unit(1);
        }

        Arc2(Vector2<Real> const& inCenter, Real inRadius,
            Vector2<Real>const& inEnd0, Vector2<Real>const& inEnd1)
            :
            center(inCenter),
            radius(inRadius)
        {
            end[0] = inEnd0;
            end[1] = inEnd1;
        }

        // Test whether P is on the arc.  The application must ensure that P
        // is on the circle; that is, |P-C| = R.  This test works for any
        // angle between B-C and A-C, not just those between 0 and pi
        // radians.
        bool Contains(Vector2<Real> const& p) const
        {
            // Assert: |P-C| = R where P is the input point, C is the circle
            // center and R is the circle radius.  For P to be on the arc from
            // A to B, it must be on the side of the plane containing A with
            // normal N = Perp(B-A) where Perp(u,v) = (v,-u).

            Vector2<Real> diffPE0 = p - end[0];
            Vector2<Real> diffE1E0 = end[1] - end[0];
            Real dotPerp = DotPerp(diffPE0, diffE1E0);
            return dotPerp >= (Real)0;
        }

        Vector2<Real> center;
        Real radius;
        std::array<Vector2<Real>, 2> end;

    public:
        // Comparisons to support sorted containers.
        bool operator==(Arc2 const& arc) const
        {
            return center == arc.center && radius == arc.radius
                && end[0] == arc.end[0] && end[1] == arc.end[1];
        }

        bool operator!=(Arc2 const& arc) const
        {
            return !operator==(arc);
        }

        bool operator< (Arc2 const& arc) const
        {
            if (center < arc.center)
            {
                return true;
            }

            if (center > arc.center)
            {
                return false;
            }

            if (radius < arc.radius)
            {
                return true;
            }

            if (radius > arc.radius)
            {
                return false;
            }

            if (end[0] < arc.end[0])
            {
                return true;
            }

            if (end[0] > arc.end[0])
            {
                return false;
            }

            return end[1] < arc.end[1];
        }

        bool operator<=(Arc2 const& arc) const
        {
            return !arc.operator<(*this);
        }

        bool operator> (Arc2 const& arc) const
        {
            return arc.operator<(*this);
        }

        bool operator>=(Arc2 const& arc) const
        {
            return !operator<(arc);
        }
    };
}