GteRectangle.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

#include <Mathematics/GteVector.h>

// Points are R(s0,s1) = C + s0*A0 + s1*A1, where C is the center of the
// rectangle and A0 and A1 are unit-length and perpendicular axes.  The
// parameters s0 and s1 are constrained by |s0| <= e0 and |s1| <= e1,
// where e0 > 0 and e1 > 0 are the extents of the rectangle.

namespace gte
{

template <int N, typename Real>
class Rectangle
{
public:
    // Construction and destruction.  The default constructor sets the origin
    // to (0,...,0), axis A0 to (1,0,...,0), axis A1 to (0,1,0,...0), and both
    // extents to 1.
    Rectangle();
    Rectangle(Vector<N, Real> const& inCenter,
        std::array<Vector<N, Real>, 2> const& inAxis,
        Vector<2, Real> const& inExtent);

    // Compute the vertices of the rectangle.  If index i has the bit pattern
    // i = b[1]b[0], then
    //   vertex[i] = center + sum_{d=0}^{1} sign[d] * extent[d] * axis[d]
    // where sign[d] = 2*b[d] - 1.
    void GetVertices(std::array<Vector<N, Real>, 4>& vertex) const;

    Vector<N, Real> center;
    std::array<Vector<N, Real>, 2> axis;
    Vector<2, Real> extent;

public:
    // Comparisons to support sorted containers.
    bool operator==(Rectangle const& rectangle) const;
    bool operator!=(Rectangle const& rectangle) const;
    bool operator< (Rectangle const& rectangle) const;
    bool operator<=(Rectangle const& rectangle) const;
    bool operator> (Rectangle const& rectangle) const;
    bool operator>=(Rectangle const& rectangle) const;
};

// Template alias for convenience.
template <typename Real>
using Rectangle3 = Rectangle<3, Real>;


template <int N, typename Real>
Rectangle<N, Real>::Rectangle()
{
    center.MakeZero();
    for (int i = 0; i < 2; ++i)
    {
        axis[i].MakeUnit(i);
        extent[i] = (Real)1;
    }
}

template <int N, typename Real>
Rectangle<N, Real>::Rectangle(Vector<N, Real> const& inCenter,
    std::array<Vector<N, Real>, 2> const& inAxis,
    Vector<2, Real> const& inExtent)
    :
    center(inCenter),
    axis(inAxis),
    extent(inExtent)
{
}

template <int N, typename Real>
void Rectangle<N, Real>::GetVertices(
    std::array<Vector<N, Real>, 4>& vertex) const
{
    Vector<N, Real> product0 = extent[0] * axis[0];
    Vector<N, Real> product1 = extent[1] * axis[1];
    Vector<N, Real> sum = product0 + product1;
    Vector<N, Real> dif = product0 - product1;

    vertex[0] = center - sum;
    vertex[1] = center + dif;
    vertex[2] = center - dif;
    vertex[3] = center + sum;
}

template <int N, typename Real>
bool Rectangle<N, Real>::operator==(Rectangle const& rectangle) const
{
    if (center != rectangle.center)
    {
        return false;
    }

    for (int i = 0; i < 2; ++i)
    {
        if (axis[i] != rectangle.axis[i])
        {
            return false;
        }
    }

    for (int i = 0; i < 2; ++i)
    {
        if (extent[i] != rectangle.extent[i])
        {
            return false;
        }
    }

    return true;
}

template <int N, typename Real>
bool Rectangle<N, Real>::operator!=(Rectangle const& rectangle) const
{
    return !operator==(rectangle);
}

template <int N, typename Real>
bool Rectangle<N, Real>::operator<(Rectangle const& rectangle) const
{
    if (center < rectangle.center)
    {
        return true;
    }

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

    if (axis < rectangle.axis)
    {
        return true;
    }

    if (axis > rectangle.axis)
    {
        return false;
    }

    return extent < rectangle.extent;
}

template <int N, typename Real>
bool Rectangle<N, Real>::operator<=(Rectangle const& rectangle) const
{
    return operator<(rectangle) || operator==(rectangle);
}

template <int N, typename Real>
bool Rectangle<N, Real>::operator>(Rectangle const& rectangle) const
{
    return !operator<=(rectangle);
}

template <int N, typename Real>
bool Rectangle<N, Real>::operator>=(Rectangle const& rectangle) const
{
    return !operator<(rectangle);
}


}