tetrees/Plugins/Wwise/Source/AkAudio/Classes/GTE/Mathematics/Projection.h

// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2020
// 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/Hyperellipsoid.h>
#include <Mathematics/Line.h>

namespace WwiseGTE
{
    // Project an ellipse onto a line.  The projection interval is
    // [smin,smax] and corresponds to the line segment P+s*D, where
    // smin <= s <= smax.
    template <typename Real>
    void Project(Ellipse2<Real> const& ellipse, Line2<Real> const& line,
        Real& smin, Real& smax)
    {
        // Center of projection interval.
        Real center = Dot(line.direction, ellipse.center - line.origin);

        // Radius of projection interval.
        Real tmp[2] =
        {
            ellipse.extent[0] * Dot(line.direction, ellipse.axis[0]),
            ellipse.extent[1] * Dot(line.direction, ellipse.axis[1])
        };
        Real rSqr = tmp[0] * tmp[0] + tmp[1] * tmp[1];
        Real radius = std::sqrt(rSqr);

        smin = center - radius;
        smax = center + radius;
    }

    // Project an ellipsoid onto a line.  The projection interval is
    // [smin,smax] and corresponds to the line segment P+s*D, where
    // smin <= s <= smax.
    template <typename Real>
    void Project(Ellipsoid3<Real> const& ellipsoid,
        Line3<Real> const& line, Real& smin, Real& smax)
    {
        // Center of projection interval.
        Real center = Dot(line.direction, ellipsoid.center - line.origin);

        // Radius of projection interval.
        Real tmp[3] =
        {
            ellipsoid.extent[0] * Dot(line.direction, ellipsoid.axis[0]),
            ellipsoid.extent[1] * Dot(line.direction, ellipsoid.axis[1]),
            ellipsoid.extent[2] * Dot(line.direction, ellipsoid.axis[2])
        };
        Real rSqr = tmp[0] * tmp[0] + tmp[1] * tmp[1] + tmp[2] * tmp[2];
        Real radius = std::sqrt(rSqr);

        smin = center - radius;
        smax = center + radius;
    }
}