GteIntrSegment3Sphere3.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/GteSegment.h>
#include <Mathematics/GteIntrIntervals.h>
#include <Mathematics/GteIntrLine3Sphere3.h>

namespace gte
{

template <typename Real>
class TIQuery<Real, Segment3<Real>, Sphere3<Real>>
{
public:
    struct Result
    {
        bool intersect;
    };

    Result operator()(Segment3<Real> const& segment,
        Sphere3<Real> const& sphere);
};

template <typename Real>
class FIQuery<Real, Segment3<Real>, Sphere3<Real>>
    :
    public FIQuery<Real, Line3<Real>, Sphere3<Real>>
{
public:
    struct Result
        :
        public FIQuery<Real, Line3<Real>, Sphere3<Real>>::Result
    {
        // No additional information to compute.
    };

    Result operator()(Segment3<Real> const& segment,
        Sphere3<Real> const& sphere);

protected:
    void DoQuery(Vector3<Real> const& segOrigin,
        Vector3<Real> const& segDirection, Real segExtent,
        Sphere3<Real> const& sphere, Result& result);
};


template <typename Real>
typename TIQuery<Real, Segment3<Real>, Sphere3<Real>>::Result
TIQuery<Real, Segment3<Real>, Sphere3<Real>>::operator()(
    Segment3<Real> const& segment, Sphere3<Real> const& sphere)
{
    // The sphere is (X-C)^T*(X-C)-1 = 0 and the line is X = P+t*D.
    // Substitute the line equation into the sphere equation to obtain a
    // quadratic equation Q(t) = t^2 + 2*a1*t + a0 = 0, where a1 = D^T*(P-C),
    // and a0 = (P-C)^T*(P-C)-1.
    Result result;

    Vector3<Real> segOrigin, segDirection;
    Real segExtent;
    segment.GetCenteredForm(segOrigin, segDirection, segExtent);

    Vector3<Real> diff = segOrigin - sphere.center;
    Real a0 = Dot(diff, diff) - sphere.radius * sphere.radius;
    Real a1 = Dot(segDirection, diff);
    Real discr = a1*a1 - a0;
    if (discr < (Real)0)
    {
        result.intersect = false;
        return result;
    }

    Real tmp0 = segExtent*segExtent + a0;
    Real tmp1 = ((Real)2)*a1*segExtent;
    Real qm = tmp0 - tmp1;
    Real qp = tmp0 + tmp1;
    if (qm*qp <= (Real)0)
    {
        result.intersect = true;
        return result;
    }

    result.intersect = (qm > (Real)0 && std::abs(a1) < segExtent);
    return result;
}

template <typename Real>
typename FIQuery<Real, Segment3<Real>, Sphere3<Real>>::Result
FIQuery<Real, Segment3<Real>, Sphere3<Real>>::operator()(
    Segment3<Real> const& segment, Sphere3<Real> const& sphere)
{
    Vector3<Real> segOrigin, segDirection;
    Real segExtent;
    segment.GetCenteredForm(segOrigin, segDirection, segExtent);

    Result result;
    DoQuery(segOrigin, segDirection, segExtent, sphere, result);
    for (int i = 0; i < result.numIntersections; ++i)
    {
        result.point[i] = segOrigin + result.parameter[i] * segDirection;
    }
    return result;
}

template <typename Real>
void FIQuery<Real, Segment3<Real>, Sphere3<Real>>::DoQuery(
    Vector3<Real> const& segOrigin, Vector3<Real> const& segDirection,
    Real segExtent, Sphere3<Real> const& sphere, Result& result)
{
    FIQuery<Real, Line3<Real>, Sphere3<Real>>::DoQuery(segOrigin,
        segDirection, sphere, result);

    if (result.intersect)
    {
        // The line containing the segment intersects the sphere; the
        // t-interval is [t0,t1].  The segment intersects the sphere as
        // long as [t0,t1] overlaps the segment t-interval
        // [-segExtent,+segExtent].
        std::array<Real, 2> segInterval = { -segExtent, segExtent };
        FIQuery<Real, std::array<Real, 2>, std::array<Real, 2>> iiQuery;
        auto iiResult = iiQuery(result.parameter, segInterval);
        if (iiResult.intersect)
        {
            result.numIntersections = iiResult.numIntersections;
            result.parameter = iiResult.overlap;
        }
        else
        {
            result.intersect = false;
            result.numIntersections = 0;
        }
    }
}


}