GteDistPoint3Cylinder3.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/GteVector3.h>
#include <Mathematics/GteDCPQuery.h>
#include <Mathematics/GteCylinder3.h>

// The queries consider the cylinder to be a solid.

namespace gte
{

template <typename Real>
class DCPQuery<Real, Vector3<Real>, Cylinder3<Real>>
{
public:
    struct Result
    {
        Real distance;
        Vector3<Real> cylinderClosest;
    };

    Result operator()(Vector3<Real> const& point,
        Cylinder3<Real> const& cylinder);

private:
    void DoQueryInfiniteCylinder(Vector3<Real> const& P, Real radius,
        Result& result);

    void DoQueryFiniteCylinder(Vector3<Real> const& P, Real radius,
        Real height, Result& result);
};


template <typename Real>
typename DCPQuery<Real, Vector3<Real>, Cylinder3<Real>>::Result
DCPQuery<Real, Vector3<Real>, Cylinder3<Real>>::operator()(
    Vector3<Real> const& point, Cylinder3<Real> const& cylinder)
{
    Result result;

    // Convert the point to the cylinder coordinate system.  In this system,
    // the point believes (0,0,0) is the cylinder axis origin and (0,0,1) is
    // the cylinder axis direction.
    Vector3<Real> basis[3];
    basis[0] = cylinder.axis.direction;
    ComputeOrthogonalComplement(1, basis);

    Vector3<Real> delta = point - cylinder.axis.origin;
    Vector3<Real> P
    {
        Dot(basis[1], delta),
        Dot(basis[2], delta),
        Dot(basis[0], delta)
    };

    if (cylinder.height == std::numeric_limits<Real>::max())
    {
        DoQueryInfiniteCylinder(P, cylinder.radius, result);
    }
    else
    {
        DoQueryFiniteCylinder(P, cylinder.radius, cylinder.height, result);
    }

    // Convert the closest point from the cylinder coordinate system to the
    // original coordinate system.
    result.cylinderClosest = cylinder.axis.origin +
        result.cylinderClosest[0] * basis[1] +
        result.cylinderClosest[1] * basis[2] +
        result.cylinderClosest[2] * basis[0];

    return result;
}

template <typename Real>
void DCPQuery<Real, Vector3<Real>, Cylinder3<Real>>::DoQueryInfiniteCylinder(
    Vector3<Real> const& P, Real radius, Result& result)
{
    Real sqrRadius = radius * radius;
    Real sqrDistance = P[0] * P[0] + P[1] * P[1];
    if (sqrDistance >= sqrRadius)
    {
        // The point is outside the cylinder or on the cylinder wall.
        Real distance = sqrt(sqrDistance);
        result.distance = distance - radius;
        Real temp = radius / distance;
        result.cylinderClosest[0] = P[0] * temp;
        result.cylinderClosest[1] = P[1] * temp;
        result.cylinderClosest[2] = P[2];
    }
    else
    {
        // The point is inside the cylinder.
        result.distance = (Real)0;
        result.cylinderClosest = P;
    }
}

template <typename Real>
void DCPQuery<Real, Vector3<Real>, Cylinder3<Real>>::DoQueryFiniteCylinder(
    Vector3<Real> const& P, Real radius, Real height, Result& result)
{
    DoQueryInfiniteCylinder(P, radius, result);

    // Clamp the infinite cylinder's closest point to the finite cylinder.
    if (result.cylinderClosest[2] > height)
    {
        result.cylinderClosest[2] = height;
        result.distance = Length(result.cylinderClosest - P);
    }
    else if (result.cylinderClosest[2] < -height)
    {
        result.cylinderClosest[2] = -height;
        result.distance = Length(result.cylinderClosest - P);
    }
}


}