GteFrustum3.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>

// Orthogonal frustum.  Let E be the origin, D be the direction vector, U be
// the up vector, and R be the right vector.  Let u > 0 and r > 0 be the
// extents in the U and R directions, respectively.  Let n and f be the
// extents in the D direction with 0 < n < f.  The four corners of the frustum
// in the near plane are E + n*D + s0*u*U + s1*r*R where |s0| = |s1| = 1 (four
// choices).  The four corners of the frustum in the far plane are
// E + f*D + (f/n)*(s0*u*U + s1*r*R) where |s0| = |s1| = 1 (four choices).

namespace gte
{

template <typename Real>
class Frustum3
{
public:
    // Construction and destruction.  The default constructor sets the
    // following values:  origin (E) to (0,0,0), dVector (D) to (0,0,1),
    // uVector (U) to (0,1,0), rVector (R) to (1,0,0), dMin (n) to 1,
    // dMax (f) to 2, uBound (u) to 1, and rBound (r) to 1.
    Frustum3();
    Frustum3(Vector3<Real> const& inOrigin, Vector3<Real> const& inDVector,
        Vector3<Real> const& inUVector, Vector3<Real> const& inRVector,
        Real inDMin, Real inDMax, Real inUBound, Real inRBound);

    // The Update() function must be called whenever changes are made to DMIN,
    // DMax, UBound, or RBound.  The values mDRatio, mMTwoUF, and mMTwoRF are
    // dependent on the changes, so call the Get*() accessors only after the
    // Update() call.
    void Update();
    inline Real GetDRatio() const;
    inline Real GetMTwoUF() const;
    inline Real GetMTwoRF() const;

    void ComputeVertices(Vector3<Real> vertex[8]) const;

    Vector3<Real> origin, dVector, uVector, rVector;
    Real dMin, dMax, uBound, rBound;

public:
    // Comparisons to support sorted containers.
    bool operator==(Frustum3 const& frustum) const;
    bool operator!=(Frustum3 const& frustum) const;
    bool operator< (Frustum3 const& frustum) const;
    bool operator<=(Frustum3 const& frustum) const;
    bool operator> (Frustum3 const& frustum) const;
    bool operator>=(Frustum3 const& frustum) const;

protected:
    // Quantities derived from the constructor inputs.
    Real mDRatio, mMTwoUF, mMTwoRF;
};


template <typename Real>
Frustum3<Real>::Frustum3()
    :
    origin(Vector3<Real>::Zero()),
    dVector(Vector3<Real>::Unit(2)),
    uVector(Vector3<Real>::Unit(1)),
    rVector(Vector3<Real>::Unit(0)),
    dMin((Real)1),
    dMax((Real)2),
    uBound((Real)1),
    rBound((Real)1)
{
    Update();
}

template <typename Real>
Frustum3<Real>::Frustum3(Vector3<Real> const& inOrigin,
    Vector3<Real> const& inDVector, Vector3<Real> const& inUVector,
    Vector3<Real> const& inRVector, Real inDMin, Real inDMax, Real inUBound,
    Real inRBound)
    :
    origin(inOrigin),
    dVector(inDVector),
    uVector(inUVector),
    rVector(inRVector),
    dMin(inDMin),
    dMax(inDMax),
    uBound(inUBound),
    rBound(inRBound)
{
    Update();
}

template <typename Real>
void Frustum3<Real>::Update()
{
    mDRatio = dMax / dMin;
    mMTwoUF = ((Real)-2) * uBound * dMax;
    mMTwoRF = ((Real)-2) * rBound * dMax;
}

template <typename Real> inline
Real Frustum3<Real>::GetDRatio() const
{
    return mDRatio;
}

template <typename Real> inline
Real Frustum3<Real>::GetMTwoUF() const
{
    return mMTwoUF;
}

template <typename Real> inline
Real Frustum3<Real>::GetMTwoRF() const
{
    return mMTwoRF;
}

template <typename Real>
void Frustum3<Real>::ComputeVertices(Vector3<Real> vertex[8]) const
{
    Vector3<Real> dScaled = dMin * dVector;
    Vector3<Real> uScaled = uBound * uVector;
    Vector3<Real> rScaled = rBound * rVector;

    vertex[0] = dScaled - uScaled - rScaled;
    vertex[1] = dScaled - uScaled + rScaled;
    vertex[2] = dScaled + uScaled + rScaled;
    vertex[3] = dScaled + uScaled - rScaled;

    for (int i = 0, ip = 4; i < 4; ++i, ++ip)
    {
        vertex[ip] = origin + mDRatio * vertex[i];
        vertex[i] += origin;
    }
}

template <typename Real>
bool Frustum3<Real>::operator==(Frustum3 const& frustum) const
{
    return origin == frustum.origin
        && dVector == frustum.dVector
        && uVector == frustum.uVector
        && rVector == frustum.rVector
        && dMin == frustum.dMin
        && dMax == frustum.dMax
        && uBound == frustum.uBound
        && rBound == frustum.rBound;
}

template <typename Real>
bool Frustum3<Real>::operator!=(Frustum3 const& frustum) const
{
    return !operator==(frustum);
}

template <typename Real>
bool Frustum3<Real>::operator<(Frustum3 const& frustum) const
{
    if (origin < frustum.origin)
    {
        return true;
    }

    if (origin > frustum.origin)
    {
        return false;
    }

    if (dVector < frustum.dVector)
    {
        return true;
    }

    if (dVector > frustum.dVector)
    {
        return false;
    }

    if (uVector < frustum.uVector)
    {
        return true;
    }

    if (uVector > frustum.uVector)
    {
        return false;
    }

    if (rVector < frustum.rVector)
    {
        return true;
    }

    if (rVector > frustum.rVector)
    {
        return false;
    }

    if (dMin < frustum.dMin)
    {
        return true;
    }

    if (dMin > frustum.dMin)
    {
        return false;
    }

    if (dMax < frustum.dMax)
    {
        return true;
    }

    if (dMax > frustum.dMax)
    {
        return false;
    }

    if (uBound < frustum.uBound)
    {
        return true;
    }

    if (uBound > frustum.uBound)
    {
        return false;
    }

    return rBound < frustum.rBound;
}

template <typename Real>
bool Frustum3<Real>::operator<=(Frustum3 const& frustum) const
{
    return operator<(frustum) || operator==(frustum);
}

template <typename Real>
bool Frustum3<Real>::operator>(Frustum3 const& frustum) const
{
    return !operator<=(frustum);
}

template <typename Real>
bool Frustum3<Real>::operator>=(Frustum3 const& frustum) const
{
    return !operator<(frustum);
}


}