GteIntrAlignedBox3OrientedBox3.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/GteAlignedBox.h>
#include <Mathematics/GteOrientedBox.h>
#include <Mathematics/GteFIQuery.h>
#include <Mathematics/GteTIQuery.h>

// The queries consider the box to be a solid.
//
// The test-intersection query uses the method of separating axes.  The set of
// potential separating directions includes the 3 face normals of box0, the 3
// face normals of box1, and 9 directions, each of which is the cross product
// of an edge of box0 and and an edge of box1.
//
// The separating axes involving cross products of edges has numerical
// robustness problems when the two edges are nearly parallel.  The cross
// product of the edges is nearly the zero vector, so normalization of the
// cross product may produce unit-length directions that are not close to the
// true direction.  Such a pair of edges occurs when a box0 face normal N0 and
// a box1 face normal N1 are nearly parallel.  In this case, you may skip the
// edge-edge directions, which is equivalent to projecting the boxes onto the
// plane with normal N0 and applying a 2D separating axis test.  The ability
// to do so involves choosing a small nonnegative epsilon .  It is used to
// determine whether two face normals, one from each box, are nearly parallel:
// |Dot(N0,N1)| >= 1 - epsilon.  If the input is negative, it is clamped to
// zero.
//
// The pair of integers 'separating', say, (i0,i1), identify the axis that
// reported separation; there may be more than one but only one is
// reported.  If the separating axis is a face normal N[i0] of the aligned
// box0 in dimension i0, then (i0,-1) is returned.  If the axis is a face
// normal box1.Axis[i1], then (-1,i1) is returned.  If the axis is a cross
// product of edges, Cross(N[i0],box1.Axis[i1]), then (i0,i1) is returned.

namespace gte
{

template <typename Real>
class TIQuery<Real, AlignedBox3<Real>, OrientedBox3<Real>>
{
public:
    struct Result
    {
        // The 'epsilon' value must be nonnegative.
        Result(Real inEpsilon = (Real)0);

        bool intersect;
        Real epsilon;
        int separating[2];
    };

    Result operator()(AlignedBox3<Real> const& box0,
        OrientedBox3<Real> const& box1);
};


template <typename Real>
TIQuery<Real, AlignedBox3<Real>, OrientedBox3<Real>>::Result::
Result(Real inEpsilon)
{
    if (inEpsilon >= (Real)0)
    {
        epsilon = inEpsilon;
    }
    else
    {
        epsilon = (Real)0;
    }
}

template <typename Real>
typename TIQuery<Real, AlignedBox3<Real>, OrientedBox3<Real>>::Result
TIQuery<Real, AlignedBox3<Real>, OrientedBox3<Real>>::operator()(
    AlignedBox3<Real> const& box0, OrientedBox3<Real> const& box1)
{
    Result result;

    // Get the centered form of the aligned box.  The axes are implicitly
    // A0[0] = (1,0,0), A0[1] = (0,1,0), and A0[2] = (0,0,1).
    Vector3<Real> C0, E0;
    box0.GetCenteredForm(C0, E0);

    // Convenience variables.
    Vector3<Real> const& C1 = box1.center;
    Vector3<Real> const* A1 = &box1.axis[0];
    Vector3<Real> const& E1 = box1.extent;

    Real const cutoff = (Real)1 - result.epsilon;
    bool existsParallelPair = false;

    // Compute the difference of box centers.
    Vector3<Real> D = C1 - C0;

    Real dot01[3][3];       // dot01[i][j] = Dot(A0[i],A1[j]) = A1[j][i]
    Real absDot01[3][3];    // |dot01[i][j]|
    Real r0, r1, r;         // interval radii and distance between centers
    Real r01;               // r0 + r1

    // Test for separation on the axis C0 + t*A0[0].
    for (int i = 0; i < 3; ++i)
    {
        dot01[0][i] = A1[i][0];
        absDot01[0][i] = std::abs(A1[i][0]);
        if (absDot01[0][i] >= cutoff)
        {
            existsParallelPair = true;
        }
    }
    r = std::abs(D[0]);
    r1 = E1[0] * absDot01[0][0] + E1[1] * absDot01[0][1] + E1[2] * absDot01[0][2];
    r01 = E0[0] + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 0;
        result.separating[1] = -1;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[1].
    for (int i = 0; i < 3; ++i)
    {
        dot01[1][i] = A1[i][1];
        absDot01[1][i] = std::abs(A1[i][1]);
        if (absDot01[1][i] >= cutoff)
        {
            existsParallelPair = true;
        }
    }
    r = std::abs(D[1]);
    r1 = E1[0] * absDot01[1][0] + E1[1] * absDot01[1][1] + E1[2] * absDot01[1][2];
    r01 = E0[1] + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 1;
        result.separating[1] = -1;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[2].
    for (int i = 0; i < 3; ++i)
    {
        dot01[2][i] = A1[i][2];
        absDot01[2][i] = std::abs(A1[i][2]);
        if (absDot01[2][i] >= cutoff)
        {
            existsParallelPair = true;
        }
    }
    r = std::abs(D[2]);
    r1 = E1[0] * absDot01[2][0] + E1[1] * absDot01[2][1] + E1[2] * absDot01[2][2];
    r01 = E0[2] + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 2;
        result.separating[1] = -1;
        return result;
    }

    // Test for separation on the axis C0 + t*A1[0].
    r = std::abs(Dot(D, A1[0]));
    r0 = E0[0] * absDot01[0][0] + E0[1] * absDot01[1][0] + E0[2] * absDot01[2][0];
    r01 = r0 + E1[0];
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = -1;
        result.separating[1] = 0;
        return result;
    }

    // Test for separation on the axis C0 + t*A1[1].
    r = std::abs(Dot(D, A1[1]));
    r0 = E0[0] * absDot01[0][1] + E0[1] * absDot01[1][1] + E0[2] * absDot01[2][1];
    r01 = r0 + E1[1];
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = -1;
        result.separating[1] = 1;
        return result;
    }

    // Test for separation on the axis C0 + t*A1[2].
    r = std::abs(Dot(D, A1[2]));
    r0 = E0[0] * absDot01[0][2] + E0[1] * absDot01[1][2] + E0[2] * absDot01[2][2];
    r01 = r0 + E1[2];
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = -1;
        result.separating[1] = 2;
        return result;
    }

    // At least one pair of box axes was parallel, so the separation is
    // effectively in 2D.  The edge-edge axes do not need to be tested.
    if (existsParallelPair)
    {
        result.intersect = true;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[0]xA1[0].
    r = std::abs(D[2] * dot01[1][0] - D[1] * dot01[2][0]);
    r0 = E0[1] * absDot01[2][0] + E0[2] * absDot01[1][0];
    r1 = E1[1] * absDot01[0][2] + E1[2] * absDot01[0][1];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 0;
        result.separating[1] = 0;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[0]xA1[1].
    r = std::abs(D[2] * dot01[1][1] - D[1] * dot01[2][1]);
    r0 = E0[1] * absDot01[2][1] + E0[2] * absDot01[1][1];
    r1 = E1[0] * absDot01[0][2] + E1[2] * absDot01[0][0];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 0;
        result.separating[1] = 1;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[0]xA1[2].
    r = std::abs(D[2] * dot01[1][2] - D[1] * dot01[2][2]);
    r0 = E0[1] * absDot01[2][2] + E0[2] * absDot01[1][2];
    r1 = E1[0] * absDot01[0][1] + E1[1] * absDot01[0][0];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 0;
        result.separating[1] = 2;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[1]xA1[0].
    r = std::abs(D[0] * dot01[2][0] - D[2] * dot01[0][0]);
    r0 = E0[0] * absDot01[2][0] + E0[2] * absDot01[0][0];
    r1 = E1[1] * absDot01[1][2] + E1[2] * absDot01[1][1];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 1;
        result.separating[1] = 0;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[1]xA1[1].
    r = std::abs(D[0] * dot01[2][1] - D[2] * dot01[0][1]);
    r0 = E0[0] * absDot01[2][1] + E0[2] * absDot01[0][1];
    r1 = E1[0] * absDot01[1][2] + E1[2] * absDot01[1][0];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 1;
        result.separating[1] = 1;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[1]xA1[2].
    r = std::abs(D[0] * dot01[2][2] - D[2] * dot01[0][2]);
    r0 = E0[0] * absDot01[2][2] + E0[2] * absDot01[0][2];
    r1 = E1[0] * absDot01[1][1] + E1[1] * absDot01[1][0];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 1;
        result.separating[1] = 2;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[2]xA1[0].
    r = std::abs(D[1] * dot01[0][0] - D[0] * dot01[1][0]);
    r0 = E0[0] * absDot01[1][0] + E0[1] * absDot01[0][0];
    r1 = E1[1] * absDot01[2][2] + E1[2] * absDot01[2][1];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 2;
        result.separating[1] = 0;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[2]xA1[1].
    r = std::abs(D[1] * dot01[0][1] - D[0] * dot01[1][1]);
    r0 = E0[0] * absDot01[1][1] + E0[1] * absDot01[0][1];
    r1 = E1[0] * absDot01[2][2] + E1[2] * absDot01[2][0];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 2;
        result.separating[1] = 1;
        return result;
    }

    // Test for separation on the axis C0 + t*A0[2]xA1[2].
    r = std::abs(D[1] * dot01[0][2] - D[0] * dot01[1][2]);
    r0 = E0[0] * absDot01[1][2] + E0[1] * absDot01[0][2];
    r1 = E1[0] * absDot01[2][1] + E1[1] * absDot01[2][0];
    r01 = r0 + r1;
    if (r > r01)
    {
        result.intersect = false;
        result.separating[0] = 2;
        result.separating[1] = 2;
        return result;
    }

    result.intersect = true;
    return result;
}


}