// 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/FIQuery.h>
#include <Mathematics/TIQuery.h>
#include <Mathematics/AlignedBox.h>
#include <Mathematics/OrientedBox.h>
#include <Mathematics/Vector3.h>
// The queries consider the box to be a solid.
//
// The test-intersection query uses the method of separating axes.
// https://www.geometrictools.com/Documentation/MethodOfSeparatingAxes.pdf
// 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 WwiseGTE
{
template <typename Real>
class TIQuery<Real, AlignedBox3<Real>, OrientedBox3<Real>>
{
public:
struct Result
{
// The 'epsilon' value must be nonnegative.
Result(Real inEpsilon = (Real)0)
:
epsilon(inEpsilon >= (Real)0 ? inEpsilon : (Real)0)
{
}
bool intersect;
Real epsilon;
int separating[2];
};
Result 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;
// dot01[i][j] = Dot(A0[i],A1[j]) = A1[j][i]
Real dot01[3][3];
// |dot01[i][j]|
Real absDot01[3][3];
// interval radii and distance between centers
Real r0, r1, r;
// r0 + r1
Real r01;
// 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::fabs(A1[i][0]);
if (absDot01[0][i] >= cutoff)
{
existsParallelPair = true;
}
}
r = std::fabs(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::fabs(A1[i][1]);
if (absDot01[1][i] >= cutoff)
{
existsParallelPair = true;
}
}
r = std::fabs(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::fabs(A1[i][2]);
if (absDot01[2][i] >= cutoff)
{
existsParallelPair = true;
}
}
r = std::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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::fabs(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;
}
};
}