// 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/ApprGaussian3.h>
#include <Mathematics/Matrix3x3.h>
#include <Mathematics/Rotation.h>
namespace WwiseGTE
{
// Compute an oriented bounding box of the points. The box center is the
// average of the points. The box axes are the eigenvectors of the
// covariance matrix.
template <typename Real>
bool GetContainer(int numPoints, Vector3<Real> const* points, OrientedBox3<Real>& box)
{
// Fit the points with a Gaussian distribution.
ApprGaussian3<Real> fitter;
if (fitter.Fit(numPoints, points))
{
box = fitter.GetParameters();
// Let C be the box center and let U0, U1, and U2 be the box axes.
// Each input point is of the form X = C + y0*U0 + y1*U1 + y2*U2.
// The following code computes min(y0), max(y0), min(y1), max(y1),
// min(y2), and max(y2). The box center is then adjusted to be
// C' = C + 0.5*(min(y0)+max(y0))*U0 + 0.5*(min(y1)+max(y1))*U1
// + 0.5*(min(y2)+max(y2))*U2
Vector3<Real> diff = points[0] - box.center;
Vector3<Real> pmin{ Dot(diff, box.axis[0]), Dot(diff, box.axis[1]),
Dot(diff, box.axis[2]) };
Vector3<Real> pmax = pmin;
for (int i = 1; i < numPoints; ++i)
{
diff = points[i] - box.center;
for (int j = 0; j < 3; ++j)
{
Real dot = Dot(diff, box.axis[j]);
if (dot < pmin[j])
{
pmin[j] = dot;
}
else if (dot > pmax[j])
{
pmax[j] = dot;
}
}
}
for (int j = 0; j < 3; ++j)
{
box.center += ((Real)0.5 * (pmin[j] + pmax[j])) * box.axis[j];
box.extent[j] = (Real)0.5 * (pmax[j] - pmin[j]);
}
return true;
}
return false;
}
template <typename Real>
bool GetContainer(std::vector<Vector3<Real>> const& points, OrientedBox3<Real>& box)
{
return GetContainer(static_cast<int>(points.size()), points.data(), box);
}
// Test for containment. Let X = C + y0*U0 + y1*U1 + y2*U2 where C is the
// box center and U0, U1, U2 are the orthonormal axes of the box. X is in
// the box if |y_i| <= E_i for all i where E_i are the extents of the box.
template <typename Real>
bool InContainer(Vector3<Real> const& point, OrientedBox3<Real> const& box)
{
Vector3<Real> diff = point - box.center;
for (int i = 0; i < 3; ++i)
{
Real coeff = Dot(diff, box.axis[i]);
if (std::fabs(coeff) > box.extent[i])
{
return false;
}
}
return true;
}
// Construct an oriented box that contains two other oriented boxes. The
// result is not guaranteed to be the minimum volume box containing the
// input boxes.
template <typename Real>
bool MergeContainers(OrientedBox3<Real> const& box0,
OrientedBox3<Real> const& box1, OrientedBox3<Real>& merge)
{
// The first guess at the box center. This value will be updated
// later after the input box vertices are projected onto axes
// determined by an average of box axes.
merge.center = (Real)0.5 * (box0.center + box1.center);
// A box's axes, when viewed as the columns of a matrix, form a
// rotation matrix. The input box axes are converted to quaternions.
// The average quaternion is computed, then normalized to unit length.
// The result is the slerp of the two input quaternions with t-value
// of 1/2. The result is converted back to a rotation matrix and its
// columns are selected as the merged box axes.
//
// TODO: When the GTL Lie Algebra code is posted, use the geodesic
// path between the affine matrices formed by the box centers and
// orientations. Choose t = 1/2 along that geodesic.
Matrix3x3<Real> rot0, rot1;
rot0.SetCol(0, box0.axis[0]);
rot0.SetCol(1, box0.axis[1]);
rot0.SetCol(2, box0.axis[2]);
rot1.SetCol(0, box1.axis[0]);
rot1.SetCol(1, box1.axis[1]);
rot1.SetCol(2, box1.axis[2]);
Quaternion<Real> q0 = Rotation<3, Real>(rot0);
Quaternion<Real> q1 = Rotation<3, Real>(rot1);
if (Dot(q0, q1) < (Real)0)
{
q1 = -q1;
}
Quaternion<Real> q = q0 + q1;
Normalize(q);
Matrix3x3<Real> rot = Rotation<3, Real>(q);
for (int j = 0; j < 3; ++j)
{
merge.axis[j] = rot.GetCol(j);
}
// Project the input box vertices onto the merged-box axes. Each axis
// D[i] containing the current center C has a minimum projected value
// min[i] and a maximum projected value max[i]. The corresponding end
// points on the axes are C+min[i]*D[i] and C+max[i]*D[i]. The point
// C is not necessarily the midpoint for any of the intervals. The
// actual box center will be adjusted from C to a point C' that is the
// midpoint of each interval,
// C' = C + sum_{i=0}^2 0.5*(min[i]+max[i])*D[i]
// The box extents are
// e[i] = 0.5*(max[i]-min[i])
std::array<Vector3<Real>, 8> vertex;
Vector3<Real> pmin{ (Real)0, (Real)0, (Real)0 };
Vector3<Real> pmax{ (Real)0, (Real)0, (Real)0 };
box0.GetVertices(vertex);
for (int i = 0; i < 8; ++i)
{
Vector3<Real> diff = vertex[i] - merge.center;
for (int j = 0; j < 3; ++j)
{
Real dot = Dot(diff, merge.axis[j]);
if (dot > pmax[j])
{
pmax[j] = dot;
}
else if (dot < pmin[j])
{
pmin[j] = dot;
}
}
}
box1.GetVertices(vertex);
for (int i = 0; i < 8; ++i)
{
Vector3<Real> diff = vertex[i] - merge.center;
for (int j = 0; j < 3; ++j)
{
Real dot = Dot(diff, merge.axis[j]);
if (dot > pmax[j])
{
pmax[j] = dot;
}
else if (dot < pmin[j])
{
pmin[j] = dot;
}
}
}
// [min,max] is the axis-aligned box in the coordinate system of the
// merged box axes. Update the current box center to be the center of
// the new box. Compute the extents based on the new center.
Real const half = (Real)0.5;
for (int j = 0; j < 3; ++j)
{
merge.center += half * (pmax[j] + pmin[j]) * merge.axis[j];
merge.extent[j] = half * (pmax[j] - pmin[j]);
}
return true;
}
}