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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// 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: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5ContBox3.h"
#include "Wm5ApprGaussPointsFit3.h"
#include "Wm5Quaternion.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Box3<Real> ContAlignedBox (int numPoints, const Vector3<Real>* points)
{
Vector3<Real> pmin, pmax;
Vector3<Real>::ComputeExtremes(numPoints, points, pmin, pmax);
Box3<Real> box;
box.Center = ((Real)0.5)*(pmin + pmax);
box.Axis[0] = Vector3<Real>::UNIT_X;
box.Axis[1] = Vector3<Real>::UNIT_Y;
box.Axis[2] = Vector3<Real>::UNIT_Z;
Vector3<Real> halfDiagonal = ((Real)0.5)*(pmax - pmin);
for (int i = 0; i < 3; ++i)
{
box.Extent[i] = halfDiagonal[i];
}
return box;
}
//----------------------------------------------------------------------------
template <typename Real>
Box3<Real> ContOrientedBox (int numPoints, const Vector3<Real>* points)
{
Box3<Real> box = GaussPointsFit3<Real>(numPoints, points);
// 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(diff.Dot(box.Axis[0]), diff.Dot(box.Axis[1]),
diff.Dot(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 = diff.Dot(box.Axis[j]);
if (dot < pmin[j])
{
pmin[j] = dot;
}
else if (dot > pmax[j])
{
pmax[j] = dot;
}
}
}
box.Center +=
(((Real)0.5)*(pmin[0] + pmax[0]))*box.Axis[0] +
(((Real)0.5)*(pmin[1] + pmax[1]))*box.Axis[1] +
(((Real)0.5)*(pmin[2] + pmax[2]))*box.Axis[2];
box.Extent[0] = ((Real)0.5)*(pmax[0] - pmin[0]);
box.Extent[1] = ((Real)0.5)*(pmax[1] - pmin[1]);
box.Extent[2] = ((Real)0.5)*(pmax[2] - pmin[2]);
return box;
}
//----------------------------------------------------------------------------
template <typename Real>
bool InBox (const Vector3<Real>& point, const Box3<Real>& box)
{
Vector3<Real> diff = point - box.Center;
for (int i = 0; i < 3; ++i)
{
Real coeff = diff.Dot(box.Axis[i]);
if (Math<Real>::FAbs(coeff) > box.Extent[i])
{
return false;
}
}
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
Box3<Real> MergeBoxes (const Box3<Real>& box0, const Box3<Real>& box1)
{
// Construct a box that contains the input boxes.
Box3<Real> box;
// 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.
box.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.
Quaternion<Real> q0, q1;
q0.FromRotationMatrix(box0.Axis);
q1.FromRotationMatrix(box1.Axis);
if (q0.Dot(q1) < (Real)0)
{
q1 = -q1;
}
Quaternion<Real> q = q0 + q1;
Real invLength = Math<Real>::InvSqrt(q.Dot(q));
q = invLength*q;
q.ToRotationMatrix(box.Axis);
// 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])
int i, j;
Real dot;
Vector3<Real> vertex[8], diff;
Vector3<Real> pmin = Vector3<Real>::ZERO;
Vector3<Real> pmax = Vector3<Real>::ZERO;
box0.ComputeVertices(vertex);
for (i = 0; i < 8; ++i)
{
diff = vertex[i] - box.Center;
for (j = 0; j < 3; ++j)
{
dot = diff.Dot(box.Axis[j]);
if (dot > pmax[j])
{
pmax[j] = dot;
}
else if (dot < pmin[j])
{
pmin[j] = dot;
}
}
}
box1.ComputeVertices(vertex);
for (i = 0; i < 8; ++i)
{
diff = vertex[i] - box.Center;
for (j = 0; j < 3; ++j)
{
dot = diff.Dot(box.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.
for (j = 0; j < 3; ++j)
{
box.Center += (((Real)0.5)*(pmax[j] + pmin[j]))*box.Axis[j];
box.Extent[j] = ((Real)0.5)*(pmax[j] - pmin[j]);
}
return box;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
Box3<float> ContAlignedBox<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
Box3<float> ContOrientedBox<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
bool InBox<float> (const Vector3<float>&, const Box3<float>&);
template WM5_MATHEMATICS_ITEM
Box3<float> MergeBoxes<float> (const Box3<float>&, const Box3<float>&);
template WM5_MATHEMATICS_ITEM
Box3<double> ContAlignedBox<double> (int, const Vector3<double>*);
template WM5_MATHEMATICS_ITEM
Box3<double> ContOrientedBox<double> (int, const Vector3<double>*);
template WM5_MATHEMATICS_ITEM
bool InBox<double> (const Vector3<double>&, const Box3<double>&);
template WM5_MATHEMATICS_ITEM
Box3<double> MergeBoxes<double> (const Box3<double>&, const Box3<double>&);
//----------------------------------------------------------------------------
}
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