GteContOrientedBox2.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/GteApprGaussian2.h>

namespace gte
{

// 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, Vector2<Real> const* points,
     OrientedBox2<Real>& box);

// Test for containment.  Let X = C + y0*U0 + y1*U1 where C is the box center
// and U0 and U1 are the orthonormal axes of the box.  X is in the box when
// |y_i| <= E_i for all i, where E_i are the extents of the box.
template <typename Real>
bool InContainer(Vector2<Real> const& point, OrientedBox2<Real> const& box);

// Construct an oriented box that contains two other oriented boxes.  The
// result is not guaranteed to be the minimum area box containing the input
// boxes.
template <typename Real>
bool MergeContainers(OrientedBox2<Real> const& box0,
    OrientedBox2<Real> const& box1, OrientedBox2<Real>& merge);


template <typename Real>
bool GetContainer(int numPoints, Vector2<Real> const* points,
    OrientedBox2<Real>& box)
{
    // Fit the points with a Gaussian distribution.
    ApprGaussian2<Real> fitter;
    if (fitter.Fit(numPoints, points))
    {
        box = fitter.GetParameters();

        // Let C be the box center and let U0 and U1 be the box axes.  Each
        // input point is of the form X = C + y0*U0 + y1*U1.  The following
        // code computes min(y0), max(y0), min(y1), and max(y1).  The box
        // center is then adjusted to be
        //   C' = C + 0.5*(min(y0)+max(y0))*U0 + 0.5*(min(y1)+max(y1))*U1

        Vector2<Real> diff = points[0] - box.center;
        Vector2<Real> pmin{ Dot(diff, box.axis[0]), Dot(diff, box.axis[1]) };
        Vector2<Real> pmax = pmin;
        for (int i = 1; i < numPoints; ++i)
        {
            diff = points[i] - box.center;
            for (int j = 0; j < 2; ++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 < 2; ++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 InContainer(Vector2<Real> const& point, OrientedBox2<Real> const& box)
{
    Vector2<Real> diff = point - box.center;
    for (int i = 0; i < 2; ++i)
    {
        Real coeff = Dot(diff, box.axis[i]);
        if (std::abs(coeff) > box.extent[i])
        {
            return false;
        }
    }
    return true;
}

template <typename Real>
bool MergeContainers(OrientedBox2<Real> const& box0,
    OrientedBox2<Real> const& box1, OrientedBox2<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);

    // The merged box axes are the averages of the input box axes.  The axes
    // of the second box are negated, if necessary, so they form acute angles
    // with the axes of the first box.
    if (Dot(box0.axis[0], box1.axis[0]) >= (Real)0)
    {
        merge.axis[0] = ((Real)0.5)*(box0.axis[0] + box1.axis[0]);
    }
    else
    {
        merge.axis[0] = ((Real)0.5)*(box0.axis[0] - box1.axis[0]);
    }
    Normalize(merge.axis[0]);
    merge.axis[1] = -Perp(merge.axis[0]);

    // 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
    // endpoints 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}^1 0.5*(min[i]+max[i])*D[i]
    // The box extents are
    //   e[i] = 0.5*(max[i]-min[i])

    std::array<Vector2<Real>, 4> vertex;
    Vector2<Real> pmin{ (Real)0, (Real)0 };
    Vector2<Real> pmax{ (Real)0, (Real)0 };

    box0.GetVertices(vertex);
    for (int i = 0; i < 4; ++i)
    {
        Vector2<Real> diff = vertex[i] - merge.center;
        for (int j = 0; j < 2; ++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 < 4; ++i)
    {
        Vector2<Real> diff = vertex[i] - merge.center;
        for (int j = 0; j < 2; ++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 < 2; ++j)
    {
        merge.center += half*(pmax[j] + pmin[j])*merge.axis[j];
        merge.extent[j] = half*(pmax[j] - pmin[j]);
    }

    return true;
}


}