GteSeparatePoints2.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/GteConvexHull2.h>

// Separate two point sets, if possible, by computing a line for which the
// point sets lie on opposite sides.  The algorithm computes the convex hull
// of the point sets, then uses the method of separating axes to determine if
// the two convex polygons are disjoint.  The ComputeType is for the
// ConvexHull2 class.

namespace gte
{

template <typename Real, typename ComputeType>
class SeparatePoints2
{
public:
    // The return value is 'true' if and only if there is a separation.  If
    // 'true', the returned line is a separating line.  The code assumes that
    // each point set has at least 3 noncollinear points.
    bool operator()(int numPoints0, Vector2<Real> const* points0,
        int numPoints1, Vector2<Real> const* points1,
        Line2<Real>& separatingLine) const;

private:
    int OnSameSide(Vector2<Real> const& lineNormal, Real lineConstant,
        int numEdges, int const* edges, Vector2<Real> const* points) const;

    int WhichSide(Vector2<Real> const& lineNormal, Real lineConstant,
        int numEdges, int const* edges, Vector2<Real> const* points) const;
};


template <typename Real, typename ComputeType>
bool SeparatePoints2<Real, ComputeType>::operator()(int numPoints0,
    Vector2<Real> const* points0, int numPoints1,
    Vector2<Real> const* points1, Line2<Real>& separatingLine) const
{
    // Construct convex hull of point set 0.
    ConvexHull2<Real, ComputeType> ch0;
    ch0(numPoints0, points0, (Real)0);
    if (ch0.GetDimension() != 2)
    {
        return false;
    }

    // Construct convex hull of point set 1.
    ConvexHull2<Real, ComputeType> ch1;
    ch1(numPoints1, points1, (Real)0);
    if (ch1.GetDimension() != 2)
    {
        return false;
    }

    int numEdges0 = static_cast<int>(ch0.GetHull().size());
    int const* edges0 = &ch0.GetHull()[0];
    int numEdges1 = static_cast<int>(ch1.GetHull().size());
    int const* edges1 = &ch1.GetHull()[0];

    // Test edges of hull 0 for possible separation of points.
    int j0, j1, i0, i1, side0, side1;
    Vector2<Real> lineNormal;
    Real lineConstant;
    for (j1 = 0, j0 = numEdges0 - 1; j1 < numEdges0; j0 = j1++)
    {
        // Look up edge (assert: i0 != i1 ).
        i0 = edges0[j0];
        i1 = edges0[j1];

        // Compute potential separating line (assert: (xNor,yNor) != (0,0)).
        separatingLine.origin = points0[i0];
        separatingLine.direction = points0[i1] - points0[i0];
        Normalize(separatingLine.direction);
        lineNormal = Perp(separatingLine.direction);
        lineConstant = Dot(lineNormal, separatingLine.origin);

        // Determine whether hull 1 is on same side of line.
        side1 = OnSameSide(lineNormal, lineConstant, numEdges1, edges1,
            points1);

        if (side1)
        {
            // Determine on which side of line hull 0 lies.
            side0 = WhichSide(lineNormal, lineConstant, numEdges0,
                edges0, points0);

            if (side0*side1 <= 0)  // Line separates hulls.
            {
                return true;
            }
        }
    }

    // Test edges of hull 1 for possible separation of points.
    for (j1 = 0, j0 = numEdges1 - 1; j1 < numEdges1; j0 = j1++)
    {
        // Look up edge (assert: i0 != i1 ).
        i0 = edges1[j0];
        i1 = edges1[j1];

        // Compute perpendicular to edge (assert: (xNor,yNor) != (0,0)).
        separatingLine.origin = points1[i0];
        separatingLine.direction = points1[i1] - points1[i0];
        Normalize(separatingLine.direction);
        lineNormal = Perp(separatingLine.direction);
        lineConstant = Dot(lineNormal, separatingLine.origin);

        // Determine whether hull 0 is on same side of line.
        side0 = OnSameSide(lineNormal, lineConstant, numEdges0, edges0,
            points0);

        if (side0)
        {
            // Determine on which side of line hull 1 lies.
            side1 = WhichSide(lineNormal, lineConstant, numEdges1,
                edges1, points1);

            if (side0*side1 <= 0)  // Line separates hulls.
            {
                return true;
            }
        }
    }

    return false;
}

template <typename Real, typename ComputeType>
int SeparatePoints2<Real, ComputeType>::OnSameSide(
    Vector2<Real> const& lineNormal, Real lineConstant, int numEdges,
    int const* edges, Vector2<Real> const* points) const
{
    // Test whether all points on same side of line Dot(N,X) = c.
    Real c0;
    int posSide = 0, negSide = 0;

    for (int i1 = 0, i0 = numEdges - 1; i1 < numEdges; i0 = i1++)
    {
        c0 = Dot(lineNormal, points[edges[i0]]);
        if (c0 > lineConstant)
        {
            ++posSide;
        }
        else if (c0 < lineConstant)
        {
            ++negSide;
        }

        if (posSide && negSide)
        {
            // Line splits point set.
            return 0;
        }

        c0 = Dot(lineNormal, points[edges[i1]]);
        if (c0 > lineConstant)
        {
            ++posSide;
        }
        else if (c0 < lineConstant)
        {
            ++negSide;
        }

        if (posSide && negSide)
        {
            // Line splits point set.
            return 0;
        }
    }

    return (posSide ? +1 : -1);
}

template <typename Real, typename ComputeType>
int SeparatePoints2<Real, ComputeType>::WhichSide(
    Vector2<Real> const& lineNormal, Real lineConstant, int numEdges,
    int const* edges, Vector2<Real> const* points) const
{
    // Establish which side of line hull is on.
    Real c0;
    for (int i1 = 0, i0 = numEdges - 1; i1 < numEdges; i0 = i1++)
    {
        c0 = Dot(lineNormal, points[edges[i0]]);
        if (c0 > lineConstant)
        {
            // Hull on positive side.
            return +1;
        }
        if (c0 < lineConstant)
        {
            // Hull on negative side.
            return -1;
        }

        c0 = Dot(lineNormal, points[edges[i1]]);
        if (c0 > lineConstant)
        {
            // Hull on positive side.
            return +1;
        }
        if (c0 < lineConstant)
        {
            // Hull on negative side.
            return -1;
        }
    }

    // Hull is effectively collinear.
    return 0;
}


}