delaunay.cpp.svn-base

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/********************************************************************************
Copyright (C) 2004-2005 Sjaak Priester	

This is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

This file is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with Tinter; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
********************************************************************************/

// Delaunay
// Class to perform Delaunay triangulation on a set of vertices
//
// Version 1.1 (C) 2005, Sjaak Priester, Amsterdam.
// - Removed bug which gave incorrect results for co-circular vertices.
//
// Version 1.0 (C) 2004, Sjaak Priester, Amsterdam.
// mailto:[e-mail]

#include <list>
#include "delaunay.h"

const REAL sqrt3 = 1.732050808F;

void triangle::SetCircumCircle()
{
    REAL x0 = m_Vertices[0]->GetX();
    REAL y0 = m_Vertices[0]->GetY();

    REAL x1 = m_Vertices[1]->GetX();
    REAL y1 = m_Vertices[1]->GetY();

    REAL x2 = m_Vertices[2]->GetX();
    REAL y2 = m_Vertices[2]->GetY();

    REAL y10 = y1 - y0;
    REAL y21 = y2 - y1;

    bool b21zero = y21 > -REAL_EPSILON && y21 < REAL_EPSILON;

    if (y10 > -REAL_EPSILON && y10 < REAL_EPSILON)
    {
        if (b21zero)	// All three vertices are on one horizontal line.
        {
            if (x1 > x0)
            {
                if (x2 > x1) x1 = x2;
            }
            else
            {
                if (x2 < x0) x0 = x2;
            }
            m_Center.X = (x0 + x1) * .5F;
            m_Center.Y = y0;
        }
        else	// m_Vertices[0] and m_Vertices[1] are on one horizontal line.
        {
            REAL m1 = - (x2 - x1) / y21;

            REAL mx1 = (x1 + x2) * .5F;
            REAL my1 = (y1 + y2) * .5F;

            m_Center.X = (x0 + x1) * .5F;
            m_Center.Y = m1 * (m_Center.X - mx1) + my1;
        }
    }
    else if (b21zero)	// m_Vertices[1] and m_Vertices[2] are on one horizontal line.
    {
        REAL m0 = - (x1 - x0) / y10;

        REAL mx0 = (x0 + x1) * .5F;
        REAL my0 = (y0 + y1) * .5F;

        m_Center.X = (x1 + x2) * .5F;
        m_Center.Y = m0 * (m_Center.X - mx0) + my0;
    }
    else	// 'Common' cases, no multiple vertices are on one horizontal line.
    {
        REAL m0 = - (x1 - x0) / y10;
        REAL m1 = - (x2 - x1) / y21;

        REAL mx0 = (x0 + x1) * .5F;
        REAL my0 = (y0 + y1) * .5F;

        REAL mx1 = (x1 + x2) * .5F;
        REAL my1 = (y1 + y2) * .5F;

        m_Center.X = (m0 * mx0 - m1 * mx1 + my1 - my0) / (m0 - m1);
        m_Center.Y = m0 * (m_Center.X - mx0) + my0;
    }

    REAL dx = x0 - m_Center.X;
    REAL dy = y0 - m_Center.Y;

    m_R2 = dx * dx + dy * dy;	// the radius of the circumcircle, squared
    m_R = (REAL) sqrt(m_R2);	// the proper radius

    // Version 1.1: make m_R2 slightly higher to ensure that all edges
    // of co-circular vertices will be caught.
    // Note that this is a compromise. In fact, the algorithm isn't really
    // suited for very many co-circular vertices.
    m_R2 *= 1.000001f;
}

// Function object to check whether a triangle has one of the vertices in SuperTriangle.
// operator() returns true if it does.
class triangleHasVertex
{
public:
    triangleHasVertex(const vertex SuperTriangle[3]) : m_pSuperTriangle(SuperTriangle)	{}
    bool operator()(const triangle& tri) const
    {
        for (int i = 0; i < 3; i++)
        {
            const vertex * p = tri.GetVertex(i);
            if (p >= m_pSuperTriangle && p < (m_pSuperTriangle + 3)) return true;
        }
        return false;
    }
protected:
    const vertex * m_pSuperTriangle;
};

// Function object to check whether a triangle is 'completed', i.e. doesn't need to be checked
// again in the algorithm, i.e. it won't be changed anymore.
// Therefore it can be removed from the workset.
// A triangle is completed if the circumcircle is completely to the left of the current vertex.
// If a triangle is completed, it will be inserted in the output set, unless one or more of it's vertices
// belong to the 'super triangle'.
class triangleIsCompleted
{
public:
    triangleIsCompleted(cvIterator itVertex, triangleSet& output, const vertex SuperTriangle[3])
        : m_itVertex(itVertex)
        , m_Output(output)
        , m_pSuperTriangle(SuperTriangle)
    {}
    bool operator()(const triangle& tri) const
    {
        if (tri.IsLeftOf(m_itVertex))
        {
            triangleHasVertex thv(m_pSuperTriangle);
            if (! thv(tri)) m_Output.insert(tri);
            return true;
        }
        return false;
    }

protected:
    cvIterator m_itVertex;
    triangleSet& m_Output;
    const vertex * m_pSuperTriangle;
};

// Function object to check whether vertex is in circumcircle of triangle.
// operator() returns true if it does.
// The edges of a 'hot' triangle are stored in the edgeSet edges.
class vertexIsInCircumCircle
{
public:
    vertexIsInCircumCircle(cvIterator itVertex, edgeSet& edges) : m_itVertex(itVertex), m_Edges(edges)	{}
    bool operator()(const triangle& tri) const
    {
        bool b = tri.CCEncompasses(m_itVertex);

        if (b)
        {
            HandleEdge(tri.GetVertex(0), tri.GetVertex(1));
            HandleEdge(tri.GetVertex(1), tri.GetVertex(2));
            HandleEdge(tri.GetVertex(2), tri.GetVertex(0));
        }
        return b;
    }
protected:
    void HandleEdge(const vertex * p0, const vertex * p1) const
    {
        const vertex * pVertex0(NULL);
        const vertex * pVertex1(NULL);

        // Create a normalized edge, in which the smallest vertex comes first.
        if (* p0 < * p1)
        {
            pVertex0 = p0;
            pVertex1 = p1;
        }
        else
        {
            pVertex0 = p1;
            pVertex1 = p0;
        }

        edge e(pVertex0, pVertex1);

        // Check if this edge is already in the buffer
        edgeIterator found = m_Edges.find(e);

        if (found == m_Edges.end()) m_Edges.insert(e);		// no, it isn't, so insert
        else m_Edges.erase(found);							// yes, it is, so erase it to eliminate double edges
    }

    cvIterator m_itVertex;
    edgeSet& m_Edges;
};

void Delaunay::Triangulate(const vertexSet& vertices, triangleSet& output)
{
    if (vertices.size() < 3) return;	// nothing to handle

    // Determine the bounding box.
    cvIterator itVertex = vertices.begin();

    REAL xMin = itVertex->GetX();
    REAL yMin = itVertex->GetY();
    REAL xMax = xMin;
    REAL yMax = yMin;

    ++itVertex;		// If we're here, we know that vertices is not empty.
    for (; itVertex != vertices.end(); itVertex++)
    {
        xMax = itVertex->GetX();	// Vertices are sorted along the x-axis, so the last one stored will be the biggest.
        REAL y = itVertex->GetY();
        if (y < yMin) yMin = y;
        if (y > yMax) yMax = y;
    }

    REAL dx = xMax - xMin;
    REAL dy = yMax - yMin;

    // Make the bounding box slightly bigger, just to feel safe.
    REAL ddx = dx * 0.01F;
    REAL ddy = dy * 0.01F;

    xMin -= ddx;
    xMax += ddx;
    dx += 2 * ddx;

    yMin -= ddy;
    yMax += ddy;
    dy += 2 * ddy;

    // Create a 'super triangle', encompassing all the vertices. We choose an equilateral triangle with horizontal base.
    // We could have made the 'super triangle' simply very big. However, the algorithm is quite sensitive to
    // rounding errors, so it's better to make the 'super triangle' just big enough, like we do here.
    vertex vSuper[3];

    vSuper[0] = vertex(xMin - dy * sqrt3 / 3.0F, yMin);	// Simple highschool geometry, believe me.
    vSuper[1] = vertex(xMax + dy * sqrt3 / 3.0F, yMin);
    vSuper[2] = vertex((xMin + xMax) * 0.5F, yMax + dx * sqrt3 * 0.5F);

    list<triangle> workset;
    workset.push_back(triangle(vSuper));

    for (itVertex = vertices.begin(); itVertex != vertices.end(); itVertex++)
    {
        // First, remove all 'completed' triangles from the workset.
        // A triangle is 'completed' if its circumcircle is entirely to the left of the current vertex.
        // Vertices are sorted in x-direction (the set container does this automagically).
        // Unless they are part of the 'super triangle', copy the 'completed' triangles to the output.
        // The algorithm also works without this step, but it is an important optimalization for bigger numbers of vertices.
        // It makes the algorithm about five times faster for 2000 vertices, and for 10000 vertices,
        // it's thirty times faster. For smaller numbers, the difference is negligible.
        list<triangle>::iterator itEnd = remove_if(workset.begin(), workset.end(), triangleIsCompleted(itVertex, output, vSuper));

        edgeSet edges;

        // A triangle is 'hot' if the current vertex v is inside the circumcircle.
        // Remove all hot triangles, but keep their edges.
        itEnd = remove_if(workset.begin(), itEnd, vertexIsInCircumCircle(itVertex, edges));
        workset.erase(itEnd, workset.end());	// remove_if doesn't actually remove; we have to do this explicitly.

        // Create new triangles from the edges and the current vertex.
        for (edgeIterator it = edges.begin(); it != edges.end(); it++)
            workset.push_back(triangle(it->m_pV0, it->m_pV1, & (* itVertex)));
    }

    // Finally, remove all the triangles belonging to the 'super triangle' and move the remaining
    // triangles tot the output; remove_copy_if lets us do that in one go.
    tIterator where = output.begin();
    remove_copy_if(workset.begin(), workset.end(), inserter(output, where), triangleHasVertex(vSuper));
}

void Delaunay::TrianglesToEdges(const triangleSet& triangles, edgeSet& edges)
{
    size_t id = 0;
    for (ctIterator it = triangles.begin(); it != triangles.end(); ++it, ++id)
    {
        HandleEdge(it->GetVertex(0), it->GetVertex(1), edges, id);
        HandleEdge(it->GetVertex(1), it->GetVertex(2), edges, id);
        HandleEdge(it->GetVertex(2), it->GetVertex(0), edges, id);
    }
}

void Delaunay::HandleEdge(const vertex * p0, const vertex * p1, edgeSet& edges, size_t triangleId)
{
    const vertex * pV0(NULL);
    const vertex * pV1(NULL);

    if (* p0 < * p1)
    {
        pV0 = p0;
        pV1 = p1;
    }
    else
    {
        pV0 = p1;
        pV1 = p0;
    }

    // Insert a normalized edge. If it's already in edges, insertion will fail,
    // thus leaving only unique edges.
    edge e(pV0, pV1);
    edgeIterator ei = edges.find(e);
    if (ei == edges.end())
    {
        e.t0 = triangleId;
        edges.insert(e);
    }
    else
    {
        ei->t1 = triangleId;
    }
}