www.pudn.com > c_delaunay.rar > Delaunay.cpp, change:2005-01-15,size:10112b
/********************************************************************************
Copyright (C) 2004-2005 Sjaak Priester
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it under the terms of the GNU General Public License as published by
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This file is distributed in the hope that it will be useful,
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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********************************************************************************/
// 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:sjaak@sjaakpriester.nl
#include "StdAfx.h"
#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
{
bool b = tri.IsLeftOf(m_itVertex);
if (b)
{
triangleHasVertex thv(m_pSuperTriangle);
if (! thv(tri)) m_Output.insert(tri);
}
return b;
}
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);
triangleSet workset;
workset.insert(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.
tIterator 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.insert(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)
{
for (ctIterator it = triangles.begin(); it != triangles.end(); ++it)
{
HandleEdge(it->GetVertex(0), it->GetVertex(1), edges);
HandleEdge(it->GetVertex(1), it->GetVertex(2), edges);
HandleEdge(it->GetVertex(2), it->GetVertex(0), edges);
}
}
void Delaunay::HandleEdge(const vertex * p0, const vertex * p1, edgeSet& edges)
{
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.
edges.insert(edge(pV0, pV1));
}