I'm trying to implement the Delaunay triangulation in C++. Currently it's working, but I'm not getting the correct amount of triangles. I try it with 4 points in a square pattern : (0,0), (1,0), (0,1), (1,1).
Here's the algorithm I use :
std::vector<Triangle> Delaunay::triangulate(std::vector<Vec2f> &vertices) {
// Determinate the super triangle
float minX = vertices[0].getX();
float minY = vertices[0].getY();
float maxX = minX;
float maxY = minY;
for(std::size_t i = 0; i < vertices.size(); ++i) {
if (vertices[i].getX() < minX) minX = vertices[i].getX();
if (vertices[i].getY() < minY) minY = vertices[i].getY();
if (vertices[i].getX() > maxX) maxX = vertices[i].getX();
if (vertices[i].getY() > maxY) maxY = vertices[i].getY();
}
float dx = maxX - minX;
float dy = maxY - minY;
float deltaMax = std::max(dx, dy);
float midx = (minX + maxX) / 2.f;
float midy = (minY + maxY) / 2.f;
Vec2f p1(midx - 20 * deltaMax, midy - deltaMax);
Vec2f p2(midx, midy + 20 * deltaMax);
Vec2f p3(midx + 20 * deltaMax, midy - deltaMax);
// Add the super triangle vertices to the end of the vertex list
vertices.push_back(p1);
vertices.push_back(p2);
vertices.push_back(p3);
// Add the super triangle to the triangle list
std::vector<Triangle> triangleList = {Triangle(p1, p2, p3)};
// For each point in the vertex list
for(auto point = begin(vertices); point != end(vertices); point++)
{
// Initialize the edges buffer
std::vector<Edge> edgesBuff;
// For each triangles currently in the triangle list
for(auto triangle = begin(triangleList); triangle != end(triangleList);)
{
if(triangle->inCircumCircle(*point))
{
Edge tmp[3] = {triangle->getE1(), triangle->getE2(), triangle->getE3()};
edgesBuff.insert(end(edgesBuff), tmp, tmp + 3);
triangle = triangleList.erase(triangle);
}
else
{
triangle++;
}
}
// Delete all doubly specified edges from the edge buffer
// Black magic by https://github.com/MechaRage
auto ite = begin(edgesBuff), last = end(edgesBuff);
while(ite != last) {
// Search for at least one duplicate of the current element
auto twin = std::find(ite + 1, last, *ite);
if(twin != last)
// If one is found, push them all to the end.
last = std::partition(ite, last, [&ite](auto const &o){ return !(o == *ite); });
else
++ite;
}
// Remove all the duplicates, which have been shoved past "last".
edgesBuff.erase(last, end(edgesBuff));
// Add the triangle to the list
for(auto edge = begin(edgesBuff); edge != end(edgesBuff); edge++)
triangleList.push_back(Triangle(edge->getP1(), edge->getP2(), *point));
}
// Remove any triangles from the triangle list that use the supertriangle vertices
triangleList.erase(std::remove_if(begin(triangleList), end(triangleList), [p1, p2, p3](auto t){
return t.containsVertex(p1) || t.containsVertex(p2) || t.containsVertex(p3);
}), end(triangleList));
return triangleList;
}
And here's what I obtain :
Triangle:
Point x: 1 y: 0
Point x: 0 y: 0
Point x: 1 y: 1
Triangle:
Point x: 1 y: 0
Point x: 1 y: 1
Point x: 0 y: 1
Triangle:
Point x: 0 y: 0
Point x: 1 y: 1
Point x: 0 y: 1
While this would be the correct output :
Triangle:
Point x: 1 y: 0
Point x: 0 y: 0
Point x: 0 y: 1
Triangle:
Point x: 1 y: 0
Point x: 1 y: 1
Point x: 0 y: 1
I have no idea why there is a triangle with the (0, 0) and the (1, 1). I need an outside eye to review the code and find out what's going wrong.
All the sources are on my Github repo. Feel free to fork it and to PR your code.
Thanks!
