OpenCV,C++: Missing Triangles in Delaunay Triangulation

Question

I am using NetBeans 7.1 on Ubuntu 11.04 and would like to obtain triangles from a set of points using OpenCV. I build the Delaunay triangulation as follows.

vector< Triangle > CTwoDTriangulation::delaunayDiv(const vector< Point_<T> > & vP,   cv::Rect boundRect, vector<Triangle>& triangles, int& numTriangles)
{
    CvSubdiv2D* subdiv;
    int numPts=vP.size();
    CvPoint newPoint;

    CvMemStorage *storage;
    storage = cvCreateMemStorage(0);
    subdiv =  cvCreateSubdivDelaunay2D( boundRect, storage );
    for (size_t e = 0; e<numPts; e++)
    {
        newPoint=vP.at(e);
        if (newPoint.x>=boundRect.y && newPoint.y>=boundRect.y && newPoint.x<boundRect.width &&  newPoint.y<boundRect.height)
                cvSubdivDelaunay2DInsert(subdiv, vP.at(e));
    }

    CvSeqReader  reader;
    int i, total = subdiv->edges->total;
    int elem_size = subdiv->edges->elem_size;

    triangles.resize(2*total-5);    // Maximum number of triangles for number of edges
    numTriangles=0;

    cvStartReadSeq( (CvSeq*)(subdiv->edges), &reader, 0 );

    Triangle V;

    for( i = 0; i < total; i++ )
    {
        CvQuadEdge2D* edge = (CvQuadEdge2D*)(reader.ptr);

        if( CV_IS_SET_ELEM( edge ))
        {
            CvSubdiv2DEdge e = (CvSubdiv2DEdge)edge;
            if (FindTriangleFromEdge(e, V)) 
        {
            triangles.at(numTriangles++)=V;
        }
    }
    CV_NEXT_SEQ_ELEM( elem_size, reader );
}
cvReleaseMemStorage(&storage);

return triangles;
}

FindTriangleFromEdge() has the following form.

void CTwoDTriangulation::FindTriangleFromEdge(CvSubdiv2DEdge e, Triangle& V)
{
   CvSubdiv2DEdge t = e;    // Number of type size_t
   CvPoint buf[3];          // Triangle vertices
   int iPointNum = 3;
   int  j;
   CvPoint pts[3];

   for(j = 0; j < iPointNum; j++ )
   {
        CvSubdiv2DPoint* point = cvSubdiv2DEdgeOrg( t );
        if( !point ) break;
        pts[j].x=point->pt.x;
        pts[j].y=point->pt.y;
        buf[j] = cvPoint( cvRound(point->pt.x), cvRound(point->pt.y));
        t = cvSubdiv2DGetEdge( t, CV_NEXT_AROUND_LEFT );
   }
  AddTriangle(buf, pts, V);
}

This gets me most of the triangles but some are missing. For example, I set a set of points that approximate a rectangular grid. I get the following (5,1);(103,101);(1,101)
(106,1);(103,101);(5,1)
(5,1);(106,1);(103,101)
(204,101);(106,1);(208,1)
(208,1);(307,101);(204,101)
(309,1);(307,101);(204,101)

So (106,1);(204,1);(103,101)is missing and at least one triangle is duplicated.

score 1 · Answer 1 · answered May 12 '12 at 23:42

1

Your if statement seems to have a bug? Why are you comparing newPoint.x with boundRect.y?

if (newPoint.x>=boundRect.y && newPoint.y>=boundRect.y && newPoint.x<boundRect.width &&  newPoint.y<boundRect.height)
            cvSubdivDelaunay2DInsert(subdiv, vP.at(e));

answered May 12 '12 at 23:42

Sammy

356
2
7

1

I think that's it. Also, could it be that @OtagoHarbour needs the last two compares to be newPoint.x<(boundRect.x + boundRect.width) && newPoint.y<(boundRect.y + boundRect.height)? – emsr May 13 '12 at 01:01
Yup, seems he needs that as well. – Sammy May 13 '12 at 01:13
Thank you very much for noticing that. Unfortunately, boundRect.x and boundRect.y are the same so that is not the problem. – OtagoHarbour May 13 '12 at 02:23
Thanks @emsr. I made that change but still have the problem. The offending triangles are mainly surrounded by other triangles so I do not think it wold be a boundary effect. Thanks, Peter. – OtagoHarbour May 13 '12 at 02:55

score 0 · Answer 2 · answered Mar 14 '13 at 21:35

0

I had the same problem. My solution was to check against

cvSubdiv2DGetEdge( t, CV_NEXT_AROUND_RIGHT );

and look! with this it found the missing ones, but misses some others. So my solution is to combine both results for now.

answered Mar 14 '13 at 21:35

Thomas Schwarze

1

pdpcosta · Answer 3 · 2013-06-05T12:42:34.073

When you use CV_NEXT_AROUND_LEFT the next edge to be chosen will be the one on LEFT facet of the specified edge. Now consider, for example, a triangle formed by vertices V1, V2 and V3, whose sides are Edge1, Edge2 and Edge3.

Additionally, imagine that V1 is the Org Point of Edge1, V2 is the Org Point of Edge2 and V3 is the Org Point of Edge3 (like vectors connected in a clockwise orientation). In this case, the left facets are always outside the given triangle so, in your code, this triangle will be missing.

I could not realize another way of preventing this except by combining CV_NEXT_AROUND_LEFT with CV_NEXT_AROUND_RIGHT and removing the duplicate triangles that will be recorded.

OpenCV,C++: Missing Triangles in Delaunay Triangulation

3 Answers3