Question

Hi i’m using a Delaunay_triangulation_2 and Delaunay_triangulation_3 for finding points for interpolation. I found how to use locate for Delaunay_triangulation_2:

Locate_type loc;
int li;
CgalPoint point(_params[0], _params[1]);
Face_handle handle = delaunay.locate(point, loc, li);

if(loc == Delaunay::VERTEX)
{
    MyData data = _handle->vertex(_li)->info();
}
else if(loc == Delaunay::EDGE)
{
    MyData data1 = handle->vertex(handle->cw(li))->info();
    MyData data2 = handle->vertex(handle->ccw(li))->info();
}
else if(loc == Delaunay::FACE)
{
    MyData data1 = handle->vertex(0)->info();
    MyData data2 = handle->vertex(1)->info();
    MyData data3 = handle->vertex(2)->info();
}

Those tricks with cw and ccw are not intuitive for me.

And when using Triangulation_3 I have a problem with implementing EDGE, FACET and VEREX cases

    Locate_type loc;
int li,lj;
Cell_handle handle = delaunay.locate(point, loc, li, lj);

switch(loc)
{
    case Delaunay::CELL:
    {
        for(int i = 0; i < 4 ; ++i)
            MyData data = handle->vertex(i)->info();
        break;
    }
    case Delaunay::EDGE:
    case Delaunay::FACET:
    case Delaunay::VERTEX:
        assert(false);
}

My test shows that case Delaunay::VERTEX behaves the same as in Triangulation_2.

Triangulation_3 gives different handle type then Triangulation_2. Do I have to use some cw and ccw tricks here?

Docs:

If query lies on a facet, an edge or on a vertex, one of the cells
having query on its boundary is returned.
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_3_ref/Class_Triangulation_3.html

I want to get two points of edge that have my query and three points of face (in case when something else is returned then Delaunay::CELL). How to get it from “one of the cells having query on its boundary”?

Answer 1

The documentation of what is a facet and an edge are inside the combinatorial part of the triangulation.

    if(loc == Delaunay::VERTEX)
    {
        MyData data = handle->vertex(li)->info();
    }
    else if(loc == Delaunay::EDGE)
    {
        MyData data1 = handle->vertex(handle->vertex(li))->info();
        MyData data2 = handle->vertex(handle->vertex(lj))->info();
    }
    else if(loc == Delaunay::FACET)
    {
        MyData data1 = handle->vertex( (li+1)%4 )->info();
        MyData data2 = handle->vertex( (li+2)%4 )->info();
        MyData data3 = handle->vertex( (li+3)%4 )->info();
    }