How to do triangulation after insert a new point

As is shown in the image,a new point D(0.5,0.5,0) is interpolated on edge OB.As result,the 2 original triangles are divided into 4 triangles.I have two matrix about the original triangls:p[0 0 0;0 0 1;0 1 0;1 0 0]which represents the coordinates of all the vertexes,t[1 2 3;1 3 4]represents the indexes of the vertexes composing each triangle.How to create a new t matrix ?

[Walter Roberson]

No image was attached.

Which triangulation routine are you using?

[LIN Hongbin]

Answer 1

[Mike Garrity]

Perhaps this post on Loren's blog will help.

[LIN Hongbin]

Thank you, Mike.I searched some papers about Delaunay Triangulation.This method works well when I do 2D geometric items.But when I deal with 3D point clouds,this method will create tetrahedrons,I only want to create triangular patches on the surface of a 3D model. Do you have any advice?Thank you.

[Mike Garrity]

I think you would have to project onto the surface of your model, or onto something that can stand in for the surface. That's easy if your surface is single valued on the projection onto some plane, but hard for more general surfaces.