Triangle Merging Algorithm

Hi, i want to reduce many triangles which are coplanar. for example, i have four triangles that make up a quad and indeed i need only two triangles so this is the result i want to have. i googled and found some algorithms, but very short and complicated explained. segment vertex extraction seems to be a good candidate, but i would be lucky if you could give me some more information/help in implementing it. thanks Gammastrahler