US Patent 7283138 Method, software and apparatus for efficient polygon rendering

One or more special merge vertices (1, 8) each of which is a root of two braches each including a monotonic (in respect to a particular coordinate) series of vertices are selected from an ordered arrangement of vertices (1-10) that defines a polygon (102). The special merge vertices (1, 8) can be sorted (according to the particular coordinate) so that they can be efficiently located when scanning through the polygon. In scanning through the polygon (102) in a process of rendering the polygon (102), the branches are used to demarcate boundaries of the polygon (102).