Quasi-triangulation

A quasi-triangulation is a subdivision of a geometric object into simplices, where vertices are not points but arbitrary sloped line segments.

{{cite book

|author1=Luzin S.Y. |author2=Lyachek Y.T. |author3=Petrosyan G.S. |author4=Polubasov O.B. | title = Models and algorithms for automated design of electronic and computer equipment (in Russian)

| publisher = BHV-Petersburg

| year = 2010

| pages = 224

| isbn = 978-5-9775-0576-5 }} This division is not a triangulation in the geometric sense. It is a topological triangulation, however. A quasi-triangulation may have some of the characteristics of a Delaunay triangulation.

[[File:Quasitriangulation.png|thumb|right|250px|Quasi-triangulation. Line segments of the topology (quasi-vertices) are shown in black, gray — quasi-edges, white — faces. a — a convex quadrangular edge,

b — a nonconvex quadrangular edge, c — a triangular edge, d — a degenerate edge, a and e — parallel edges,

f — a quasi-edge contains a part of the line segment.]]