A quasi-triangulation is a subdivision of a geometric object into simplices, where vertiсes are not points but arbitrary sloped line segments. 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.
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.
^Luzin S.Y., Lyachek Y.T., Petrosyan G.S., Polubasov O.B. (2010). Models and algorithms for automated design of electronic and computer equipment (in Russian). BHV-Petersburg. p. 224. ISBN978-5-9775-0576-5.