When and Why Ruppert's Algorithm Works

An “adaptive” variant of Ruppert’s Algorithm for producing quality triangular planar meshes is introduced. The algorithm terminates for arbitrary Planar Straight Line Graph (PSLG) input. The algorithm outputs a Delaunay mesh where no triangle has minimum angle smaller than 26.45◦ except “across” from small angles of the input. No angle of the output mesh is smaller than arctan [(sin θ∗ )/(2 − cos θ∗ )] where θ∗ is the minimum input angle. Moreover no angle of the mesh is larger than 137.1◦ . The adaptive variant is unnecessary when θ∗ is larger than 36.53◦ , and thus Ruppert’s Algorithm (with concentric shell splitting) can accept input with minimum angle as small as 36.53◦ . An argument is made for why Ruppert’s Algorithm can terminate when the minimum output angle is as large as 30◦ .

• Type: Conference
• Year: 2003
• Where: IMR
• Authors: Gary L. Miller, Steven E. Pav, Noel Walkington
• Keywords: Algorithm, Computational Geometry, IMR 2003, Minimum Angle, Minimum Input Angle