Abstract
Several examples are given to demonstrate non-termination of Ruppert’s Delaunay refinement algorithm for triangular mesh generation exploring the relationship between the minimum angle in the input and the minimum allowable angle in the output. These examples show non-termination despite requiring a minimum output angle of less than 30° which is smaller than the value generally observed in practice. For input containing only points, an example demonstrates failure of the algorithm with a minimum angle of 30° showing that the theoretical analysis in that context is sharp.
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