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In this paper, we provide proofs of termination and size-optimality of the LEPP-Delaunay algorithm, for the quality generation of triangulations. We first prove that the algorithm cannot insert points arbitrarily close to each other. We also show that the algorithm terminates, producing well-graded triangulations with internal angles greater than 25.66 degrees for geometries with input constrained angles of at least 30 degrees. c 2015 The Authors. Published by Elsevier Ltd. Peer-review underdoi:10.1016/j.proeng.2015.10.142 fatcat:eyesrfs32naptkhmujkh52hey4