Laplacian Smoothing and Delaunay Triangulations

Communications in Applied Numerical Methods, Wiley, Vol 4, pp.709-712, 1988

MESHING
RESEARCH
CORNER

Mathematics Department, General Motors Research Laboratories, Warren, MI 48090- 9057, U.S.A. Abstract
In contrast to most triangulation algorithms which implicitly assume that triangulation point locations are fixed, Laplacian' smoothing focuses on moving point locations to improve triangulation. Laplacian smoothing is attractive for its simplicity but it does require an existing triangulation. In this paper the effect of Laplacian smoothing on Delaunay triangulations is explored. It will become clear that constraining Laplacian smoothing to maintain a Delaunay triangulation measurably improves Laplacian smoothing.