  An extension of the restricted Delaunay-refinement algorithm for surface mesh
generation is described, where a new point-placement scheme is introduced to
improve element quality in the presence of mesh size constraints. Specifically,
it is shown that the use of off-centre Steiner points, positioned on the faces
of the associated Voronoi diagram, typically leads to significant improvements
in the shape- and size-quality of the resulting surface tessellations. The new
algorithm can be viewed as a Frontal-Delaunay approach -- a hybridisation of
conventional Delaunay-refinement and advancing-front techniques in which new
vertices are positioned to satisfy both element size and shape constraints. The
performance of the new scheme is investigated experimentally via a series of
comparative studies that contrast its performance with that of a typical
Delaunay-refinement technique. It is shown that the new method inherits many of
the best features of classical Delaunay-refinement and advancing-front type
methods, leading to the construction of smooth, high quality surface
triangulations with bounded radius-edge ratios and convergence guarantees.
Experiments are conducted using a range of complex benchmarks, verifying the
robustness and practical performance of the proposed scheme.
