CGALmesh
Restricted Delaunay Triangulation (RDT)

• approximate curved bounding surfaces
• handle multi-domains in a single refinement process

Definition of RDT

Point set sampled on a smooth curve (1-manifold)	Delaunay triangulation and Voronoi diagram of point set	The Delaunay triangulation restricted to the manifold is the set of Delaunay faces whose dual voronoi faces have a non-empty intersection with the manifold

Sampling theorem for RDT

If the sampling of the manifold is dense enough: the RDT is homeomorphic to the manifold the Hausdorff distance between the manifold and the RDT is small normals, curvature and areas of the manifold can be estimated from the RDT.

Delaunay Refinement and RDT

The Delaunay refinement is tuned to satisfy the sampling condition An RDT facet is considered bad if either too big or too far from the manifold or too badly shaped Each RDT facets has a surface Delaunay ball, i.e., a circumball empty of sampled points and centered on the manifold Each bad RDT facet is refined by inserting the center of a surface Delaunay ball.