Summary. We present a method to decompose an arbitrary 3D piecewise linear complex (PLC) into a constrained Delaunay tetrahedralization (CDT). It successfully resolves the problem of non-existence of a CDT by updating the input PLC into another PLC which is topologically and geometrically

of enforcing boundary conformity---ensuring that triangulation edges cover the boundaries (both interior and exterior) of the domain being modeled. This paper discusses the three-dimensional analogue, constrained Delaunay tetrahedralizations (also called CDTs), and their advantages in mesh generation. CDTs

To facilitate and encourage the exchange and interoperability of geographical information, the ISO1 and the OGC2 have developed in recent years standards that define what the basic geographical primitives are (ISO, TC211), and also how they can be implemented (OGC, 2007, 2006). While the definitions for the primitives are not restricted to 2D, most of the efforts for the implementation of these

Summary. Constrained Delaunay tetrahedralizations (CDTs) are valuable for generating meshes of nonconvex domains and domains with internal boundaries, but they are difficult to maintain robustly when finite-precision coordinates yield vertices on a line that are not perfectly collinear

The problem of determining whether a polyhedron has a constrained Delaunay tetrahedralization is NPcomplete. However, if no five vertices of the polyhedron lie on a common sphere, the problem has a polynomial-time solution. Constrained Delaunay tetrahedralization has the unusual status (for a

The problem of determining whether a polyhedron has a constrained Delaunay tetrahedralization is NP-complete. However, if no five vertices of the polyhedron lie on a common sphere, the problem has a polynomial-time solution. Constrained Delaunay tetrahedralization has the unusual status (for a

Summary. This paper discusses the problem of refining constrained Delaunay tetrahedralizations (CDTs) into good quality meshes suitable for adaptive numerical simulations. A practical algorithm which extends the basic Delaunay refinement scheme is proposed. It generates an isotropic mesh

Given a complex of vertices, constraining segments, and planar straight-line constraining facets in E 3 , with no input angle less than 90 ffi , an algorithm presented herein can generate a conforming mesh of Delaunay tetrahedra whose circumradius-to-shortest edge ratios are no greater than

Given a set of n vertices in the plane together with a set of noncrossing edges, the constrained Delaunay triangulation (CDT) is the triangulation of the vertices with the following properties: (1) the prespecified edges are included in the triangulation, and (2) it is as close as possible

. This paper presents a procedure for efficient generation of three-dimensional unstructured meshes of tetrahedral elements. Initially, a constrained Delaunay mesh is generated wherein internal points are created using advancing-front point placement and are inserted using a Delaunay method