PURPOSE To explore various types of triangulation strategies and to indicate when different types of triangulation should be used in research. METHODS Reviews included literature on triangulation and multimethod strategies published since 1960 and research books specifically focusing on triangulation. FINDINGS Triangulation is the combination of at least two or more theoretical perspectives...

Definition 3 (Polygonal Triangulation). Let K be a two-dimensional simplicial complex (i.e., a collection of triangles). If K is homeomorphic to a disk, then it is called a triangulation of a disk. Furthermore, if K is a k-gon divided by diagonals into k − 2 triangles, then K will be called a polygonal triangulation. See Figure 1. A k-gon dissected into k − 2 triangles will be called a k-triang...

We describe a method to approximate a closed surface triangulation using simulated annealing. Our approach guarantees that all vertices and triangles in an approximating surface triangulation are within a user-de ned distance of the original surface triangulation. We introduce the idea of atomic envelopes to guarantee error bounds that are independent of the surface geometry. Atomic envelopes a...

We introduce the restricted constrained Delaunay triangulation (restricted CDT). The restricted CDT generalizes the restricted Delaunay triangulation, allowing us to define a triangulation of a surface that includes a set of constraining segments. Under certain sampling conditions, the restricted CDT includes every constrained segment and suggests an algorithm that produces a triangulation of t...

A comprehensive uncertainty, baseline, and noise analysis in computing 3D points using a recent L1-based triangulation algorithm is presented. This method is shown to be not only faster and more accurate than its main competitor, linear triangulation, but also more stable under noise and baseline changes. A Monte Carlo analysis of covariance and a confidence ellipsoid analysis were performed ov...

We consider the following problem given a pla nar straight line graph nd a covering triangulation whose maximum angle is as small as possible A cov ering triangulation is a triangulation whose vertex set contains the input vertex set and whose edge set con tains the input edge set The covering triangulation problem di ers from the usual Steiner triangulation problem in that we may not add a ver...

In this paper a dynamic image representation is proposed by combining advantages of both raster and vector graphics in the triangulation. In order for a dynamic mesh to remain a triangulation, a method which maintains integrity of representation is devised. Together with techniques for synthesizing paint, the end result is a configurable scheme demonstrating potential as a viable alternative fo...