Ming-Jun Lai Abstract. FVS-triangulation is a special but very exible triangulation. We survey the results on bivariate spline spaces over such triangulations. x

OBJECTIVES To develop a new and inexpensive model for training in fluoroscopic puncture into the pelvicalyceal system, and to use this model to compare the learning curve of two fluoroscopic techniques, the 'eye of the needle' (EN) and triangulation techniques. MATERIALS AND METHODS For the trial we used a commercial plastic model (a shop-window mannequin) in which a bovine kidney, embedded i...

We present an algorithm that takes as input a finite point set in R, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the we...

Choosing the best triangulation of a point set is a question that has been debated for many years. Two of the most well known choices are the mitt-max criterion and the max-min criterion. The max-min triangulation criterion has received the most attention over the years because efficient algorithms have been developed for determining this triangulation. The ability to construct such efficient a...

Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a triangulation), (2) the angular balanced triangulation which minimizes the sum of the ratios of the maximum angle to the minimum angle for each triangle and (3) the area balanced triangulation wh...

We propose the triangulation axis as an alternative skeletal structure for a simple polygon P . This axis is a straight-line tree that can be interpreted as an anisotropic medial axis of P , where inscribed disks are line segments or triangles. The underlying triangulation that specifies the anisotropy can be varied, to adapt the axis so as to reflect predominant geometrical and topological fea...

This paper focuses on the application of triangulation and rubber-sheeting techniques to the problem of merging two digitized map files. The Census Bureau is currently developing a map merging procedure called conflation. Reproducibility, quality control, and a desire for mathematical consistency in conflation lead to a need for well-defined procedures. The Delaunay triangulation is well-define...

A plane triangulation is an embedding of a maximal planar graph in the Euclidean plane. Foulds and Robinson (1979) first studied the problem of transforming one triangulation to another by a sequence of diagonal operations. where a diagonal operation deletes one edge and inserts the other diagonal of the resulting quadrilateral face. An edge which cannot be removed by a single diagonal operatio...

Spatial sampling methods have acquired great popularity due to the number of applications that need to triangulate portions of space in various dimensions. One limitation of the current techniques is the handling of the final models, which are large, complex and need to register neighborhood relationships explicitly. Additionally, most techniques are limited to Euclidean bidimensional or tridim...

We show that there is no triangulation of the infinite real Grassmannian G(k, R∞) nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of G(k, R∞) subdividing the matroid stratification. This is proved by an argument in projective geometry, considering a specific sequence of configurations of points in the plane. The Grassmannian G...