We give a technique for obtaining a lower bound on the bandwidth of any planar graph with an embedding in which all bounded faces are triangles. This technique is applied to show that, for each positive integer 1, the triangulated triangle T~ with side-length 1 has bandwidth exactly I + 1. This settles a question of Douglas West.

The ancient Greeks posed and solved the problem of finding all right triangles with rational sidelengths. There are 4 natural nonEuclidean generalizations of this problem. We solve them all. The result is that the only rational-sided nonEuclidean triangle with one right angle is the isoceles spherical triangle with legs of length 45 and hypotenuse 60. We next ask which simplices have rational d...

This survey article considers moduli of algebraic curves using techniques from the complex analytic Teichmüller theory of deformations for the underlying Riemann surfaces and combinatorial topology of surfaces. The aim is to provide a readable narrative, suitable for people with a little background in complex analysis, hyperbolic plane geometry and discrete groups, who wish to understand the in...

Non-rigid 3D shape retrieval has become an important research direction in content-based 3D object retrieval. The aim of this track is to measure and compare the performance of non-rigid 3D shape retrieval methods implemented by different participants around the world. The track is based on a new non-rigid 3D shape benchmark, which contains 600 watertight triangle meshes that are equally classi...

Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Tr...

In this note I review the current determination of the unitarity triangle parameters by using the theoretical and experimental informations available until summer 2000.

Superquadrics are able to represent a large variety of objects with only a few parameters and a single equation. We present a superquadric representation strategy for automotive parts composed of 3-D triangle meshes. Our strategy consists of two major steps of part decomposition and superquadric fitting. The originalities of this approach include the following two features. First, our approach ...

The r-Hofstadter triangle and the (1 − r)-Hofstadter triangle are proved perspective, and homogeneous trilinear coordinates are found for the perspector. More generally, given a triangle DEF inscribed in a reference triangle ABC, triangles A′B′C′ and A′′B′′C′′ derived in a certain manner from DEF are perspective to each other and to ABC. Trilinears for the three perspectors, denoted by P ∗, P1,...