Mesh model simplification has received increasing attention recent years. However, few algorithms are developed for the application of manufacturing. We have developed a simplification algorithm from the character of surface sculpture manufacturing, which can rapidly produce faithful approximations of the triangle mesh models. Moreover, the simplified mesh generated by our algorithm is composed...

In this paper, we propose a valence-driven, single-resolution encoding technique for lossless compression of triangle mesh connectivity. Building upon a valence-based approach pioneered by Touma and Gotsman 22, we design a new valence-driven conquest for arbitrary meshes that always guarantees smaller compression rates than the original method. Furthermore, we provide a novel theoretical entrop...

A binary triangle of size n is a triangle of zeroes and ones, with n rows, built with the same local rule as the standard Pascal triangle modulo 2. A binary triangle is said to be balanced if the absolute difference between the numbers of zeroes and ones that constitute this triangle is at most 1. In this paper, the existence of balanced binary triangles of size n, for all positive integers n, ...

The soft-tissue triangle is one of the least areas attended to in rhinoplasty. Any postoperative retraction, notching, or asymmetries of soft triangles can seriously affect the rhinoplasty outcome. A good understanding of the risk factors predisposing to soft triangle deformities is necessary to prevent such problems. The commonest risk factors in our study were the wide vertical domal angle be...

The self-assembly of an equilateral triangle that is both heterobimetallic and heteroleptic, its metal exchange to a homometallic triangle and further ligand exchange (= edge of the triangle) were elaborated.

Recently, a wealth of algorithms for the efficient coding of 3D triangle meshes have been published (e.g. [1,2,4,5,6,7,8]). All these focus on achieving the most compact code for the connectivity data, resulting in between 0.7 and 2 bits per triangle on the average. The geometric data, i.e. the vertex coordinates, are then coded in an order induced by the connectivity code, which is probably no...

We investigate asphericity of the relative group presentation 〈G, t | atbtctdtet = 1〉 and prove it aspherical provided the subgroup of G generated by {ab−1, bc−1, cd−1, de−1} is neither finite cyclic nor a finite triangle group. We also prove a similar result for the closely related relative group presentation 〈G, s, t | αsβsγt = 1 = δtεtζs−1〉.

We present a Virtual Reality application enabling interactive, physically correct simulation of tube-like flexible objects. Our objective was to describe flexible objects by a set of parameters (length, diameter and material constants) instead of rigid geometry (triangle meshes) and to give the user the possibility to add, delete and manipulate those flexible objects in a stereo projected envir...

We determine the unique triangle given its orthocenter, circumcenter and another particular triangle point. The main technique is to realize the triangle as special intersection points of the circumcircle and a rectangular hyperbola in Poncelet’s pencil.