We introduce a new manifold-based construction for fitting a smooth surface to a triangle mesh of arbitrary topology. Our construction combines in novel ways most of the best features of previous constructions and, thus, it fills the gap left by them. We also introduce a theoretical framework that provides a sound justification for the correctness of our construction. Finally, we demonstrate th...

First, we apply Thurston’s construction of pseudo-Anosov homeomorphisms to grid graphs and obtain translation surfaces whose Veech groups are commensurable to (m, n,∞) triangle groups. Many (if not all) of the surfaces we construct were first discovered by Bouw and Möller, however our treatment of the surfaces differs. We construct these surfaces by gluing together polygons in two ways. We use ...

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to their boundaries, where boundaries mean the triangles and rectangles which confine gaskets and carpets. As an application, we construct diffusion processes on ...

Given two points p and q of the Sierpinski universal plane curve S, necessary and/ or sufficient conditions are discussed in the paper under which there is a mapping I of S onto itself such that I(P) = q and I belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.

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...