We describe a subdivision algorithm for isolating the complex roots of a polynomial F ∈ C[x]. Our model assumes that each coefficient of F has an oracle to return an approximation to any absolute error bound. Given any box B in the complex plane containing only simple roots of F , our algorithm returns disjoint isolating disks for the roots in B. Our complexity analysis bounds the absolute erro...

Haptic rendering of meshes of arbitrary topology is a difficult and time-consuming process. This paper presents the use of subdivision surfaces in order to solve this problem. An overview of subdivision surfaces is given and the algorithms needed to calculate the surface contact point are discussed. We will show that this algorithm is faster than traditional algorithms. Introduction and Related...

A set D of vertices in a graph G = (V, E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdiv...

This paper describes a successful approach to improving the robustness and speed of Sandia National Laboratory’s 3-D MEMS geometry modeler through a combination of mask subdivision and code parallelization. Symptoms of the robustness problems experienced with the original modeler that suggested the need for the subdivision strategy pursued here are explained. The basic elements of the subdivisi...

This paper presents an algorithm dealing with the data reduction and the approximation of 3D polygonal curves. Our method is able to approximate efficiently a set of straight 3D segments or points with a piecewise smooth subdivision curve, in a near optimal way in terms of control point number. Our algorithm is a generalization for subdivision rules, including sharp vertex processing, of the Ac...

We discuss the use of subdivision surfaces in the procedural design of imprint rolls for use in the roller imprinting process. Roller imprinting is being developed for the fabrication of microfluidic devices in polymer substrates. Imprint rolls are modeled using Catmull-Clark subdivision surfaces, and are procedurally designed based on feedback from finite-element simulations of the imprinting ...

A subdivision surface is deened by a polygonal mesh which is iteratively re-ned into an innnite sequence of meshes converging to the desired smooth surface. Classical subdivision schemes are those described and analyzed by Cat-mull/Clark and Doo/Sabin. A graphical representation can be obtained by stopping the iteration on a level of reenement suucient to yield a smooth representation when draw...

We investigate bounds on the dichromatic number of digraphs which avoid a fixed digraph as topological minor. For F , denote by mader ? ? ( ) smallest integer k such that every -dichromatic contains subdivision . As our first main result, we prove if is an orientation cycle then = v This settles conjecture Aboulker, Cohen, Havet, Lochet, Moura and Thomassé. also extend this result to more gener...

In this paper, we present a method for constructing Loop’s subdivision surface patches with given G boundary conditions and a given topology of control polygon of the subdivision surface, using several fourth-order geometric partial differential equations. These equations are solved by a mixed finite element method in a functional space defined by the extended Loop’s subdivision scheme. The met...