scholarly journals Expansion properties for finite subdivision rules II

2020 ◽  
Vol 24 (2) ◽  
pp. 29-50
Author(s):  
William Floyd ◽  
Walter Parry ◽  
Kevin M. Pilgrim
Keyword(s):  
Subdivision Rules

Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by Least‐Squares Data Fitting

1999 ◽  
Vol 18 (2) ◽  
pp. 97-119 ◽  
Author(s):  
Faramarz F. Samavati ◽  
Richard H. Bartels
Keyword(s):  
Least Squares ◽  
Data Fitting ◽  
Surface Representation ◽  
Subdivision Rules

Subdivision rules and virtual endomorphisms

2009 ◽  
Vol 141 (1) ◽  
pp. 181-195 ◽  
Author(s):  
J. W. Cannon ◽  
W. J. Floyd ◽  
W. R. Parry ◽  
K. M. Pilgrim
Keyword(s):  
Subdivision Rules

Racially Restrictive Covenants—Were They Dignity Takings?

2016 ◽  
Vol 41 (04) ◽  
pp. 939-955 ◽  
Author(s):  
Carol M. Rose
Keyword(s):  
United States ◽  
South Africa ◽  
Twentieth Century ◽  
Public Policies ◽  
The United States ◽  
Restrictive Covenants ◽  
State Involvement ◽  
Subdivision Rules

Racially restrictive covenants—subdivision rules or neighborhood agreements that “run with the land” to bar sales of rentals by minority members—were common and legally enforceable in the United States in the first half of the twentieth century. In spite of their demeaning character, these racial covenants took away opportunities from excluded minorities, rather than things, and thus they amounted to something less than the dramatic “dignity takings” that Bernadette Atuahene (2014) describes in her new book on dignity takings in South Africa. In this article, I explore some significant ways in which racially restrictive covenants differed from dignity takings as Atuahene defines them, as well as the shadowy similarities between racial covenants and Atuahene's dignity takings; I focus here on the dimensions of dehumanization, state involvement, and property takings. I conclude with a discussion of remedies, particularly considering measures that restore dignity through both public policies and private actions.

scholarly journals Expansion properties for finite subdivision rules I

2018 ◽  
Vol 61 (12) ◽  
pp. 2237-2266
Author(s):  
William J. Floyd ◽  
Walter R. Parry ◽  
Kevin M. Pilgrim
Keyword(s):  
Subdivision Rules

scholarly journals Constructing subdivision rules from alternating links

2010 ◽  
Vol 14 (01) ◽  
pp. 1-13 ◽  
Author(s):  
Brian Rushton
Keyword(s):  
Alternating Links ◽  
Subdivision Rules

scholarly journals Constructing subdivision rules from polyhedra with identifications

2012 ◽  
Vol 12 (4) ◽  
pp. 1961-1992
Author(s):  
Brian Rushton
Keyword(s):  
Subdivision Rules

scholarly journals Constructing subdivision rules from rational maps

2007 ◽  
Vol 11 (10) ◽  
pp. 128-137 ◽  
Author(s):  
J. W. Cannon ◽  
W. J. Floyd ◽  
W. R. Parry
Keyword(s):  
Rational Maps ◽  
Subdivision Rules

An Algorithm Subdividing the Intersection Triangle for Realizing Boolean Operations of STL Models

2012 ◽  
Vol 220-223 ◽  
pp. 2458-2461
Author(s):  
Kai Bo Guo ◽  
Ming Di Wang ◽  
Cheng Feng Sun ◽  
Shi Hong Shi
Keyword(s):  
Data Processing ◽  
Efficient Implementation ◽  
Boolean Operations ◽  
Stl Model ◽  
Linked List ◽  
Data Processing Software ◽  
Intersection Points ◽  
Processing Software ◽  
Subdivision Rules

The efficient implementation of Boolean operatio between STL models is a bottleneck problem to develop excellent RP data processing software, and the subdivision of the intersection is an important step of realization the Boolean operations. An algorithm is proposed in this paper. Based on the closed character of the STL model, the position relationship between the intersection lines and the triangle are classified, and the subdivision rules is summarized. The two data linked list of the intersection points and vertex points are created, a searching process to obtain the subdivision polygon is described.

scholarly journals Convergence analysis of subdivision processes on the sphere

2020 ◽  
Author(s):  
Svenja Hüning ◽  
Johannes Wallner
Keyword(s):  
Convergence Analysis ◽  
Input Data ◽  
Positive Curvature ◽  
A Priori ◽  
First Time ◽  
Subdivision Rules

Abstract We analyse the convergence of nonlinear Riemannian analogues of linear subdivision processes operating on data in the sphere. We show how for curve subdivision rules we can derive bounds guaranteeing convergence if the density of input data is below that threshold. Previous results only yield thresholds that are several magnitudes smaller and are thus useless for a priori checking of convergence. It is the first time that such a result has been shown for a geometry with positive curvature and for subdivision rules not enjoying any special properties like being interpolatory or having non-negative mask.

scholarly journals Creases and boundary conditions for subdivision curves

2020 ◽  
Author(s):  
J Kosinka ◽  
M Sabin ◽  
Neil Dodgson
Keyword(s):  
Control Points ◽  
Knot Insertion ◽  
Degree Polynomial ◽  
Arbitrary Degree ◽  
B Splines ◽  
Novel Approach ◽  
Low Degree ◽  
Subdivision Curves ◽  
Subspace Selection ◽  
Subdivision Rules

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

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