Paper Info
Title
Topological design of sculptured surfaces
Abstract
Topology is primal geometry. Our design philosophy embodies this principle. We report on a new surface &sign perspective based on a “marked” polygon for each object. The marked polygon captures the topology of the object surface. We construct multiply periodic mappings from polygon to sculptured surface. The mappings arise naturally from the topology and other design considerations. Hence we give a single domain global parameteriration for surfaces with handles. Examples demonstrate the design of sculptured objects and their ntanufimture. boundaries. The burden of maintaining topological integrity falls to the designer. In these methods, there is no single parameter space, there are many sets of separate coordinate functions. Control of the topology may be simple for some shapes, but it is difficult for topologically complex ones. Some “solid” modelling systems check topology after the design stage, e.g. via the Euler-Poincark formulae mof89]. The check only determines when an invalid operation has occured. but does not participate in the design process. This paper describes a design philosophy that includes surface topology as an integral part. Our interest in this subject came from a desire to automate the sculpture of mathematical concepts such as in Figures 1.1 and 1.2 (see [Ferf39, Fer90, or Roc861).
Year
DOI
Venue
1992
10.1145/142920.134031
Special Interest Group on Computer Graphics
Keywords
Field
DocType
automorphic functions,boundary value problems,computer-aided design,marked polygon,multiply periodic functions,sculptured surfaces,topology
Topology,Boundary value problem,Computer graphics (images),Computer science,Computer Aided Design
Conference
Volume
Issue
ISSN
26
2
0097-8930
ISBN
Citations 
PageRank 
0-89791-479-1
22
5.39
References 
Authors
2
3
Name
Order
Citations
PageRank
Helaman Ferguson1377.14
Alyn Rockwood2950179.19
Jordan Cox329525.73