Using the CW-complex to represent the topological structure of implicit surfaces and solids

Research output: Contribution to conferencePaper

Abstract

We investigate the CW-complex as a data structure for visualizing and controlling the topology of implicit surfaces. Previous methods for contolling the blending of implicit surfaces redefined the contribution of a metaball or unioned blended components. Morse theory provides new insight into the topology of the surface a function implicitly defines by studying the critical points of the function. These critical points are organized by a separatrix structure into a CW-complex. This CW-complex forms a topological skeleton of the object, indicating connectedness and the possibility of connectedness at various locations in the surface model. Definitions, algorithms and applications for the CW-complex of an implicit surface and the solid it bounds are given as a preliminary step toward direct control of the topology of an implicit surface.

Original languageEnglish (US)
DOIs
StatePublished - Jul 31 2005
Externally publishedYes
EventACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005 - Los Angeles, United States
Duration: Jul 31 2005Aug 4 2005

Other

OtherACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005
CountryUnited States
CityLos Angeles
Period7/31/058/4/05

Fingerprint

Topology
Data structures

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Human-Computer Interaction
  • Software

Cite this

Hart, J. C. (2005). Using the CW-complex to represent the topological structure of implicit surfaces and solids. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States. https://doi.org/10.1145/1198555.1198643

Using the CW-complex to represent the topological structure of implicit surfaces and solids. / Hart, John C.

2005. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States.

Research output: Contribution to conferencePaper

Hart, JC 2005, 'Using the CW-complex to represent the topological structure of implicit surfaces and solids' Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States, 7/31/05 - 8/4/05, . https://doi.org/10.1145/1198555.1198643
Hart JC. Using the CW-complex to represent the topological structure of implicit surfaces and solids. 2005. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States. https://doi.org/10.1145/1198555.1198643
Hart, John C. / Using the CW-complex to represent the topological structure of implicit surfaces and solids. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States.
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