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

John C. Hart

doi:10.1145/1198555.1198643

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

Research output: Contribution to conference › Paper › peer-review

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 language	English (US)
DOIs	https://doi.org/10.1145/1198555.1198643
State	Published - Jul 31 2005
Externally published	Yes
Event	ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005 - Los Angeles, United States Duration: Jul 31 2005 → Aug 4 2005

Other

Other	ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005
Country/Territory	United States
City	Los Angeles
Period	7/31/05 → 8/4/05

ASJC Scopus subject areas

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

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10.1145/1198555.1198643

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title = "Using the CW-complex to represent the topological structure of implicit surfaces and solids",

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.",

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note = "Funding Information: This research was funded by a grant by the National Science Foundation. The author is grateful to fellow faculty members Ulrike Axen for discussions on the CW-complex and locating otherwise obscure references, and Bob Lewis for discussions on applications of computational topology to modeling illumination.; ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005 ; Conference date: 31-07-2005 Through 04-08-2005",

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N2 - 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.

AB - 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.

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

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