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 | |
| 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 | United States |
| City | Los Angeles |
| Period | 7/31/05 → 8/4/05 |
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ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Human-Computer Interaction
- Software
Cite this
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 conference › Paper
}
TY - CONF
T1 - Using the CW-complex to represent the topological structure of implicit surfaces and solids
AU - Hart, John C
PY - 2005/7/31
Y1 - 2005/7/31
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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UR - http://www.scopus.com/inward/citedby.url?scp=85027722009&partnerID=8YFLogxK
U2 - 10.1145/1198555.1198643
DO - 10.1145/1198555.1198643
M3 - Paper
AN - SCOPUS:85027722009
ER -