Abstract
Morse theory shows how the topology of an implicit surface is affected by its function's critical points, whereas catastrophe theory shows how these critical points behave as the function's parameters change. Interval analysis finds the critical points, and they can also be tracked efficiently during parameter changes. Changes in the function value at these critical points cause changes in the topology. Techniques for modifying the polygonization to accommodate such changes in topology are given. These techniques are robust enough to guarantee the topology of an implicit surface polygonization, and are efficient enough to maintain this guarantee during interactive modeling. The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
| 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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Keywords
- Catastrophe theory
- Critical points
- Implicit surfaces
- Interactive modeling
- Interval analysis
- Morse theory
- Particle systems
- Polygonization
- Topology
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Human-Computer Interaction
- Software
Cite this
Guaranteeing the topology of an implicit surface polygonization for interactive modeling. / Stander, Barton T.; 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 - Guaranteeing the topology of an implicit surface polygonization for interactive modeling
AU - Stander, Barton T.
AU - Hart, John C
PY - 2005/7/31
Y1 - 2005/7/31
N2 - Morse theory shows how the topology of an implicit surface is affected by its function's critical points, whereas catastrophe theory shows how these critical points behave as the function's parameters change. Interval analysis finds the critical points, and they can also be tracked efficiently during parameter changes. Changes in the function value at these critical points cause changes in the topology. Techniques for modifying the polygonization to accommodate such changes in topology are given. These techniques are robust enough to guarantee the topology of an implicit surface polygonization, and are efficient enough to maintain this guarantee during interactive modeling. The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
AB - Morse theory shows how the topology of an implicit surface is affected by its function's critical points, whereas catastrophe theory shows how these critical points behave as the function's parameters change. Interval analysis finds the critical points, and they can also be tracked efficiently during parameter changes. Changes in the function value at these critical points cause changes in the topology. Techniques for modifying the polygonization to accommodate such changes in topology are given. These techniques are robust enough to guarantee the topology of an implicit surface polygonization, and are efficient enough to maintain this guarantee during interactive modeling. The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.
KW - Catastrophe theory
KW - Critical points
KW - Implicit surfaces
KW - Interactive modeling
KW - Interval analysis
KW - Morse theory
KW - Particle systems
KW - Polygonization
KW - Topology
UR - http://www.scopus.com/inward/record.url?scp=84874940676&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874940676&partnerID=8YFLogxK
U2 - 10.1145/1198555.1198642
DO - 10.1145/1198555.1198642
M3 - Paper
AN - SCOPUS:84874940676
ER -