Abstract
Curvature-based energy and forces are used in a broad variety of contexts, ranging from modeling of thin plates and shells to surface fairing and variational surface design. The approaches to discretization preferred in different areas often have little in common: engineering shell analysis is dominated by finite elements, while spring-particle models are often preferred for animation and qualitative simulation due to their simplicity and low computational cost. Both types of approaches have found applications in geometric modeling. While there is a well-established theory for finite element methods, alternative discretizations are less well understood: many questions about mesh dependence, convergence and accuracy remain unanswered. We discuss the general principles for defining curvature-based energy on discrete surfaces based on geometric invariance and convergence considerations. We show how these principles can be used to understand the behavior of some commonly used discretizations, to establish relations between some well-known discrete geometry and finite element formulations and to derive new simple and efficient discretizations.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings - International Conference on Shape Modeling and Applications, SMI'05 |
| Pages | 198-206 |
| Number of pages | 9 |
| Volume | 2005 |
| DOIs | |
| State | Published - 2005 |
| Event | International Conference on Shape Modeling and Applications, SMI'05 - Cambridge, MA, United States Duration: Jun 13 2005 → Jun 17 2005 |
Other
| Other | International Conference on Shape Modeling and Applications, SMI'05 |
|---|---|
| Country | United States |
| City | Cambridge, MA |
| Period | 6/13/05 → 6/17/05 |
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ASJC Scopus subject areas
- Engineering(all)
Cite this
Curvature-based energy for simulation and variational modeling. / Zorin, Denis.
Proceedings - International Conference on Shape Modeling and Applications, SMI'05. Vol. 2005 2005. p. 198-206 1563225.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Curvature-based energy for simulation and variational modeling
AU - Zorin, Denis
PY - 2005
Y1 - 2005
N2 - Curvature-based energy and forces are used in a broad variety of contexts, ranging from modeling of thin plates and shells to surface fairing and variational surface design. The approaches to discretization preferred in different areas often have little in common: engineering shell analysis is dominated by finite elements, while spring-particle models are often preferred for animation and qualitative simulation due to their simplicity and low computational cost. Both types of approaches have found applications in geometric modeling. While there is a well-established theory for finite element methods, alternative discretizations are less well understood: many questions about mesh dependence, convergence and accuracy remain unanswered. We discuss the general principles for defining curvature-based energy on discrete surfaces based on geometric invariance and convergence considerations. We show how these principles can be used to understand the behavior of some commonly used discretizations, to establish relations between some well-known discrete geometry and finite element formulations and to derive new simple and efficient discretizations.
AB - Curvature-based energy and forces are used in a broad variety of contexts, ranging from modeling of thin plates and shells to surface fairing and variational surface design. The approaches to discretization preferred in different areas often have little in common: engineering shell analysis is dominated by finite elements, while spring-particle models are often preferred for animation and qualitative simulation due to their simplicity and low computational cost. Both types of approaches have found applications in geometric modeling. While there is a well-established theory for finite element methods, alternative discretizations are less well understood: many questions about mesh dependence, convergence and accuracy remain unanswered. We discuss the general principles for defining curvature-based energy on discrete surfaces based on geometric invariance and convergence considerations. We show how these principles can be used to understand the behavior of some commonly used discretizations, to establish relations between some well-known discrete geometry and finite element formulations and to derive new simple and efficient discretizations.
UR - http://www.scopus.com/inward/record.url?scp=33846078647&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846078647&partnerID=8YFLogxK
U2 - 10.1109/SMI.2005.14
DO - 10.1109/SMI.2005.14
M3 - Conference contribution
AN - SCOPUS:33846078647
SN - 076952379X
SN - 9780769523798
VL - 2005
SP - 198
EP - 206
BT - Proceedings - International Conference on Shape Modeling and Applications, SMI'05
ER -