Cited By
View all- Tang ZZou QGao S(2023)A decision-support method for multi-parameter editing of parametric CAD modelsAdvanced Engineering Informatics10.1016/j.aei.2023.10199756(101997)Online publication date: Apr-2023
A constructive approach to calculate parameter ranges for systems of geometric constraints
Pages 135 - 142
Abstract
Geometric constraints are at the heart of parametric and feature-based CAD systems. Changing values of geometric constraint parameters is one of the most common operations in such systems. However, because allowable parameter values are not known to the user beforehand, this is often a trial-and-error process. We present a solution for automatically determining the allowable range for parameters of geometric constraints. Considered are systems of distance and angle constraints on points in 3D that can be decomposed into triangular and tetrahedral subproblems, by which most practical situations in parametric and feature-based CAD systems can be represented. Our method uses the decomposition to find critical parameter values for which subproblems degenerate. By solving one problem instance for each interval between two subsequent critical values, the exact parameter ranges are determined for which a solution exists.
References
[1]
Bettig, B., and Shah, J. 2003. Solution selectors: a user-oriented answer to the multiple solution problem in constraint solving. Journal of Mechanical Design 125, 3, 443--451.
[2]
Bidarra, R., and Bronsvoort, W. F. 2000. Semantic feature modelling. Computer-Aided Design 32, 3, 201--225.
[3]
Bouma, W., Fudos, I., Hoffmann, C., Cai, J., and Paige, R. 1995. A geometric constraint solver. Computer-Aided Design 27, 6, 487--501.
[4]
Essert-Villard, C., Schreck, P., and Dufourd, J.-F. 2000. Sketch-based pruning of a solution space within a formal geometric constraint solver. Artificial Intelligence 124, 1, 139--159.
[5]
Fudos, I., and Hoffmann, C. M. 1997. A graph-constructive approach to solving systems of geometric constraints. ACM Transactions on Graphics 16, 2, 179--216.
[6]
Hoffmann, C. M., and Kim, K.-J. 2001. Towards valid parametric CAD models. Computer-Aided Design 33, 1, 81--90.
[7]
Hoffmann, C. M., and Vermeer, P. J. 1995. Geometric constraint solving in R2 and R3. In Computing in Euclidean Geometry, Second Edition, World Scientific Publishing, Singapore, D. Du and F. Hwang, Eds., 266--298.
[8]
Hoffmann, C. M., Lomonosov, A., and Sitharam, M. 2001. Decomposition plans for geometric constraint systems, Part I: performance measures for CAD. Journal of Symbolic Computation 31, 4, 376--408.
[9]
Joan-Arinyo, R., and Mata, N. 2001. Applying constructive geometric constaint solvers to geometric problems with interval parameters. Nonlinear Analysis - Theory, Methods & Application 47, 1, 213--224.
[10]
Noort, A., and Bronsvoort, W. F. 2001. Enforcing model validity by automatic adjustment. Journal of Computing and Information Science in Engineering 1, 4, 311--319.
[11]
Oung, J., Sitharam, M., Moro, B., and Arbree, A. 2001. FRONTIER: fully enabling geometric constraints for feature-based modeling and assembly. In Proceedings of Solid Modeling '01, Sixth ACM Symposium on Solid Modeling and Applications, June 4--8, Ann Arbor, USA, ACM Press, New York, D. C. Anderson and K. Lee, Eds., 307--308.
[12]
Podgorelec, D. 2002. A new constructive approach to constraint-based geometric design. Computer-Aided Design 34, 11, 769--785.
[13]
Raghothama, S., and Shapiro, V. 2000. Consistent updates in dual representation systems. Computer-Aided Design 32, 8--9, 463--477.
[14]
Shapiro, V., and Vossler, D. L. 1995. What is a parametric family of solids? In Proceedings of the Third ACM/IEEE Symposium on Solid Modelling and Applications, May 17--19, Salt Lake City, USA, ACM Press, New York, C. M. Hoffmann and J. R. Rossignac, Eds., 43--54.
[15]
van der Meiden, H. A., and Bronsvoort, W. F. 2004. An efficient method to determine the intended solution for a system of geometric constraints. Submitted for publication; available upon request.
[16]
Weisstein, E. W. 2004. Degenerate. From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/Degenerate.html.
Index Terms
- A constructive approach to calculate parameter ranges for systems of geometric constraints
Recommendations
A graph-constructive approach to solving systems of geometric constraints
A graph-constructive approach to solving systems of geometric constraints capable of effeciently handling well-constrained, overconstrained, and underconstrained configurations is presented. The geometric constraint solver works in two phases: in the ...
A constructive approach to calculate parameter ranges for systems of geometric constraints
Geometric constraints are at the heart of parametric and feature-based CAD systems. Changing values of geometric constraint parameters is one of the most common operations in such systems. However, because allowable parameter values are not known to the ...
Computing parameter ranges in constructive geometric constraint solving: Implementation and correctness proof
In parametric design, changing values of parameters to get different solution instances to the problem at hand is a paramount operation. One of the main issues when generating the solution instance for the actual set of parameters is that the user does ...
Comments
Information & Contributors
Information
Published In
Copyright © 2005 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 13 June 2005
Check for updates
Author Tags
Qualifiers
- Article
Conference
SPM05
Sponsor:
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 253Total Downloads
- Downloads (Last 12 months)5
- Downloads (Last 6 weeks)0
Reflects downloads up to 05 Mar 2025
Other Metrics
Citations
Cited By
View all- Tang ZZou QGao S(2023)A decision-support method for multi-parameter editing of parametric CAD modelsAdvanced Engineering Informatics10.1016/j.aei.2023.10199756(101997)Online publication date: Apr-2023
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in