Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Mourrain et al. Synaps Library, web interface http://www-sop.inria.fr/ galaad/logiciels/synaps/html/index.html
R. Latham and A. Middleditch. Connectivity analysis: a tool for processing geometric constraints. Computer Aided Design, 28:917-928, 1996.
C. M. Hoffmann, A. Lomonosov and M. Sitharam. Geometric constraint decom-position. In Bruderlin and Roller Ed.s, editor, Geometric Constraint Solving. Springer-Verlag, 1998.
C. M. Hoffmann, A. Lomonosov and M. Sitharam. Decomposition of geometric constraints systems, part i: performance measures. Journal of Symbolic Computation, 31(4), 2001.
C. M. Hoffmann, A. Lomonosov and M. Sitharam. Decomposition of geometric constraints systems, part ii: new algorithms. Journal of Symbolic Computation, 31 (4),2001.
J. E. Graver, B. Servatius and H. Servatius. Combinatorial Rigidity. Graduate Studies in Math., AMS, 1993.
I. Fudos and C. M. Hoffmann. A graph-constructive approach to solving systems of geometric constraints. ACM Transactions on Graphics, 16:179-216, 1997.
A. Middleditch and C. Reade. A kernel for geometric features. In ACM/SIGGRAPH Symposium on Solid Modeling Foundations and CAD/CAM Applications. ACM press, 1997.
D. Cox, J. Little and D. O’Shea. Using algebraic geometry. Springer, 1998.
I. Emiris and J. Canny. A practical method for the sparse resultant. In In-ternational Conference on Symbolic and Algebraic Computation, Proceedings of the 1993 international symposium on Symbolic and algebraic computation, pages 183-192, 1993.
C Hoffman, M Sitharam and B Yuan. Making constraint solvers more useable: the overconstraint problem. CAD, 36(4), 377-399, 2004. 216Jörg Peters, Meera Sitharam, Yong Zhou, and JianHua Fan
A. Lomonosov and M. Sitharam. Graph algorithms for geometric constraint solving. In submitted, 2004.
S. Ait-Aoudia, R. Jegou and D. Michelucci. Reduction of constraint systems. In Compugraphics, pages 83-92, 1993.
J Gaukel. Effiziente Lösung polynomialer und nichtpolynomialer Gleichungssys-teme mit Hilfe von Subdivisionsalgorithmen, PhD thesis, Mathematics, TU Darmstadt, Germany, 2003.
M Sitharam and Y Zhou. A tractable, approximate, combinatorial 3d rigidity characterization. proceedings of ADG 2004, 2004.
H. Crapo. Structural rigidity. Structural Topology, 1:26-45, 1979.
H. Crapo. The tetrahedral-octahedral truss. Structural Topology, 7:52-61, 1982.
M Sitharam, J. Peters and Y Zhou. Solving minimal, wellconstrained, 3D geo-metric constraint systems: combinatorial optimization of algebraic complexity submitted, http://www.cise.ufl.edu/∼sitharam, 2004.
M Sitharam, A. Arbree, Y Zhou and N Kohareswaran. Solution management and navigation for 3d geometric constraint systems. to appear, ACM TOG, 2005.
D. Eppstein. Representing all minimum spanning trees with applications to counting and generation. Technical Report 95-50, Univ. of California, Irvine, Dept. of Information & Computer Science, Irvine, CA, 92697-3425, USA, 1995.
I. Fudos. Geometric Constraint Solving. PhD thesis, Purdue University, Dept of Computer Science, 1995.
G. Kramer. Solving Geometric Constraint Systems. MIT Press, 1992.
G. Laman. On graphs and rigidity of plane skeletal structures. J. Engrg. Math., 4:331-340, 1970.
J. Owen. www.d-cubed.co.uk/. In D-cubed commercial geometric constraint solving software.
J. Owen. Algebraic solution for geometry from dimensional constraints. In ACM Symp. Found. of Solid Modeling, pages 397-407, Austin, Tex, 1991.
J. Owen. Constraints on simple geometry in two and three dimensions. In Third SIAM Conference on Geometric Design. SIAM, November 1993. To appear in Int J of Computational Geometry and Applications.
J.A. Pabon. Modeling method for sorting dependencies among geometric enti-ties. In US States Patent 5,251,290, Oct 1993.
M. Sitharam. Frontier, an opensource 3d geometric constraint solver: algorithms and architecture. monograph, in preparation, 2004.
M. Sitharam. Graph based geometric constraint solving: problems, progress and directions. In Dutta and Janardhan and Smid, editor, AMS-DIMACS volume on Computer Aided Design, 2004.
M. Sitharam. Frontier, opensource gnu geometric constraint solver: Version 1 (2001) for general 2d systems; version 2 (2002) for 2d and some 3d systems; version 3 (2003) for general 2d and 3d systems. In http://www.cise.ufl.edu/ ∼sitharam, http://www.gnu.org, 2004.
B. Huber and B. Sturmfels. A polyhedral method for solving sparse polynomial system. Math. Comp., 64:1541-1555, 1995.
W. Whiteley. Rigidity and scene analysis. In Handbook of Discrete and Computational Geometry, pages 893 -916. CRC Press, 1997.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peters, J., Sitharam, M., Zhou, Y., Fan, J. (2006). Elimination in generically rigid 3D geometric constraint systems. In: Elkadi, M., Mourrain, B., Piene, R. (eds) Algebraic Geometry and Geometric Modeling. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33275-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-33275-6_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33274-9
Online ISBN: 978-3-540-33275-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)