Linear constraints for deformable B-Spline surfaces

Proceedings of the Symposium on Interactive 3D Graphics

Volumn Part F129616, Issue , 1992, Pages 165-170

  Celnikera, George ^a   Welchb, Will ^b  

^a SCHLUMBERGER   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; INTERPOLATION; MECHANICS; TENSORS;

DEFORMATION ENERGY; FREE-FORM SURFACE; GEOMETRIC CONSTRAINT; INTERPOLATED POINTS; LINEAR CONSTRAINTS; QUADRATIC FUNCTIONALS; TENSOR PRODUCT B-SPLINES; UNCONSTRAINED SYSTEMS;

DEGREES OF FREEDOM (MECHANICS);

EID: 33747941641     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/147156.147191     Document Type: Conference Paper

References (22)

1. Baumgarte, J., "Stabilization of Constraints and Integrals of Motion in Dynamical Systems", Computer Methods in Applied Mechanics and Engineering, 1972.
2. Bloor, M.I.G. and Wilson, M.J., "Blend Design as a Boundary-Value Problem", Theory and Practice of Geometric Modeling, Wolfgang Staber and Hans-Peter Seidel (Eds.), 1989.
3. Celniker G., Gossard D., "Deformable Curve and Surface Finite-Elements for Free-Form Shape Design", Proceedings Siggraph '91, Las Vegas Nevada, 28 July - 2 August 1991.
4. Celniker G., Shape Wright: Finite Element Based Free- Form Shape Design, M.I.T. Ph.D., Dept. of Mechanical Engineering, September, 1990.
5. Gill, Phillip and Murray, Walter and Wright, Margaret, Practical Optimization. Academic Press, 1981.
6. Golub, Gene and Van Loan, Charles, Matrix Computations. 2nd ed., p 571. Johns Hopkins University Press, 1989.
7. Kass, Michael and Witkin, Andrew, and Terzopoulos, Demetri, "Snakes: Active Contour Models", International Journal of Computer Vision, 1988.
8. Kramer, Glen A., Solving Geometric Constraint Systems: A case study in kinematic, MIT Press, 1991, Cambridge Mass.
9. Lancos Cornelius, The variational Principles of Mechanics", 4th Edition, Dover, 1970.
10. Light, R.A. and Gossard, D.C., "Modification of Geometric Models through Variational Geometry", Computer Aided Design, 1982, vol. 14, no. 4.
11. Nielson, G.M., "Some piecewise polynomial alternatives to splines in tension", in Barnhill, RE and Riesenfeld, RF (eds) Computer Aided Geometric Design, Academic Press, 1974.
12. Nowacki, H. and Reese, D., "Design and fairing of ship surfaces", in Barnhill R.E. and Boehm, W. (eds), Surfaces in CAGD, North-Holland, Amsterdam, pp 121-134, 1983.
13. Piegl, Les, "On NURBS: A Survey", IEEE Computer Graphics and Applications, Jan 1991.
14. Piatt, John, "Constraint Methods for Neural Networks and Computer Graphics", PhD thesis, California Institute of Technology, 1989.
15. Pramila, A., "Ship Hull Surface design using finite elements", Int. Shipbuild. Prog. Vol. 25 No. 284, pp. 97-107, 1978.
16. Schweikert, D.G., "An interpolation curve using a spline in tension", Journal of Math and Phys. No 45, pp. 312-317, 1966.
17. Serano, D. and Gossard, D.C., "Constraint Management: A prerequisite to Conceptual Design", in Knowledge Based Expert Systems in Engineering: Planning and Design, Sriram, D. and Adey, R.A., editors, Computational Mechanics Publications, UK, 1987.
18. Strang, Gilbert, Introduction to Applied Mathematics, Wellesley-Cambridge Press, Massachusetts, 1986.
19. Welch, W., and Gleicher, M. and Witkin, A., "Manipulating surfaces differentially", proceedings Compugraphics 91 (Springer Verlog) also Carnegie Mellon Technical report CMU-CS-91-75.
20. Witkin, Andrew, and Fleischer, Kurt, and Barr, Alan, "Energy Constraints on Parameterized Models", Proceedings Siggraph '87, Anaheim, July 27-31 1987.
21. Terzopoulos, Demetri and Piatt, John and Barr, Alan and Fleischer, Kurt, "Elastic Deformable Models", ACM, Computer Graphics, vol. 21, no. 4, July, 1987.
22. Zienkiewicz, The Finite Element Method, third edition, McGraw-Hill Book Co., U.K., 1967.