George Celniker
Abstract
The finite element method is applied to generate primitives that build continuous deformable shapes designed to support a new free-form modeling paradigm. The primitives autonomously deform to minimize an energy functional subject to user controlled geometric constraints and loads. The approach requires less user input than conventional free-form modeling approaches because the shape can be parameterized independently of the number of degrees of freedom needed to describe the shape.Both a curve and a surface finite element are developed. The properties of these geometric primitives have been engineered to support an interactive three phase approach for defining very fair free-form shapes as found in automobiles, ship hulls and car bodies. The shape's character lines or folds and edges are defined with deformable curve segments. These character lines are then "skinned" with a deformable surface. The final shape is sculpted interactively by applying loads to the surface to control the surface shape between character lines. Shapes created with this technique enjoy the advantage that they are already meshed for further finite element analysis.
- 1 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 Google Scholar
Digital Library
- 2 Celniker G., Gossard D., "Energy-Based Models for Free-Form Surface Shape Design", ASME Design Automation Conference, Montreal Canada. Sep. 1989Google Scholar
- 3 Celniker G., ShapeWright: Finite Element Based Free- Form Shape Design, M.I.T. Ph.D., Dept. of Mechanical Engineering, September, 1990Google Scholar
- 4 Farin, Gerald and Sapidis, Nickolas, "Shape Representation of Sculpted Objects: the Fairness of Curves and Surfaces", Proceeding of Sea Grant Conference, MIT, October, 1988Google Scholar
- 5 Farin, Gerald, Curves and Surfaces for Computer Aided Geometric Design, Academic Press Inc., Harcourt Brace Jovanovich Publishers, Boston, 1988 Google ScholarDigital Library
- 6 Hagen, H., and Schulze, G., "Automatic Smoothing with Geometric Surface Patches", Computer Aided Geometric Design, Vol. 4, pp. 231-236, 1987 Google ScholarDigital Library
- 7 Kass, Michael and Witkin, Andrew, and Terzopoulos, Demetri, "Snakes" Active Contour Models", International Journal of Computer Vision, 1988Google ScholarCross Ref
- 8 Kallay, Michael and Ravani B., "Optimal twist vectors as a tool for interpolation a Network of curves with a minimal energy surface", CAGD, 1990 Google ScholarDigital Library
- 9 Kjellander, J.A., "Smoothing of bicubic parametric surfaces", Computer-Aided Design, Vol. 15, pp. 288- 293, 1983Google ScholarCross Ref
- 10 Kjellander, J.A.P., "Smoothing of cubic parametric splines", Computer-Aided Design, vol 15, No. 3, May, 1983Google Scholar
- 11 Lott, N.J. and Pullin, D.I., "Methods for fairing B- Spline surfaces", Computer-Aided Design, vol. 20, no. 10, December, 1988 Google ScholarDigital Library
- 12 Nielson, G.M., "Some piecewise polynomial alternatives to splines in tension", in Bamhill, RE and Riesenfeld, RF (eds) Computer Aided Geometric Design, Academic Press, 1974Google Scholar
- 13 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, 1983Google Scholar
- 14 Pramila. A., "Ship Hull Surface design using finite elements", Int. Shipbuild. Prog. Vol. 25 No. 284, pp. 97-I07, 1978Google ScholarCross Ref
- 15 Sacks, E., and Stoops, D. and Roberts, A., "3-Draw: A Three Dimensional Computer Aided Design Tool", proceedings IEEE international conference of systems, man, and cybernetics, pp 1194-1196, November 1989Google ScholarCross Ref
- 16 Sapidis, N. and Farin, G., "Automatic fairing algorithm for B-spline curves", Computer-Aided Design, Vol. 22, No. 2 pp. 121-129, March 1990 Google ScholarDigital Library
- 17 Schweikert, D.G., "An interpolation curve using a spline in tension", Journal of Math and Phys. No 45, pp. 312-317, 1966Google ScholarCross Ref
- 18 Strang, Gilbert, Introduction to Applied Mathematics, Wellesley-Cambridge Press, Massachusetts, 1986Google Scholar
- 19 Terzopoulos, Demetri and Plait, John and Barr, Alan and Fleischer, Kurt, "Elastic Deformable Models", ACM, Computer Graphics, vol. 21, no. 4, July, 1987 Google ScholarDigital Library
- 20 Zienkiewicz, The Finite Element Method, third edition, McGraw-Hill Book Co., U.K., 1967Google Scholar
Index Terms
- Deformable curve and surface finite-elements for free-form shape design
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