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TECHNICAL PAPERS

Surface Feature Parametrization Analogous to Conductive Heat Flow

[+] Author and Article Information
Anne L. Marsan

Yifan Chen, Paul J. Stewart

Manufacturing Systems Department, Ford Research Laboratory, 2010 Village Road, P.O. Box 2053, MD 3135, SRL, Dearborn, MI 48121-2053

J. Comput. Inf. Sci. Eng 2(2), 77-85 (Sep 25, 2002) (9 pages) doi:10.1115/1.1510860 History: Received January 01, 2002; Revised August 01, 2002; Online September 25, 2002
Copyright © 2002 by ASME
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References

Stewart, P. J., 1991, Direct Shape Control of Free-Form Curves and Surfaces with Generalized Basis Functions, Ph.D. dissertation, The University of Michigan, Ann Arbor.
Stewart, P. J., and Chen, Y., 1999, “Geometric Features Applied to Composite Surfaces Using Spherical Reparameterization,” Proceedings of the ASME 1999 Design Engineering Technical Conferences, Sept. 12–15, Las Vegas, NV.
Chen, Y., Stewart, P. J., Buttolo, P., and Ren, F., 2000, “A Real-time, Interactive Method for Fast Modification of Large-scale CAE Mesh Models,” Proceedings of the ASME 2000 Design Engineering Technical Conferences, Sept. 10–13, Baltimore, MD.
Sederberg,  T. W., and Parry,  S. R., 1986, “Free-form Deformation of Solid Geometric Models,” Proceedings of the ACM SIGGRAPHComputer Graphics, 20(4), pp. 151–160.
Farin, G., 1993, Curves and Surface for CAGD: A Practical Guide, 3d. ed., Academic Press, Boston.
Bloor, M. I. G., and Wilson, M. J., 1989, “Blend Design as a Boundary-value Problem,” Theory and Practice of Geometric Modeling, W. Staber and H.-P. Seidel, eds., Springer-Verlag, Berlin.
Celniker, G., and Gossard, D., 1989, “Energy-based Models for Free-form Surface Shape Design,” Proceedings of the ASME 1989 Design Automation Conference, Sept. 17–21, Montreal, QC, Canada.
Celniker,  G., and Gossard,  D., 1991. “Deformable Curve and Surface Finite-elements for Free-form Shape Design,” Comput. Graphics, 25(4), pp. 257–266.
Terzopoulos,  D., and Qin,  H., 1994. “Dynamic NURBS with Geometric Constraints for Interactive Sculpting,” ACM Trans. Graphics, 13(2), pp. 103–136.
Du, H., and Qin, H., 2001, “Integrating Physicals-based Modeling with PDE Solids for Geometric Design,” Proceedings of Ninth Pacific Conference on Computer Graphics and Applications (Pacific Graphics, 2001), Tokyo, Japan, October 16–18, pp. 198–207.
Du, H., and Qin, H., 2000, “Dynamic PDE Surfaces with Flexible and General Geometric Constraints,” Proceedings of Eighth Pacific Conference on Computer Graphics and Applications (Pacific Graphics, 2000), Hong Kong, October 3–5, pp. 213–222.
Du, H., and Qin, H., 2000, “Direct Manipulation and Interactive Sculpting of PDE Surfaces,” Computer Graphics Forum (Proceedings of Eurographics 2000 Graphics), 19 (3), C261-C270, Interlaken, Switzerland, August 21–25.
Qin,  H., and Terzopoulos,  D., 1996. “D-NURBS: A Physics-based Geometric Design Framework,” IEEE Trans. Vis. Comput. Graph., 2(1), pp. 85–96.
Incropera, F. P., and Dewitt, D. P., 1996, Fundamentals of Heat and Mass Transfer, 4th ed., John Wiley & Sons, New York.
Edwards, C. H. Jr., and Penney, D. E., 1993, Elementary Differential Equations with Boundary Value Problems, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ.
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Figures

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A basis function used to compute the magnitude of displacement within a DSM feature
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DSM features with various influence centers: a point (a), an open curve (b), and a closed curve (c). In all figures the DSM features have been added to a finite element model of the hood of an automobile for an aerodynamics simulation.
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An automobile floorpan showing some of the many features that can be modeled with DSM
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Computing the parameter value for a point p when the influence center is a point (a) and a closed curve (b)
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Two cases in which radial parameterization does not work: (a) the constructed line crosses the boundary curve at more than one point; and (b) more than one line can be constructed normal to the influence center.
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A car door inner panel. The base shape in the middle of the lower half of the door assembly (as indicated by a thick border curve) can be modeled by a non-convex DSM feature.
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(a) Shown is the boundary and influence center for a DSM feature. (b) The DSM feature has been mapped to an annulus.
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This plot shows the parameter value u as a function of r for an annulus with inner radius of 0.25 and outer radius of 1.0.
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These two graphs show parameter distributions for two different annuli. The one in (a) has an inner radius of 0.1 and the one in (b) has an inner radius of 0.001.
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The linear triangular element used to solve the Dirichlet problem
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Two DSM features, both with the same boundary curve and point influence center. The feature in (a) uses a radial parameterization, while the one in (b) uses a Dirichlet parameterization.
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Two DSM features, both with the same boundary curve and open curve influence center. The feature in (a) uses a radial parameterization, while the one in (b) uses a Dirichlet parameterization.
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Two DSM features, both with the same boundary curve and closed curve influence center. The feature in (a) uses a radial parameterization, while the one in (b) uses a Dirichlet parameterization.
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A single DSM feature with three different basis functions applied to it. The basis function for each case is shown next to the feature.
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A DSM feature with a non-star-shaped closed curve influence center computed using (a) radial parameterization and (b) Dirichlet parameterization
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A non-star-shaped DSM feature using (a) radial and (b) Dirichlet parameterization used to modify the hood of a vehicle near the windshield
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A multiply connected DSM feature created with Dirichlet parameterization.

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