“Modeling surfaces of arbitrary topology using manifolds” by Grimm and Hughes
Conference:
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Title:
- Modeling surfaces of arbitrary topology using manifolds
Presenter(s)/Author(s):
Abstract:
We describe an extension of B-splines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of B-splines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral control mesh instead of a rectangular one; the resulting surface approximates the polyhedral mesh much as a B-spline approximates its rectangular control mesh. Like a B-spline, the surface is a single, continuousobject. This is achieved by modeling the domain of the surface with a manifold whose topology matches that of the polyhedral mesh, then embedding this domain into 3-space using a basis-function/control-point formulation. We provide a constructive approach to building a manifold.
References:
1. R. Bartels, J. Beatty, and B. Barsky. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann, 1987.
2. E. Catmull andJ. Clark. Recursively Generated B-spline Surfaces on Arbitrary Topological Meshes. Computer Aided Design, 10(6):350-355, November 1978.
3. G. Farin. Curves and Sulfaces for Computer Aided Geometric Design. Academic Press, 1988.
4. C. Grimm. Sulfaces of Arbitrary Topology using Manifolds. PhD thesis, Brown University (in progress).
5. M. Halstead, T. DeRose, and M. Kass. Efficient, Fair Interpolation Using Catmull-Clark Surfaces. Computer Graphics, 27(2):35-44, July 1993. Proceedings of SIG- GRAPH ’93 (Los Angeles).
6. K. Hollig and H. Mogerle. G-splines. Computer Aided Geometric Design, 7:197-207, 1990.
7. E King. On Local Combinatorial Pontrjagin Numbers (I). Topology, 16:99-106, 1977.
8. C. Loop and T. DeRose. A Multisided Generalization of B6zier Surfaces. ACM TOG, 8(3):204-234, July 1989.
9. C. Loop. Smooth Subdivision Surfaces Based on Triangles. Master’s thesis, University of Utah, 1987.
10. C. Loop. Smooth Spline Surfaces Over Irregular Meshes. Computer Graphics, 28(2):303-310, July 1994. Proceedings of SIGGRAPH ’94.
11. J. Milnor and J. Stasheff. Annals of Mathematical Studies. Princeton University Press, Princeton, New Jersey, 1974.
12. J. Maillot, H. Yahia, and A. Verroust. Interactive Texture Mapping. Computer Graphics, 27(4):27-35, July 1993. Proceedings of SIGGRAPH ’93.
13. E.H. Spanier. Algebraic Topology. McGraw-Hill Inc., New York, New York, 1966.
14. M. Spivak. Differential Geomen7 Volume 1. Publish or Perish Inc., 1970.
15. I.M. Singer and J. A. Thorpe. Lecture Notes on Elemental7 Topology and Geomet~7. Scott, Foresman and Company, Glenview, Illinois, 1967.
16. N. Steenrod. The Topology of Fibre Bundles. Princeton University Press, Princeton, New Jersey, 1974.
17. G. Turk. Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion. Computer Graphics, 25(2):289-298, July 1991. Proceedings of SIGGRAPH ’91 (Las Vegas).
18. W. Welch and A. Witkin. Variational Surface Modeling. Computer Graphics, 22(2):157-166, July 1992. Proceedings of SIGGRAPH ’92.
19. W. Welch and A. Witkin. Free Form Shape Design Using Triangulated Surfaces. Computer Graphics, 28(2):247-256, July 1994. Proceedings of SIGGRAPH ’94.
