“Smooth spline surfaces over irregular meshes” by Loop

  • ©Charles Loop

Conference:


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Title:

    Smooth spline surfaces over irregular meshes

Presenter(s)/Author(s):



Abstract:


    An algorithm for creating smooth spline surfaces over irregular meshes is presented. The algorithm is a generalization of quadratic B-splines; that is, if a mesh is (locally) regular, the resulting surface is equivalent to a B-spline. Otherwise, the resulting surface has a degree 3 or 4 parametric polynomial representation. A construction is given for representing the surface as a collection of tangent plane continuous triangular Be´zier patches. The algorithm is simple, efficient, and generates aesthetically pleasing shapes.

References:


    1. E. Catmull and J. Clark. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design, 10(6):350-355, 1978.
    2. H. Chiyokura and F. Kimura. Design of solids with free-form surfaces. In Proceedings of SIGGRAPH ’83, pages 289-298. 1983.
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    4. D. Doo. A subdivision algorithm for smoothing down irregularly shaped polyhedrons. In Proceedings on Interactive Techniques in Computer Aided Design, pages 157-165. Bologna, 1978.
    5. G. Farin. Curves and Surfaces for Computer Aided Geometric Design. Academic Press, third edition, 1993.
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    8. K. H~ ollig and Harald M~ ogerle. G-splines. Computer Aided Geometric Design, 7:197-207, 1990.
    9. C. Loop. Generalized B-spline Surfaces of Arbitrary Topological Type. PhD thesis, University of Washington, 1992.
    10. C. Loop. Smooth low degree polynomial spline surfaces over irregular meshes. Technical Report 48, Apple Computer Inc., Cupertino, CA, January 1993.
    11. C. Loop. A G 1 triangular spline surface of arbitrary topological type. Computer Aided Geometric Design, 1994. to appear.
    12. C. Loop and T. DeRose. Generalized B-spline surfaces of arbitrary topology. In Proceedings of SIGGRAPH ’90, pages 347-356. 1990.
    13. J. Peters. C 1 free-form surface splines. Technical Report CSD-TR-93-019, Dept. of Comp. Sci., Purdue University, W-Lafayette, IN, March 1993.
    14. J. Peters. Smooth free-form surfaces over irregular meshes generalizing quadratic splines. Computer Aided Geometric Design, 10:347-361, 1993.
    15. J. Peters. Constructing C 1 surfaces of arbitrary topology using biquadratic and bicubic splines. In N. Sapidis, editor, Designing Fair Curves and Surfaces. 1994. to appear.
    16. U. Reif. Biquadratic G-spline surfaces. Technical report, Mathematisches Institut A, Universit~ at Stuttgart, Pfaffenwaldring 57, D-7000 Stuttgart 80, Germany, 1993.
    17. M. Sabin. Non-rectangular surface patches suitable for inclusion in a B-spline surface. In P. ten Hagen, editor, Proceedings of Eurographics ’83, pages 57-69. North-Holland, 1983.
    18. J. van Wijk. Bicubic patches for approximating nonrectangular control-point meshes. Computer Aided Geometric Design, 3(1):1-13, 1986.


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