The Visual Computer

, Volume 11, Issue 5, pp 253–262 | Cite as

Quadric and cubic bitetrahedral patches

  • Baining Guo
Original Articles

Abstract

Algebraic surface patches bounded by tetrahedra are promising building blocks for low-degree implicit spline surfaces. General algebraic surface patches may have topological anomalies such as singular points and multiple sheets. The A-patch technique avoids many of these anomalies but does not ensure that the surface patches are connected and have no holes. Requiring these qualities often places overly restrictive conditions on the patch. We present a technique for building a bitetrahedral patch that is single sheeted, smooth, and singly connected in a pair of face-adjacent tetrahedra. The bitetrahedral patch technique is applicable to most low-degree algebraic surface patches, and it establishes single sheetedness, smoothness, and single connectness when existing techniques fail.

Key words

Solid modeling Algebraic surface 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bajaj C, Chen J, Xu G (1994) Modeling with cubic A-patches. Interactive modeling with A-patches. CSD-TR-93-002, revised version, West Lafayette, IndianaGoogle Scholar
  2. Blinn J (1982) A generalization of algebraic surface drawing. ACM Trans Graph 1:235–256Google Scholar
  3. Bloomenthal J, Wyvill B (1990) Interactive techniques for implicit modeling. Comput Graph 24:109–116Google Scholar
  4. Boehm W, Farin Q, Kahmann J (1984) A survey of curve and surface methods in CAGD. Computer-aided Geometric Design 1:1–60Google Scholar
  5. Dahmen W (1989) Smooth piecewise quadric surfaces. In: Lyche T, Schumaker L (eds) Mathematical methods in CAGD pp 181–193Google Scholar
  6. Dahmen W, Thamm-Schaar T-M (1993) Cubicoids: modeling and visualization. Computer-aided Geometric Design 10:89–108Google Scholar
  7. Duff T (1992) Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry. Comput Graph 26:131–138Google Scholar
  8. Farin G (1985) Triangular Bernstein Bézier patches. Computer-aided Geometric Design 3:83–127Google Scholar
  9. Guo B (1991) Modeling arbitrary smooth objects with algebraic surfaces. Ph.D. Thesis, Department of Computer Science, Cornell University, Ithaca, New York, USAGoogle Scholar
  10. Ihm I (1991) Surface design with implicit algebraic surfaces. Ph.D. Thesis, Department of Computer Science, Purdue University, West Lafayette, Indiana, USAGoogle Scholar
  11. Lodha S (1992) Surface approximation with low-degree patches with multiple representations. Ph.D. Thesis, Department of Computer Science, Rice University, Houston, Texas, USAGoogle Scholar
  12. Lounsgery M, Mann S, DeRose T (1992) Parametric surface interpolation. IEEE Comput Graph Appl 9:45–52Google Scholar
  13. Menon J (1994) Constructive shell representations for free-form surfaces and solids. IEEE Comput Graph Appl 14:24–36Google Scholar
  14. Moore D, Warren J (1990) Adaptive approximation of scattered contour data using piece-wise implicit surfaces. Technical Report TR90-135, Department of Computer Science, Rice University, Houston, Texas, USAGoogle Scholar
  15. Patrikalakis N, Kriezis G (1989) Representation of piecewise continuous algebraic surfaces in terms of B-splines. Vis Comp 5:360–374Google Scholar
  16. Peters J (1990) Fitting smooth parametric surfaces to 3D data. Ph.D. Thesis, Center for Mathematical Sciences, University of Wisconsin-Madison, Madison, Wisconsin, USAGoogle Scholar
  17. Rockwood A, Owen J (1987) Blending surfaces in solid geometric modeling. In: Farin G (ed) Geometric modeling: algorithms and new trendsGoogle Scholar
  18. Sclaroff S, Pentland A (1991) Generalized implicit functions for computer graphics. Comput Graph 25:247–250Google Scholar
  19. Sederberg TW (1985) Piecewise algebraic surface patches. Computer-aided Geometric Design, 2:53–59Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Baining Guo
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada

Personalised recommendations