Advertisement

Feasibility of design in stereolithography

  • B. Asberg
  • G. Blanco
  • P. Bose
  • J. Garcia-Lopez
  • M. Overmars
  • G. Toussaint
  • G. Wilfong
  • B. Zhu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 761)

Abstract

We study the feasibility of design for a layer-deposition manufacturing process called stereolithography which works by controlling a vertical laser beam which when targeted on a photocurable liquid causes the liquid to harden. Given an object (modeled as a polygon or a polyhedron), we give algorithms that decide in O(n) time whether or not the object can be constructed using stereolithography. Furthermore, if the answer is in the affirmative, the algorithm reports a description of all the positions in space in which the object can be made. We also determine feasibility of both polygonal and polyhedral objects constructed using variable-angle stereolithography. We give an O(n) time algorithm for polygons and O(n log n) as well as O(n) time algorithms for polyhedra. We show that objects formed using variable-angle stereolithography can also be constructed using another manufacturing process known as injection molding. Finally, we show that the polyhedral objects formed by stereolithography are closely related to polyhedral terrains which are important structures in geographic information systems (GIS) and computational geometry. In fact, our algorithms recognize whether a polyhedral surface is a terrain that allows overhangs, thus initiating the study of more realistic terrains than the standard ones considered in geographic information systems.

Keywords

Geographic Information System Convex Hull Geographic Information System Injection Molding Time Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Bose and G. Toussaint. Geometric and computational aspects of injection molding. Technical Report No. SOCS 92.16, School of Computer Science, McGill University, 1992.Google Scholar
  2. 2.
    P. Bose and G. Toussaint. Geometric and computational aspects of injection molding. Proc. Third International Conf. on CAD and Computer Graphics, August 1993, Beijing, China, p. 237–242.Google Scholar
  3. 3.
    P. Bose, M. Van Kreveld and G. Toussaint. Filling Polyhedral Molds. Technical Report No. SOCS 93.1, School of Computer Science, McGill University, 1993.Google Scholar
  4. 4.
    P. Bose, M. Van Kreveld and G. Toussaint. Filling Polyhedral Molds, Proc. Third WADS (1993), Lecture Notes in Computer Science 709, Springer-Verlag, p. 210–221.Google Scholar
  5. 5.
    P. Bose, T. Shermer, G. Toussaint, and B. Zhu. Guarding Polyhedral Terrains, Proc. Allerton Conf., Urbana-Champaign, Ill., October 1992.Google Scholar
  6. 6.
    J. Bown. Injection Moulding of Plastic Components. McGraw-Hill, England, 1979.Google Scholar
  7. 7.
    R. Cole and M. Sharir. Visibility Problems for Polyhedral Terrains. Journal of Symbolic Computation, 7, p.11–30, 1989.Google Scholar
  8. 8.
    L. DeFloriani, B. Falcidieno, C. Pienovi, D. Allen, and G. Nagy. A visibility-based model for terrain features. Proc, 2nd International Symposium on Spatial Data Handling, p.235–250, 1986.Google Scholar
  9. 9.
    S. Fekete and J. Mitchell. Geometric aspects of injection molding. Manuscript, 1993.Google Scholar
  10. 10.
    A. Melkman. On-line construction of the convex hull of a simple polyline. Information Processing Letters, 25, p.11–12, 1987.Google Scholar
  11. 11.
    F. Preparata and S. Hong. Convex hulls of finite sets of points in two and three dimensions, Communications of the ACM, 2,20, p. 87–93, 1977.Google Scholar
  12. 12.
    F. Preparata and M. Shamos. Computational Geometry: An Introduction, Springer-Verlag, New York, New York, 1985.Google Scholar
  13. 13.
    A. Gajentaan and M.H. Overmars. O(n2) difficult problems in computational geometry. Technical Report, Dept of Computer Science, Utrecht University, 1993.Google Scholar
  14. 14.
    M. Goodchild and J. Lee. Coverage problems in visibility regions on topological surfaces. Annals of Operations Research, 18, p.175–186, 1989.Google Scholar
  15. 15.
    J. Lee. Analyses of visibility sites on topographic surfaces. Int. J. Geographic Information Systems, 5,4, p.413–429, 1991.Google Scholar
  16. 16.
    D. McCallum and D. Avis. A linear algorithm for finding the convex hull of a simple polygon, Information Processing Letters, 9, p.201–206, 1979.Google Scholar
  17. 17.
    A. Rosenbloom and R. Rappaport. Moldable and Castable Polygons, Proc. of the Fourth Canadian Conference on Computational Geometry, St. John's, Newfoundland, p. 322–327, 1992.Google Scholar
  18. 18.
    D. Watson and M. Yeung. Geometric modelling from CT scans for stereolithography. Proc. Third International Conf. on CAD and Computer Graphics, August 1993, Beijing, China, p. 417–422.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • B. Asberg
    • 1
    • 2
    • 3
    • 4
  • G. Blanco
    • 1
    • 2
    • 3
    • 4
  • P. Bose
    • 1
    • 2
    • 3
    • 4
  • J. Garcia-Lopez
    • 1
    • 2
    • 3
    • 4
  • M. Overmars
    • 1
    • 2
    • 3
    • 4
  • G. Toussaint
    • 1
    • 2
    • 3
    • 4
  • G. Wilfong
    • 1
    • 2
    • 3
    • 4
  • B. Zhu
    • 1
    • 2
    • 3
    • 4
  1. 1.Utrecht UniversityUtrechtNetherlands
  2. 2.Escuela Universitaria de Informatica MadridSpain
  3. 3.McGill UniversityMontrealCanada
  4. 4.AT & T Bell LabsNew JerseyUSA

Personalised recommendations