A New Point Containment Algorithm for B_Regions in the Discrete Plane

  • Marc Corthout
  • Hans Jonkers
Conference paper
Part of the NATO ASI Series book series (volume 40)

Abstract

The point containment predicate which specifies if a point is part of a mathematically defined region or not is one of the most basic notions in raster graphics. In many applications spatial coherence is used to compute the value of this predicate for a set of points at the same time: scan conversion filling is the most wide spread technique. Although the mathematics behind these techniques may seem straightforward, we show that their computer implementations are far from trivial. The latter fact may even preclude the beneficial use of coherence if one strives for simple, robust, and parallel hardware.

Keywords

Coherence Hull Borate Lution Dition 

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References

  1. [Ado]
    Adobe Systems. Postscript language reference manual. Addison-Wesley, 1985.Google Scholar
  2. [Bau]
    Bauer, F.L., et al. The Munich Project CIP, Volume I: the Wide Spectrum Language CIP-L. Lecture Notes in Computer Science 183. Springer-Verlag (1985).MATHGoogle Scholar
  3. [Boh]
    Bohm, W., Farin, G., Kahmann, J. A Survey of Curve and Surface Methods in CAGD. Computer Aided Geometric Design, Vol. 1 (1984), 1–60.CrossRefGoogle Scholar
  4. [Bre]
    Bresenham, J.E. Algorithm for computer control of a digital plotter. IBM Systems J.4, 1 (1965), 25–30.CrossRefGoogle Scholar
  5. [Bur]
    Burton, F.W., Kollias, V.J., KOLLIAS, J.G. Consistency in Point-in-Polygon Tests. The Computer Journal, Vol. 27, No.4 (1984).Google Scholar
  6. [Cha]
    Chazelle, B., Dobkin, D. Detection is Easier than Computation. Annual ACM Symposium on Theory of Computing, Los Angeles (1980), 146–153.Google Scholar
  7. [CoJoa]
    Corthout, M.E., Jonkers, H.B.M. The transformational development of a new point containment algorithm. Philips Journal of Research, Vol.41 (1986), 83–174.MATHGoogle Scholar
  8. [CoJob]
    Corthout, M.E., Jonkers, H.B.M. A Formal Framework for Discrete Geometry: Theory and Graphics Applications. Submitted for publication in ACM Transactions on Graphics.Google Scholar
  9. [Cou]
    Courant, R., Robbins, H. What is mathematics? Oxford University Press (1941).Google Scholar
  10. [Dijk]
    Dπkstra, E.W. A Discipline of Programming. Prentice-Hall (1976).Google Scholar
  11. [Dun]
    Dunlavey, M.R. Efficient Polygon-Filling Algorithms for Raster Displays. ACM Transactions on Graphics, Vol. 2, No.4 (October 1983), 264–273.Google Scholar
  12. [For]
    Forrest, A.R. Computational Geometry in Practice. Fundamental Algorithms for Computer Graphics Ed.R.A.Earnshaw. Springer-Verlag (1985).Google Scholar
  13. [Gui]
    Guibas, L.J., Ramshaw, L., Stolfi, J. A kinetic framework for computational geometry. IEEE 24th Annual Symposium on Foundations of Computer Science (1983), 100–111.Google Scholar
  14. [HiLe]
    Hill, C, Lee, K.P. Two Proofs of a Sign Propagation Property in a Labeled Graph. Internal Report PL-TN-86–068 (1986).Google Scholar
  15. [Jon]
    Jonkers, H.B.M. The single linguistic framework. Technical Report, ESPRIT Project FAST (Formal Approach to Software Technology) (1984).Google Scholar
  16. [Lan]
    Lane, J.M., Riesenfeld, R.F. A theoretical development for the computer generation and display of piecewise polynomial surfaces. IEEE Transactions on PAMI, Vol. PAMI-2, No.l (1980), 35–46.Google Scholar
  17. [Pavfl]
    Pavlidis, T. Algorithms for Graphics and Image Processing. Springer-Verlag (1982).CrossRefGoogle Scholar
  18. [Pavfc]
    Pavlidis, T. Scan Conversion of Regions Bounded by Parabolic Splines. IEEE CG&A, (June 1985), 47–53.Google Scholar
  19. [Pep]
    Pepper, P. Programming Transformation and Programming Environments. Report on a Workshop directed by F.L. Bauer and H. Remus. Springer-Verlag (1984).MATHGoogle Scholar
  20. [Praα]
    Pratt, V. Techniques for Conic Splines. Computer Graphics, Vol. 19, No.3 (1985), 151–159.CrossRefGoogle Scholar
  21. [Prafc]
    Pratt, V. Private Communication, August 1, 1985.Google Scholar
  22. [Spr]
    Sproull, R.F. Using Program Transformations to Derive Line-Drawing Algorithms. ACM Transactions on Graphics, Vol.1, No.4 (October 1982), 259–273.CrossRefGoogle Scholar
  23. [Wyk]
    VAN Wyk, C.J. Clipping on the Boundary of a Circular-arc Polygon. Computer Vision, Graphics, and Image Processing, Vol. 25 (1984), 383–392.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Marc Corthout
    • 1
  • Hans Jonkers
    • 1
  1. 1.Philips Research LaboratoriesEindhovenThe Netherlands

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