Collinearity Constraints on Geometric Figures

  • Maharaj Mukherjee
  • George Nagy
Conference paper
Part of the IFIP Series on Computer Graphics book series (IFIP SER.COMP.)

Abstract

The preservation of collinearity relationships under geometric operations is important in computer-graphics applications that manipulate line arrangements in engineering drawings and geographic information systems. Finite-precision computer implementations of these operations do not generally preserve these relationships. We show that for a wide class of line arrangements, any specified collinearity relationships can be preserved, without extending the precision, at the expense of a bounded displacement of the vertices of the arrangement.

Keywords

Expense Line Intersection Sine Itan 

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References

  1. Coxeter, H.S.M. (1961) Introduction to Geometry, John Wiley & Sons.MATHGoogle Scholar
  2. Dobkin, D., Silver, D. (1988) Recipes for geometry and numerical analysis - part I: An empirical study, Proceedings of the ACM Symposium on Computational Geometry, Champaign-Urbana, Illinois, pp. 93–105.Google Scholar
  3. Franklin, W.R. (1984) Cartographic errors symptomatic of underlying algebra problems, Proceedings of the International Symposium on Spatial Data Handling, pp. 190–208, Zurich, Switzerland.Google Scholar
  4. Knuth, D.E. (1981) The Art of Computer Programming - Seminumerical Algorithms (Vol. II), Addison Wesley, Reading, Massachusetts.Google Scholar
  5. Mehta, S., Mukherjee, M., Nagy, G. (1991) Constrained integer approximation to planar line intersections, Information Processing Letters, V.40, N. 3, pp. 137–139.MathSciNetMATHCrossRefGoogle Scholar
  6. Mehta, S., Mukheijee, M., Nagy, G. (1992) Integer approximation of collinear rational points, Rensselaer Polytechnic Institute Computational Geometry Laboratory Technical Report #92-1122.Google Scholar
  7. Mukherjee, M., Nagy, G. (1992a) Collinearity constraints on spatial subdivision algorithms with finite precision, Proc. Int. Symp. on Spatial Data Handling, Charleston, pp. 424–433.Google Scholar
  8. Mukherjee, M., Mehta, S., Nagy, G. (1992b) Integer approximation to the intersection of three planes with planar constraints, in Computer Graphics and Mathematics, Ed: B. Falcidieno, I. Herman, C. Pienovi, Springer-Verlag, pp 3–22.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Maharaj Mukherjee
    • 1
  • George Nagy
    • 2
  1. 1.Indian Institute of TechnologyKharagpurIndia
  2. 2.Rensselaer Polytechnic InstituteTroyUSA

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