Collinearity Constraints on Geometric Figures
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.
KeywordsInteger Point Geographic Information System Rensselaer Polytechnic Institute Collinear Point Line Arrangement
Unable to display preview. Download preview PDF.
- 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
- 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
- Knuth, D.E. (1981) The Art of Computer Programming - Seminumerical Algorithms (Vol. II), Addison Wesley, Reading, Massachusetts.Google Scholar
- 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
- 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
- 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