Translating polygons with applications to hidden surface removal

  • Mark de Berg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 447)


Let S be a set of polygons in the plane with a total number of n vertices. A translation ordering for S (in direction d) is an ordering of the polygons such that, if the polygons are moved one by one to infinity in direction d according to this ordering, no collisions occur between the polygons. We show that, after O(n log n) preprocessing using O(n) space, it is possible to determine, for any given d, in O(log n) time whether such an ordering exists and, if so, to compute an ordering in O(n) time.

Translation orderings correspond to valid orderings for hidden surface removal schemes where objects that are closer to the viewpoint are displayed later than objects that are farther away. Thus our technique can be used to generate displaying orderings for polyhedral terrains. One of the main advantages of our approach is that it can easily be adapted to handle perspective views within the same time and space bounds.


Computational geometry separation problems hidden surface removal relative convex hulls 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Mark de Berg
    • 1
  1. 1.Dept. of Computer ScienceUniversity of UtrechtUtrechtthe Netherlands

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