Geometric data structures for computer graphics: an overview
The quad-tree is probably the most well-known data structure in computer graphics. Quad-trees can be used to store planar objects, both in image space and in object space. They use little storage and often allow for fast retrieval of geometric information.
Range trees are a clear example of so-called multi-dimensional data structures. They allow for very fast searching to locate e.g. the points in a set lying in a given rectangle.
Segment trees store intervals in an efficient way. They can be used for solving problems concerning e.g. line segments.
Many geometric data structures are static, i.e., they don’t allow for insertions and deletions of objects. Some general dynamisation techniques will be discussed that can be used for turning static data structures into dynamic structures. With the description of the different data structures examples are given to show how the structures can be used for solving actual geometric problems. For example we will show how the segment tree can be used to solve the windowing problem efficiently.
With the description of the different data structures examples are given to show how the structures can be used for solving actual geometric problems. For example we will show how the segment tree can be used to solve the windowing problem efficiently.
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- Bentley, J.L., Multidimensional binary search trees in database applications, IEEE Trans. on Software Eng. SE-5 (1979), 333–340.Google Scholar
- Edelsbrunner, H., A note on dynamic range searching, Bull of the EATCS 15 (1981), 34–40.Google Scholar
- Edelsbrunner, H., Intersection problems in computational geometry ,Techn. Rep. F93, Inst. f. Information Processing, TU Graz, 1982.Google Scholar
- Edelsbrunner, H., and J. van Leeuwen, Multidimensional data structures and algorithms: a bibliography ,Techn. Rep. F105, Inst. f. Information Processing, TU Graz, 1982.Google Scholar
- Kersten, M.L., and P. van Emde Boas, Local optimizations of quad-trees ,Techn. Rep. IR-51, Free University Amsterdam, 1979.Google Scholar
- Lueker, G.S., A data structure for orthogonal range queries, Proc. 19th IEEE Symp. on Foundations of Computer Science ,1978, 28–34.Google Scholar
- Overmars, M.H., The design of dynamic data structures ,Lect. Notes in Computer Science 156, Springer-Verlag, 1983.Google Scholar
- Overmars, M.H., Range searching in a set of line segments, Proc. 1st ACM Symp. on Computational Geometry ,1985, 177–185.Google Scholar
- Preparata, F.P., and M.I. Shamos, Computational geometry ,Springer-Verlag, New York, 1985.Google Scholar
- Rogers, D.F., Procedural elements for computer graphics ,McGraw-Hill, New York, 1985.Google Scholar
- Samet, H., Deletion in two dimensional quad trees, C. ACM23 (1980), 703–10.Google Scholar
- Scholten, H.W., and M.H. Overmars, Genereal methods for adding range restrictions to decomposable searching problems ,Techn. Rep. RUU-CS-85-21, Dept. of Comp. Science, University of Utrecht, 1985.Google Scholar
- Warnock, J.E., A hidden line algorithm for halftone picture representation ,Techn. Rep. 4–5, Computer Science Dept., University of Utah, 1968.Google Scholar
- Warnock, J.E., A hidden-surface algorithm for computer generated halftone pictures ,Techn. Rep. 4–15, Computer Science Dept., University of Utah, 1969.Google Scholar
- Willard, D.E., Predicate-oriented database search algorithms ,Garland Publishing Company, New York, 1979.Google Scholar