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Octree Data Structures and Creation by Stacking

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Computer-Generated Images

Abstract

Efficient, compact data structures are necessary for the representation of octrees. First, several concrete data structures for the octree abstract data type will be compared in terms of storage space required and execution time needed to perform operations such as to find a certain node or obei. We compare information theoretic minimal representations, digital search trees sometimes storing some information in an immediate mode without pointers, and storing the set of rays, which is often the most compact.

This material is based upon work supported by the National Science Foundation under grant number ECs- 8351942, and by the Schlumberger-Doll Research Labs, Ridgefield, CT. The second authors was also supported in part by a fulbright award.

Until June 1986 visiting at: Computer Science Division, Electrical Engneering and Computer Science Dept., 543 Evans Hall, Univesity of California, Berkeley CA 94720 USA.

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References

  • Abramson, N. (1963) Information Theory and Coding, McGraw-Hill Electronic Sciences Series.

    Google Scholar 

  • Baer, A., Eastman, C., and Henrion, M. (Sept. 1979) “Geometric Modelling: A Survey,” Computer Aided Design, vol. 11, no. 5.

    Google Scholar 

  • Bentley, J.L. and Stanat, D.F. (July 1975) “Analysis of Range Searches in Quad Trees,” Information Processing Letters, vol. 3, no. 6, pp. 170–173.

    Article  MATH  MathSciNet  Google Scholar 

  • Doctor, L. J. and Torborg, J. G. (1981) “Display Techniques for Octree Encoded Objects,” IEEE Computer Graphics and Applications, vol. 1, no. 3, pp. 29–38.

    Article  Google Scholar 

  • Finkel, R.A. and Bentley, J.L. (1974) “Quad Trees: A Data Structure For Retrieval On Composite Key,” Acta Informatica, vol. 4, pp. 1–9.

    Article  MATH  Google Scholar 

  • Franklin, Wm. Randolph (July 1980) “A Linear Time Exact Hidden Surface Algorithm,” ACM Computer Graphics, vol. 14, no. 3, pp. 117–123.

    Google Scholar 

  • Franklin, Wm. Randolph (April 1981) “An Exact Hidden Sphere Algorithm That Operates In Linear Time,” Computer Graphics and Image Processing, vol. 15, no. 4, pp. 364–379.

    Google Scholar 

  • Franklin, Wm. Randolph and Akman, Varol (October 1985) “Building an Octree from a Set of Parallelepipeds,” IEEE Computer Graphics and Applications.

    Google Scholar 

  • Franklin, Wm. Randolph (16–21 October 1983) “Adaptive Grids For Geometric Operations,” Proc. Sixth International Symposium on Automated Cartography (Auto-Carto Six), vol. 2, pp. 230–239, Ottawa, Canada.

    Google Scholar 

  • Hoskins, E.M. (November 1979) “Design Development and Description Using 3D Box Geometries,” Computer Aided Design, vol. 11, no. 6, pp. 329–336.

    Article  Google Scholar 

  • Hunter, G.M. (April 1979) “Operations on Images Using Quad Trees,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. PAMI-1, no. 2, pp. 145–153.

    Google Scholar 

  • Jackins, C. L. and Tanimoto, S. L. (1980) “Quadtree, octree, and K-trees: A Generalized Approach to Recursive Decomposition of Euclidean Space,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 5, pp. 533–539.

    Article  Google Scholar 

  • Knuth, D.E. (1973) The Art of Computer Programming, Volume S: Sorting and Searching, Addison-Wesley.

    Google Scholar 

  • Meagher, Donald J. (October 1980) Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer, DPL-TR-80-111, Rensselaer Polytechnic Institute, Image Processing Lab.

    Google Scholar 

  • Meagher, Donald J. (April 1982) The Octree Encoding Method for Efficient Solid Modelling, Rensselaer Polytechnic Institute, Electrical, Computer, and Systems Engineering Dept., Ph.D. thesis.

    Google Scholar 

  • Meagher, Donald J. (1982b) “Geometric Modelling Using Octree Encoding,” Computer Graphics and Image Processing, vol. 19, pp. 129–147.

    Google Scholar 

  • Meagher, Donald J. (November 1984) “The Solids Engine: A Processor for Interactive Solid Modelling,” Proc. Nicograph.

    Google Scholar 

  • Requicha, Aristides A. G. (December 1980) “Representations for Rigid Solids: Theory, Methods, and Systems,” ACM Computing Surveys, vol. 12, no. 4, pp. 437–464.

    Google Scholar 

  • Samet, H. (December 1980) “Deletion in Two-Dimensional Quad Trees,” Comm. ACM, vol. 23, no. 12, pp. 703–710.

    Google Scholar 

  • Srihari, S. N. (1981) “Representation of Three-Dimensional Digital Images,” ACM Computing Surveys, vol. 13, no. 4, pp. 400–424.

    Article  Google Scholar 

  • Tamminen, M. (1981) Expected Performance of Some Cell Based File Organization Schemes, REPORT-HTKKTKO-B28, Helsinki University of Technology, Laboratory of Information Processing Science, SF-02150 Espool 5, Finland.

    Google Scholar 

  • Tamminen, M. (June 1982) “The Excell Method for Efficient Geometric Access to Data,” ACM IEEE Nineteenth Design Automation Conference Proceedings, pp. 345–351.

    Google Scholar 

  • Tamminen, M. and Samet, H. (1984) “Efficient Octree Conversion by Connectivity Labelling,” ACM Computer Graphics, vol. 18, no. 3, pp. 43–51. (SIGGRAPH’84 Proceedings)

    Google Scholar 

  • Tanimoto, S.L. (June 1977) “A Pyramid Model for Binary Picture Complexity,” Proc. IEEE Computer Society Conference on Pattern Recognition and Image Processing, Rensselaer Polytechnic Institute.

    Google Scholar 

  • Willard, Dan E. (1984) personal communication, State University of New York at Albany.

    Google Scholar 

  • Yamaguchi, K., Kunii, T. L., Fujimura, K., and Toriya, H. (1984) “Octree-related Data Structures and Algorithms,” IEEE Computer Graphics and Applications, vol. 4, no. 1, pp. 53–59.

    Article  Google Scholar 

  • Yao, F. F. (April 1983) “A 3-Space Partition and Its Applications (extended abstract),” ACM 15th Symposium on the Theory of Computing, pp. 258-263, Boston.

    Google Scholar 

  • Yau, M. and Srihari, S. N. (1983) “A Hierarchical Data Structure for Multidimensional Images,” Comm. ACM, vol. 26, no. 7, pp. 504–515.

    Google Scholar 

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© 1985 Springer-Verlag Tokyo

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Franklin, W.R., Akman, V. (1985). Octree Data Structures and Creation by Stacking. In: Magnenat-Thalmann, N., Thalmann, D. (eds) Computer-Generated Images. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68033-8_16

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  • DOI: https://doi.org/10.1007/978-4-431-68033-8_16

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68035-2

  • Online ISBN: 978-4-431-68033-8

  • eBook Packages: Springer Book Archive

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