Combinatorial analysis of ramified patterns and computer imagery of trees

Proceedings of the 16th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1989

Volumn , Issue , 1989, Pages 31-40

  Viennot, Xavier Gérard ^a   Eyrolles, Georges ^a   Janey, Nicolas ^b   Arquès, Didier ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

Analysis of form; Branching patterns in physics; Combinatorics; Fractals; Ramification matrix; Self similarity; Stochastic modeling

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTER GRAPHICS; FRACTALS; GROUNDWATER; HYDROGEOLOGY; INTERACTIVE COMPUTER GRAPHICS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

BRANCHING PATTERNS; COMBINATORIAL ANALYSIS; COMBINATORIAL PARAMETERS; COMBINATORICS; DEVELOPMENT PROCESS; MORPHOLOGICAL STUDY; SELF-SIMILARITIES; TRIANGULAR MATRICES;

TREES (MATHEMATICS);

EID: 0002466696     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/74333.74336     Document Type: Conference Paper

References (47)

1. Aono M., and Kunii T.L. Botanical tree image generation, IEEE Computer Graphics & Applications 4, 5 (1984), 10-34.
2. Ball, R.C. DLA in the real world, in On growth and form: fractal and non-fractal patterns in Physics, Stanley, H.E., and Ostrowski, N.t eds., Martinus Nijhoff, Boston (1986) 69-78.
3. Beyer, T., and Friedel, M. Generative scene modelling. Proceeding of EUROGRAPHICS '87 (1987), 151-158 & 571.
4. Bloomenthal, J. Modeling the Mighty Maple. Proceedings of SIGGRAPH '85 (San Francisco, CA, July 22-26, 1985). In Computer Graphics 19, 3 (1985), 305-311.
5. Cole, V.C. The artistic anatomy of trees. Dover Publication, N-Y (1965) (orginally Seely Servi & Co., Lond., 1915).
6. D'Arcy Thompson, W. On growth and form. University Press, Cambridge, 2nd ed., (1952).
7. Demko, S., Hodges, L., and Naylor, B. Construction of fractal objects with iterated function systems. Proceedings of SIGGRAPH '85 (San Francisco, CA, July 22-26, 1985). In Computer Graphics 19, 3 (1985), 271-278.
8. De Reffye, P., Edelin, C., Francon, J., Jaeger, M., Puech, C. Plant Models Faithful to Botanical Structure and Development. Proceedings SIGGRAPH '88 (Atlanta, August 1-15, 1988). Computer Graphics 22, 4(1988), 151-158.
9. Eyrolles G. Synthese d'images figuratives d'arbres par des mdthodes combinatoires. Ph.D. Thesis, Un. Bordeaux I 1986.
10. Flajolet, P., Raoult, J.C., and Vuillemin, J. The number of registers required for evaluating arithmetic expressions. Theor. Computer Science 9 (1979) 99-125.
11. Gardner, G., Simulation of natural scenes using textured quadric surfaces. Computer Graphics 18, 3 (1984).
12. Green, M., and Sun, H. A langage and system for procedural modeling and motion. IEEE Comp. Graph. & Ap., (1988) 52-64.
13. Halle F., Oldeman R., and Tomlinson P. Tropical trees and forests: An architectural analysis. Springer Berlin 1978.
14. Honda, H. Description of the form of trees by the parameters of the tree-like body: Effects of the branching angle and the branch length of the shape of the tree-like body, J. Theor. Biol. 31 (1971), 331-338.
15. Horton, R.E. Erosioned development of systems and their drainage basins, hydrophysical approach to quantitative morphology. Bull. Geol. Soc. America 56 (1945), 275-370.
16. Kawaguchi, Y. A morphological study of the form of nature. Proceedings of SIGGRAPH '82 (July 1982). In Computer Graphics 16, 3 (1982), 223-232.
17. Kemp, R. The average number of registers needed to evaluate a binary tree optimally. Acta Infor. 11 (1979), 363-372.
18. Knuth, D.E. The Art of Computer Programming, vol. 3, Addison-Wesley, Reading (1973).
19. Leopold, L.B. Trees and streams: The efficency of branching patterns, J. Theor. Biol. 31 (1971), 339-354.
20. Lienhardt, P. Modelisation et evolution de surfaces libres. Ph.D. Thesis, Univ. Louis Pasteur, Strasbourg (1987).
21. Lienhardt P. & Francon J .Vegetal leaves synthesis. Proc. COGNIHVA'87 (Paris La Villette, May 18-22, 1987)212-18.
22. MacMahon, T.A. The mechanical design of trees. Scientific American 233 (1975), 92-102.
23. Mandelbrot, B. The fractal geometry of nature. Freeman & Co., San Francisco (1982).
24. Marshall, R., Wilson, R., and Carlson, W. Procedure models for generating three-dimensional terrain. SIGGRAPH '80, Computer Graphics 14, 3 (July 1980), 154-162.
25. Meier A., Moon J.W. & Pounder J.R. On the order of random channel networks. SIAM J. Alg. Disc. Mat.l (1980) 25-33.
26. Mendes-France M., De I'arbre de Leonardo da Vinci a la theorie de la dimension. Rev. du Palais de la Decouverte, Paris, 10, 52-60.
27. Naudin, J.J., and Prud'homme, R. Methodes d'analyse morphologiques et morphostructurales d'interpretation des topographies et des bathymetries dans les domaines continentaux marins. Bull, de l'lnst. de Geologie du Bassin D'Aquitaine 10 (1971) 111-114.
28. Niemeyer, L., Pietronero, L., and Wiesmann, A.J. Fractal structure of dielectric breakdown patterns. Phys. Rev. Letters 52 (1984) 1033.
29. Nittmann, J., Daccord, G., and Stanley, H.E. Fractal growth of viscous fingers. Nature 314 (1985) 141-144.
30. Niklas, K.J., Computer-simulated plant evolution. Scientific American (1986) 78-86.
31. Oppenheimer, P. Real time design and animation of fractal plants and trees. Proceedings of SIGGRAPH '86 (Dallas, Texas, August 18-22, 1985). In Computer Graph. 20, 4 (1986), 55-64.
32. Penaud, J.G. The ramification matrix of random binary trees. Research report, LABRI n° 8832, Departement d'Informatique, University de Bordeaux I (1988).
33. Percheron, G., Principles and methods of the graph theoretical analysis of natural binary arborescences. J. Theor. Biology 99 509-552.
34. Prudhomme, R., and Vigneaux, M. Methodes morphologiques et morphostructurales appliquees a I'etude des reseaux hydrographiques du Bordelais. Revue geographique des Pyrenees du Sud-Ouest 41 (1970), 5-14.
35. Prusinkiewicz P.Graphical applications of L-systems. Proc. of Graphics Interface '86-Vision Interface'86 (1986), 247-53.
36. Prusinkiewicz, P., Lindenmayer, A., and Hanan, J. Developmental models of herbaceous plants for computer imagery purposes. Proceedings of SIGGRAPH '88 (Atlanta, August 1-15, 1988).In Computer Graph. 22, 4(1988), 141-150.
37. Reeves, W.T. & Blau, R.Approximate and probabilistic algorithms for shading and rendering structured particle systems Proceedings of SIGGRAPH '85 (San Francisco, CA, july 22-26, 1985).In Computer Graphics 19, 3 (1985), 313-322.
38. Sawada, Y., Dougherty, A., and Gollub, J.P. Dentritic and fractal patterns in electrolytic metal deposits. Phys. Review Letters 56 (1986) 1260-1263.
39. Smith, A.R., Plants, fractals, and formal languages. Proceedings of SIGGRAPH '84 (Minneapolis, Minnesota, July 23-27, 1984). Computer Graphics 18, 3 (1984), 1-10.
40. Stevens, P.S. Patterns in Nature. Little, Brown & Co., Boston (1974).
41. Strahler, A.N .Hypsometric (area-Altitude) analysis of erosional topology. Bull. Geol. Soc. Amer. 63 (1952) 1117-42.
42. Van Damme, H., Obrecht, F., Levitz, P., Gatineau, L., Laroche, C. Nature 320 (1986), 731.
43. Vannimenus, J., On the shape of trees: Tools to describe ramified patterns. Proc. sum. school in Theor. Physics, Les Houches (1987).
44. Vannimenus, J., and Viennot, X.G. Combinatorial Tools for the Analysis of Ramified Patterns. J. Stat. Physics, 54 (1989) 1529-1538.
45. Vauchaussade de Chaumont, M., and Viennot X.G. Enumeration of RNAs secondary structures by complexity, in Mathematics in Medecine and Biology, Lecture Notes in Biomathematics n°57, Capasso, V., Grosso, E., and Paven- Fontana, S.L., eds., Springer-Verlag, Berlin (1985), 360-365.
46. Witten, T.A., and Sanders, L.M. Phys. Rev. 47 (1981) 1400.
47. Woldenberg, M.J. A structural taxonomy of spatial hierarchies, in Colston papers, v. 22, Butterworth Sci. Publ., London (1970) 147-175.