“Modeling dense inflorescences”

  • ©Andrew Owens, Mikolaj Cieslak, Jeremy Hart, Regine Classen-Bockhoff, and Przemyslaw Prusinkiewicz



Session Title:



    Modeling dense inflorescences




    Showy inflorescences – clusters of flowers – are a common feature of many plants, greatly contributing to their beauty. The large numbers of individual flowers (florets), arranged in space in a systematic manner, make inflorescences a natural target for procedural modeling. We present a suite of biologically motivated algorithms for modeling and animating the development of inflorescences with closely packed florets. These inflorescences share the following characteristics: (i) in their ensemble, the florets form a relatively smooth, often approximately planar surface; (ii) there are numerous collisions between petals of the same or adjacent florets; and (iii) the developmental stage and type of a floret may depend on its position within the inflorescence, with drastic or gradual differences. To model flat-topped branched inflorescences (corymbs and umbels), we propose a florets-first algorithm, in which the branching structure self-organizes to support florets in predetermined positions. This is an alternative to previous branching-first models, in which floret positions were determined by branch arrangement. To obtain realistic visualizations, we complement the algorithms that generate the inflorescence structure with an interactive method for modeling floret corollas (petal sets). The method supports corollas with both separate and fused petals. We illustrate our techniques with models from several plant families.


    1. Anastacio, F., Costa Sousa, M., Samavati, F., and Jorge, J. 2006. Modeling plant structures using concept sketches. In Proceedings of the 4th International Symposium on Non-photorealistic Animation and Rendering, ACM, 105–113. Google ScholarDigital Library
    2. Battjes, J., and Prusinkiewicz, P. 1998. Modeling meristic characters of Asteracean flowerheads. In Symmetry in Plants, D. Barabé and R. Jean, Eds. World Scientific, Singapore, 281–312.Google Scholar
    3. Battjes, J., Vischer, N., and Bachmann, K. 1993. Capitulum phyllotaxis and numerical canalization in Microseris pygmaea (Asteraceae: Lactuceae). American Journal of Botany, 419–428.Google Scholar
    4. Bender, J., Müller, M., Otaduy, M. A., Teschner, M., and Macklin, M. 2014. A survey on position-based simulation methods in computer graphics. Computer Graphics Forum 33, 6, 228–251.Google ScholarDigital Library
    5. Bloomenthal, J. 1990. Calculation of reference frames along a space curve. In Graphics Gems, A. Glassner, Ed., vol. 1. Academic Press, Boston, 567–571. Google ScholarDigital Library
    6. Brochu, T., Edwards, E., and Bridson, R. 2012. Efficient geometrically exact continuous collision detection. ACM Transactions on Graphics (TOG) 31, 4, 96. Google ScholarDigital Library
    7. Classen-Bockhoff, R., and Bull-Hereñu, K. 2013. Towards an ontogenetic understanding of inflorescence diversity. Annals of Botany 112, 1523–1542.Google ScholarCross Ref
    8. Classen-Bockhoff, R. 1992. Florale Differenzierung in komplex organisierten Asteraceenköpfen. Flora 186, 1-2, 1–22.Google ScholarCross Ref
    9. Classen-Bockhoff, R. 1994. Functional units beyond the level of the capitulum and cypsela in Compositae. In Compositae: Biology and Utilization. Proceedings of the International Compositae Conference, P. Caligari and D. Hind, Eds., vol. 2. Royal Botanic Gardens, Kew, 129–160.Google Scholar
    10. Douady, S., and Couder, Y. 1996. Phyllotaxis as a dynamical self organizing process. Parts I–III. Journal of Theoretical Biology 178, 255–312.Google ScholarCross Ref
    11. Erickson, R. O. 1983. The geometry of phyllotaxis. In The growth and functioning of leaves, J. E. Dale and F. L. Milthrope, Eds. University Press, Cambridge, 53–88.Google Scholar
    12. Fowler, D., Hanan, J., and Prusinkiewicz, P. 1989. Modelling spiral phyllotaxis. Computers & Graphics 13, 3, 291–296.Google ScholarCross Ref
    13. Fowler, D. R., Prusinkiewicz, P., and Battjes, J. 1992. A collision-based model of spiral phyllotaxis. Computer Graphics 26, 2, 361–368. Google ScholarDigital Library
    14. Frijters, D. 1978. Principles of simulation of inflorescence development. Annals of Botany 42, 549–560.Google ScholarCross Ref
    15. Green, A. A., Kennaway, J. R., Hanna, A. I., Bangham, J. A., and Coen, E. 2010. Genetic control of organ shape and tissue polarity. PLoS Biology 8, e1000537.Google ScholarCross Ref
    16. Harder, D., and Prusinkiewicz, P. 2013. The interplay between inflorescence development and function as the crucible of architectural diversity. Annals of Botany 112, 1477–1493.Google ScholarCross Ref
    17. Harris, E., Tucker, S., and Urbatsch, L. 1991. Floral initiation and early development in Erigeron philadelphicus (Asteraceae). American Journal of Botany, 108–121.Google Scholar
    18. Hernandez, L., and Palmer, J. 1988. Regeneration of the sunflower capitulum after cylindrical wounding of the receptacle. American Journal of Botany, 1253–1261.Google Scholar
    19. Hirmer, M. 1931. Zur Kenntnis der Schraubenstellungen im Pflanzenreich. Planta 14, 1, 132–206.Google ScholarCross Ref
    20. Ijiri, T., Owada, S., Okabe, M., and Igarashi, T. 2005. Floral diagrams and inflorescences: Interactive flower modeling using botanical structural constraints. ACM Transactions on Graphics 24, 3, 720–726. Google ScholarDigital Library
    21. Ijiri, T., Owada, S., and Igarashi, T. 2006. Seamless integration of initial sketching and subsequent detail editing in flower modeling. Computer Graphics Forum 25, 3, 617–624.Google ScholarCross Ref
    22. Ijiri, T., Yokoo, M., Kawabata, S., and Igarashi, T. 2008. Surface-based growth simulation for opening flowers. In Proceedings of Graphics Interface 2008, Canadian Information Processing Society, 227–234. Google ScholarDigital Library
    23. Kim, Y., Sinclair, R., Chindapol, N., Kaandorp, J., and De Schutter, E. 2012. Geometric theory predicts bifurcations in minimal wiring cost trees in biology are flat. PLoS Computational Biology 8, 4, e1002474.Google ScholarCross Ref
    24. Kirchoff, B. 2003. Shape matters: Hofmeister’s rule, pri-mordium shape, and flower orientation. International Journal of Plant Sciences 164, 4, 505–517.Google ScholarCross Ref
    25. Li, J., Liu, M., Xu, W., Liang, H., and Liu, L. 2015. Boundary-dominant flower blooming simulation. Computer Animation and Virtual Worlds 26, 3-4, 433–443. Google ScholarDigital Library
    26. Liang, H., and Mahadevan, L. 2011. Growth, geometry, and mechanics of a blooming lily. Proceedings of the National Academy of Sciences 108, 14, 5516–5521.Google ScholarCross Ref
    27. Lintermann, B., and Deussen, O. 1999. Interactive modeling of plants. IEEE Computer Graphics and Applications 19, 1, 56–65. Google ScholarDigital Library
    28. Lipman, Y., Cohen-Or, D., Gal, R., and Levin, D. 2007. Volume and shape preservation via moving frame manipulation. ACM Transactions on Graphics 26, 1, 5. Google ScholarDigital Library
    29. MacDonald, N. 1983. Trees and Networks in Biological Models. J. Wiley & Sons, New York.Google Scholar
    30. Müller, M., Heidelberger, B., Hennix, M., and Ratcliff, J. 2007. Position based dynamics. Journal of Visual Communication and Image Representation 18, 2, 109–118. Google ScholarDigital Library
    31. Neubert, B., Franken, T., and Deussen, O. 2007. Approximate image-based tree-modeling using particle flows. ACM Transactions on Graphics (TOG) 26, 3, 88. Google ScholarDigital Library
    32. O’Connor, et al. 2014. A division in PIN-mediated auxin patterning during organ initiation in grasses. PLoS Computational Biology 10, 1, e1003447.Google ScholarCross Ref
    33. Provot, X. 1997. Collision and self-collision handling in cloth model dedicated to design garments. In Proceedings of the Eurographics Workshop on Computer Animation and Simulation, Springer, 177–189.Google ScholarCross Ref
    34. Prusinkiewicz, P., and Lindenmayer, A. 1990. The Algorithmic Beauty of Plants. Springer, New York. With J. Hanan, F. Fracchia, D. Fowler, M. de Boer, and L. Mercer. Google ScholarDigital Library
    35. Prusinkiewicz, P., Lindenmayer, A., and Hanan, J. 1988. Developmental models of herbaceous plants for computer imagery purposes. Computer Graphics 22, 4, 141–150. Google ScholarDigital Library
    36. Prusinkiewicz, P., Hammel, M. S., and Mjolsness, E. 1993. Animation of plant development. In Proceedings of SIGGRAPH 93, Annual Conference Series, 351–360. Google ScholarDigital Library
    37. Prusinkiewicz, P., Mündermann, L., Karwowski, R., and Lane, B. 2001. The use of positional information in the modeling of plants. In Proceedings of SIGGRAPH 2001, Annual Conference Series, 289–300. Google ScholarDigital Library
    38. Reinhardt, D., et al. 2003. Regulation of phyllotaxis by polar auxin transport. Nature 426, 255–260.Google ScholarCross Ref
    39. Ridley, J. N. 1986. Ideal phyllotaxis on general surfaces of revolution. Mathematical Biosciences 79, 1–24.Google ScholarCross Ref
    40. Rodkaew, Y., Chongstitvatana, P., Siripant, S., and Lursinsap, C. 2003. Particle systems for plant modeling. In Plant growth modeling and applications. Proceedings of PMA03, B.-G. Hu and M. Jaeger, Eds. Tsinghua University Press and Springer, Beijing, 210–217.Google Scholar
    41. Sachs, T. 1991. Pattern Formation in Plant Tissues. Cambridge University Press, Cambridge.Google Scholar
    42. Sammataro, D., Garment, M., and Erickson Jr, E. 1986. Anatomical features of the sunflower floret. Reprints — US Department of Agriculture, Agricultural Research Service.Google Scholar
    43. Sederberg, T., and Parry, S. 1986. Free-form deformation of solid geometric models. Computer Graphics 20, 4, 151–160. Google ScholarDigital Library
    44. Sederberg, T., Gao, P., Wang, G., and Mu, H. 1993. 2-D shape blending: an intrinsic solution to the vertex path problem. In Proceedings of the SIGGRAPH, ACM, 15–18. Google ScholarDigital Library
    45. Shinozaki, K., Yoda, K., Hozumi, K., and Kira, T. 1964. A quantitative analysis of plant form — the pipe model theory. I. Basic analyses. Japanese Journal of Ecology 14, 3, 97–105.Google Scholar
    46. Smith, R., Kuhlemeier, C., and Prusinkiewicz, P. 2006. Inhibition fields for phyllotactic pattern formation: A simulation study. Canadian Journal of Botany 84, 1635–1649.Google ScholarCross Ref
    47. Teschner, M., Heidelberger, B., Müller, M., Pomerantes, D., and Gross, M. 2003. Optimized spatial hashing for collision detection of deformable objects. In VMV, vol. 3, 47–54.Google Scholar
    48. Thompson, d. 1942. On Growth and Form, 2nd edition. University Press, Cambridge.Google Scholar
    49. Vogel, H. 1979. A better way to construct the sunflower head. Mathematical Biosciences 44, 179–189.Google ScholarCross Ref
    50. Weberling, F. 1992. Morphology of flowers and inflorescences. Cambridge University Press, Cambridge.Google Scholar
    51. Zhao, Y., and Barbič, J. 2013. Interactive authoring of simulation-ready plants. ACM Transactions on Graphics (TOG) 32, 4, 84. Google ScholarDigital Library

ACM Digital Library Publication: