Modeling and visualization of leaf venation patterns

ACM Transactions on Graphics - Tập 24 Số 3 - Trang 702-711 - 2005
Adam Runions1, Martin Fuhrer1, Brendan Lane1, Pavol Federl1, Anne‐Gaëlle Rolland‐Lagan1, Przemysław Prusinkiewicz1
1University of Calgary

Tóm tắt

We introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

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Tài liệu tham khảo

10.1007/s00425-002-0937-8

Andrade , D. , and De Figueiredo , L. 2001 . Good approximations for the relative neighbourhood graph . In Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01) , 25--28. Andrade, D., and De Figueiredo, L. 2001. Good approximations for the relative neighbourhood graph. In Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01), 25--28.

Baranoski , G. , and Rokne , J ., 2002. Light interaction with plants . SIGGRAPH 2002 Course Notes 26 . Baranoski, G., and Rokne, J., 2002. Light interaction with plants. SIGGRAPH 2002 Course Notes 26.

10.1145/355921.355927

Bohn S. Andreotti B. Douady S. Munzinger J. and Couder Y. 2002. Constitutive property of the local organization of leaf venation networks. Physical Review E 65. Bohn S. Andreotti B. Douady S. Munzinger J. and Couder Y. 2002. Constitutive property of the local organization of leaf venation networks. Physical Review E 65.

10.1093/comjnl/24.2.162

10.1073/pnas.0306308101

10.1145/7529.8927

10.1140/epjb/e2002-00211-1

10.1016/S1369-5266(00)00135-7

10.1111/j.1467-8659.2004.00765.x

10.1145/1073204.1073308

10.1007/978-3-540-24687-9_18

10.1145/142920.134096

Gomes. J. Darsa L. Costa B. and Velho L. 1999. Warping and morphing of graphical objects. Morgan Kaufmann San Francisco. Gomes. J. Darsa L. Costa B. and Velho L. 1999. Warping and morphing of graphical objects. Morgan Kaufmann San Francisco.

Gottlieb , M. E. 1993. Angiogenesis and vascular networks: complex anatomies from deterministic non-linear physiologies . In Growth patterns in physical sciences and biology , J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander, Eds. Plenum Press , New York , 267--276. Gottlieb, M. E. 1993. Angiogenesis and vascular networks: complex anatomies from deterministic non-linear physiologies. In Growth patterns in physical sciences and biology, J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander, Eds. Plenum Press, New York, 267--276.

10.1145/166117.166139

10.1016/S0022-5193(84)80017-X

Hickey , L. 1979. A revised classification of the architecture of dicotyledonous leaves . In Anatomy of the dicotyledons . Second Edition, Vol. 1 , C. R. Metcalfe and L. Chalk, Eds . Clarendon Press , Oxford, 25--39. Hickey, L. 1979. A revised classification of the architecture of dicotyledonous leaves. In Anatomy of the dicotyledons. Second Edition, Vol. 1, C. R. Metcalfe and L. Chalk, Eds. Clarendon Press, Oxford, 25--39.

10.1109/5.163414

Judd W. W. Campbell C. S. Kellogg E. A. and Stevens P. F. 1999. Plant systematics: A phylogenetic approach. Sinauer Associates Sunderland MA. Judd W. W. Campbell C. S. Kellogg E. A. and Stevens P. F. 1999. Plant systematics: A phylogenetic approach. Sinauer Associates Sunderland MA.

Lefebvre , S. , and Neyret , F . 2002. Synthesizing bark . In Proceedings of the 13th Eurographics Workshop on Rendering, 105--116 . Lefebvre, S., and Neyret, F. 2002. Synthesizing bark. In Proceedings of the 13th Eurographics Workshop on Rendering, 105--116.

MacDonald , N. 1983. Trees and networks in biological models . J. Wiley & Sons , New York . MacDonald, N. 1983. Trees and networks in biological models. J. Wiley & Sons, New York.

10.1111/j.1432-0436.1976.tb01478.x

10.1145/37402.37410

10.1098/rspb.1980.0015

10.1073/pnas.12.3.207

Okabe A. Boots B. and Sugihara K. 1992. Spatial tesselations: Concepts and applications of Voronoi diagrams. J. Wiley and Sons Chichester. Okabe A. Boots B. and Sugihara K. 1992. Spatial tesselations: Concepts and applications of Voronoi diagrams. J. Wiley and Sons Chichester.

Popinet S. 2004. The GNU triangulated surface library. http://gts.sourceforge.net. Popinet S. 2004. The GNU triangulated surface library. http://gts.sourceforge.net.

Preparata F. and Shamos M. 1985. Computational geometry: An introduction. Springer New York. Preparata F. and Shamos M. 1985. Computational geometry: An introduction. Springer New York.

10.1145/166117.166161

10.1162/artl.1993.1.61

Prusinkiewicz P. 1998. In search of the right abstraction: the synergy between art science and information technology in the modeling of natural phenomena. In Art @ Science C. Sommerer and L. Mignonneau Eds. Springer Wien 60--68. Prusinkiewicz P. 1998. In search of the right abstraction: the synergy between art science and information technology in the modeling of natural phenomena. In Art @ Science C. Sommerer and L. Mignonneau Eds. Springer Wien 60--68.

Roberts , J. 2001 . Sticky pixels: Evolutionary growth by random drop ballistic aggregation . In Eurographics UK 2001 Conference Proceedings, 149--155 . Roberts, J. 2001. Sticky pixels: Evolutionary growth by random drop ballistic aggregation. In Eurographics UK 2001 Conference Proceedings, 149--155.

Rodkaew , Y. , Siripant , S. , Lursinsap , C. , and Chongstitvatana , P . 2002. An algorithm for generating vein images for realistic modeling of a leaf . In Prodeedings of the International Conference on Computational Mathematics and Modeling, 9 pp. Rodkaew, Y., Siripant, S., Lursinsap, C., and Chongstitvatana, P. 2002. An algorithm for generating vein images for realistic modeling of a leaf. In Prodeedings of the International Conference on Computational Mathematics and Modeling, 9 pp.

10.1038/nature01443

Rolland-Lagan , A.-G. , Federl , P. , and Prusinkiewicz , P . 2004. Reviewing models of auxin canalisation in the context of vein pattern formation in Arabidopsis leaves . In Proceedings of the 4th International Workshop on Functional-Structural Plant Models, 376--381 . Rolland-Lagan, A.-G., Federl, P., and Prusinkiewicz, P. 2004. Reviewing models of auxin canalisation in the context of vein pattern formation in Arabidopsis leaves. In Proceedings of the 4th International Workshop on Functional-Structural Plant Models, 376--381.

10.1006/anbo.2001.1391

Sachs , T. 1981. The control of patterned differentation of vascular tissues . In Advances in botanical research , H. W. Woolhouse, Ed., vol. 6 . Academic Press , London , 152--262. Sachs, T. 1981. The control of patterned differentation of vascular tissues. In Advances in botanical research, H. W. Woolhouse, Ed., vol. 6. Academic Press, London, 152--262.

10.1002/bies.10328

10.1242/dev.01182

Scholten H. and Lindenmayer A. 1981. A mathematical model for the laminar development of simple leaves. In Morphologie-Anatomie und Systematic der Pflanzen 5 W. van Cotthem Ed. Waegeman Ninove Belgium 29--37. Scholten H. and Lindenmayer A. 1981. A mathematical model for the laminar development of simple leaves. In Morphologie-Anatomie und Systematic der Pflanzen 5 W. van Cotthem Ed. Waegeman Ninove Belgium 29--37.

10.1104/pp.121.4.1179

Smith C. Prusinkiewicz P. and Samavati F . 2003 . Relational specification of surface subdivision algorithms. In Proceedings of AGTIVE 2003 vol. 3062 of Lecture Notes in Computer Science 313--327. Smith C. Prusinkiewicz P. and Samavati F. 2003. Relational specification of surface subdivision algorithms. In Proceedings of AGTIVE 2003 vol. 3062 of Lecture Notes in Computer Science 313--327.

10.1016/0031-3203(80)90066-7

10.1145/127719.122749

10.1049/el:19800386

Walter , M. , Fournier , A. , and Reimers , M . 1998. Clonal mosaic model for the synthesis of mammalian coat patterns . In Proceedings of Graphics Interface '98 , 82--91. Walter, M., Fournier, A., and Reimers, M. 1998. Clonal mosaic model for the synthesis of mammalian coat patterns. In Proceedings of Graphics Interface '98, 82--91.

10.1002/cav.v15:3/4

10.1145/1073204.1073252

10.1093/comjnl/24.2.167