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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.<\/jats:p>","DOI":"10.1145\/1073204.1073251","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"702-711","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":231,"title":["Modeling and visualization of leaf venation patterns"],"prefix":"10.1145","volume":"24","author":[{"given":"Adam","family":"Runions","sequence":"first","affiliation":[{"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Fuhrer","sequence":"additional","affiliation":[{"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brendan","family":"Lane","sequence":"additional","affiliation":[{"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pavol","family":"Federl","sequence":"additional","affiliation":[{"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anne-Ga\u00eblle","family":"Rolland-Lagan","sequence":"additional","affiliation":[{"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Przemyslaw","family":"Prusinkiewicz","sequence":"additional","affiliation":[{"name":"University of Calgary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00425-002-0937-8"},{"key":"e_1_2_2_2_1","volume-title":"Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG'01)","author":"Andrade D.","year":"2001","unstructured":"Andrade , D. , and De Figueiredo , L. 2001 . 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