Implicit Visualization and Inverse Modeling of Growing Trees

A method is proposed for photo‐realistic modeling and visualization of a growing tree. Recent visualization methods have focused on producing smoothly blending branching structures, however, these methods fail to account for the inclusion of non‐smooth features such as branch bark ridges and bud scale scars. These features constitute an important visual aspect of a living tree, and are also observed to vary over time. The proposed method incorporates these features by using an hierarchical implicit modeling system, which provides a variety of tools for combining surface components in both smooth and non smooth configurations. A procedural interface to this system supports the use of inverse modeling, which is a global‐to‐local methodology, where the local properties of plant organs are described in terms of their global position within the tree architecture. Inverse modeling is used to define both the tree structure at any time, and a continuous developmental sequence for the tree from a seedling. These techniques provide an intuitive paradigm for the definition of complex tree growth sequences and their subsequent visualization, based solely on observed phenomena. Thus, a key advantage is that they do not require any knowledge of, or simulation of, the underlying biological processes.

[1]  P. Prusinhiewicz,et al.  Inverse modeling of plants , 2004 .

[2]  Jules Bloomenthal,et al.  Convolution surfaces , 1991, SIGGRAPH.

[3]  Xavier Gérard Viennot,et al.  Combinatorial analysis of ramified patterns and computer imagery of trees , 1989, SIGGRAPH.

[4]  Marc Jaeger,et al.  Plant models faithful to botanical structure and development , 1988, SIGGRAPH.

[5]  M. Holton,et al.  Strands, Gravity and Botanical Tree Imagery , 1994, Comput. Graph. Forum.

[6]  Brendan Lane,et al.  The use of positional information in the modeling of plants , 2001, SIGGRAPH.

[7]  John Hart,et al.  Implicit Modeling of Tree Surfaces , 1996 .

[8]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[9]  Brian Wyvill,et al.  Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System , 1999, Comput. Graph. Forum.

[10]  Peter Oppenheimer,et al.  Real time design and animation of fractal plants and trees , 1986, SIGGRAPH.

[11]  Karl Maritaud.  Rendu réaliste d'arbres vus de près en images de synthèse , 2003 .

[12]  Jules Bloomenthal,et al.  Modeling the mighty maple , 1985, SIGGRAPH.

[13]  Valery Adzhiev,et al.  HyperFun project: a framework for collaborative multidimensional F-rep modeling , 2000 .

[14]  H. Honda.  Description of the form of trees by the parameters of the tree-like body: effects of the branching angle and the branch length on the sample of the tree-like body. , 1971, Journal of theoretical biology.

[15]  A. Bell,et al.  Plant Form: An Illustrated Guide to Flowering Plant Morphology , 1991 .

[16]  D'arcy W. Thompson.  On Growth and Form , 1945 .

[17]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[18]  J. H. PRIESTLEY,et al.  The Growing Tree , 1932, Nature.

[19]  Tosiyasu L. Kunii,et al.  Bounded Blending Operations , 2002, Shape Modeling International.

[20]  Stefan Maierhofer,et al.  A multiresolution mesh generation approach for procedural definition of complex geometry , 2002, Proceedings SMI. Shape Modeling International 2002.

[21]  Jason Weber,et al.  Creation and rendering of realistic trees , 1995, SIGGRAPH.

[22]  Julian Shaw,et al.  Lord of the Rings: The Two Towers , 2002 .

[23]  Ergun Akleman,et al.  A minimal and complete set of operators for the development of robust manifold mesh modelers , 2003, Graph. Model..

[24]  Mathieu Desbrun,et al.  Active Implicit Surface for Animation , 1998, Graphics Interface.

[25]  Christophe Godin,et al.  Exploring plant topological structure with the AMAPmod software: an outline. , 1997 .

[26]  Marie-Paule Cani,et al.  Controlled blending in contact situations , 2002, Proceedings SMI. Shape Modeling International 2002.

[27]  Xiaogang Jin,et al.  Convolution Surfaces for Line Skeletons with Polynomial Weight Distributions , 2001, J. Graphics, GPU, & Game Tools.

[28]  Brian Wyvill,et al.  Introduction to Implicit Surfaces , 1997 .

[29]  Stefan Maierhofer,et al.  A Multiresolution Mesh Generation Approach for Procedural Definition of Complex Geometry , 2002, Shape Modeling International.

[30]  A. Lindenmayer,et al.  Models for the control of branch positions and flowering sequences of capitula in mycelis muralis (l , 1987 .

[31]  Oliver Deussen,et al.  Interactive Modeling of Plants , 1999, IEEE Computer Graphics and Applications.

[32]  Donald S. Fussell,et al.  Computer rendering of stochastic models , 1982, Commun. ACM.

[33]  Marie-Paule Cani,et al.  Implicit Modelling with Skeleton Curves: Controlled Blending in Contact Situation , 2002, Shape Modeling International.

[34]  R. Hosie,et al.  Native Trees of Canada , 1979 .

[35]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[36]  Jules Bloomenthal,et al.  Skeletal design of natural forms , 1996 .

[37]  Marie-Paule Cani,et al.  An implicit formulation for precise contact modeling between flexible solids , 1993, SIGGRAPH.

[38]  Ricki Blau,et al.  Approximate and probabilistic algorithms for shading and rendering structured particle systems , 1985, SIGGRAPH.