Leaf Modeling and Growth Process Simulation Using the Level Set Method

This paper presents a simulation of the growth process of leaves for computer graphics, visualization, and virtual reality applications. The following two-stage simulation is presented in this paper. First, a reference image is used to guide the early stage growth of the leaf; second, a growth function was created based on several vector fields controlled by a generalized logistic function. This growth function allows the leaf growth to continue beyond the information provided by the reference image. The core of both stages is the use of the level set method to extract and evolve the leaf shape. The proposed method facilitates the creation of frequently needed objects in an easy and flexible way that releases the user, usually an animator, from the burden of animating a leaf, which is usually a background object in a scene. We present several results from our experiments using various growth parameters and different leaves to showcase the advantages of using our method.

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

[2]  Tony F. Chan,et al.  Active contours without edges , 2001, IEEE Trans. Image Process..

[3]  R. A. Silverman,et al.  Vector and Tensor Analysis with Applications , 1969 .

[4]  W. Marsden I and J , 2012 .

[5]  Jon G. Rokne,et al.  An Algorithmic Reflectance and Transmittance Model for Plant Tissue , 1997, Comput. Graph. Forum.

[6]  Oliver Deussen,et al.  Digital Design of Nature - Computer Generated Plants and Organics , 2010, X.media.publishing.

[7]  Xuejin Chen,et al.  Sketch-based tree modeling using Markov random field , 2008, SIGGRAPH 2008.

[8]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[9]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[10]  Przemyslaw Prusinkiewicz,et al.  Animation of plant development , 1993, SIGGRAPH.

[11]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..

[12]  M. Malek Vector Calculus , 2014 .

[13]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[14]  Ross T. Whitaker,et al.  A Level-Set Approach to 3D Reconstruction from Range Data , 1998, International Journal of Computer Vision.

[15]  Chang-Hun Kim,et al.  Simulation of Morphology Changes in Drying Leaves , 2013, Comput. Graph. Forum.

[16]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[17]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[18]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[19]  Justin W. L. Wan,et al.  Physically‐based simulation of plant leaf growth , 2004, Comput. Animat. Virtual Worlds.

[20]  Jia Liu,et al.  Simulation and visualization of adapting venation patterns , 2017, Comput. Animat. Virtual Worlds.

[21]  F. J. Richards A Flexible Growth Function for Empirical Use , 1959 .