Procedural modeling of trees based on convolution sums of divisor functions for real‐time virtual ecosystems

Abstract

ABSTRACTThis study proposes a novel procedural modeling method using convolution sums of divisor functions to model a variety of natural trees in a virtual ecosystem efficiently. The basic structure of the modeling method defines the growth grammar, including the branch propagation, a growth pattern of branches and leaves, and a process of growth deformation for various tree generation. Here, the proposed procedural method for trees is to utilize convolution sums of divisor functions as a novel approach. The structure of convolution sums has branch propagation of a uniform pattern, which is controllable, so that it is efficient for real‐time virtual ecosystem construction. Furthermore, it can process changes of environment factors or growth deformation for various and unique tree generation simply through the properties of divisor functions. Finally, an experiment is performed in order to evaluate our proposed modeling method whether it can generate natural and various tree models, and a real‐time virtual ecosystem of a large area where a variety of trees are presented using the modeling method can be constructed efficiently.Copyright © 2013 John Wiley & Sons, Ltd.