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

摘要

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