Computer animation of swaying trees based on physical simulation

This paper presents a series of techniques for generating animations of trees swaying in the wind, in consideration of the influences that the tree shapes and leaf sizes give to the air current. To do the simulation of the wind around a tree having a complicated shape, it is necessary to consider the influence that some objects obstructing the wind such as leaves or branches give. Generally, the following problem occurs when we use the incompressible Navier Stokes equations in a physical simulation model of the wind. Computational complexity increases because of considering the details of tree shapes, so it is difficult to generate the animations in real-time. Therefore, this paper proposes a novel method that reduces the computational complexity and realizes an animation in real-time, by means of a boundary condition map expressing space distribution of resistances from tree models automatically. In this case, we treat the parts that have similar shapes such as leaves and branches as simple damping factors decreasing the wind velocity. And also, it has another advantage that the influences between a tree and others can be rapidly calculated by using a hierarchical calculation method. Finally, through many experiments using these methods, it is shown that real-time animations of swaying trees in the wind can be realized. (c) 2006 Elsevier Ltd. All rights reserved.