Realistic animation of interactive trees

Abstract

We present a mathematical model for animating trees realistically by taking into account the influence of natural frequencies and damping ratios. To create realistic motion of branches, we choose three basic mode shapes from the modal analysis of a curved beam, and combine them with a driven harmonic oscillator to approximate Lissajous curve which is observed in pull-and-release test of real trees. The forced vibration of trees is animated by utilizing local coordinate transformation before applying the forced vibration model of curved beams. In addition, we assume petioles are flexible to create natural motion of leaves. A wind field is generated by three-dimensional 1/f β noises to interact with the trees. Besides, our animation model allows users to interactively manipulate trees. We demonstrate several examples to show the realistic motion of interactive trees without using pre-computation or GPU acceleration. Various motions of trees can be achieved by choosing different combinations of natural frequencies and damping ratios according to tree species and seasons. Electronic supplementary materialThe online version of this article (

Animating 3D vegetation in real-time using a 2D approach

“…[Diener et al 2009] proposed to apply modal analysis to compute a wind basis and project directional wind at run time. A common geometrical model to represent branches is the beam model [Chuang et al 2005;Habel et al 2009;Hu et al 2012]. Moreover, [Weber 2008] presented an interactive simulation method using a cloth dynamics model.…”

A Simple Method to Animate Vegetation in Images Using Simulation-Guided Grid-Based Warping

“…In general, physics-based methods requires high computational cost and they lack intuitive direct control. Procedural method usually is based on noise functions to heuristically model the appearance of tree's motion instead of performing a simulation, for example, Ota et al [17], Sousa [18] and Hu et al [19], [20] used noise functions to drive the animation. Zhang et al [21], [22] used pre-recorded motion graphs to create animation for trees.…”

Interactive authoring of simulation-ready plants

“…Simulations can be augmented with a proper randomized wind model [Ota et al 2004], accelerated using level-of-detail techniques [Beaudoin and Keyser 2004], and stabilized using recursive fully implicit methods [Hadap 2006]. Flexible branches have been modeled using 1D linear EulerBernoulli beams [Habel et al 2009;Hu et al 2012] or nonlinear Kirchhoff rods [Bergou et al 2008;Bertails 2009]. Plants consisting of deformable branches and leaves can be simulated using oriented particles [Müller and Chentanez 2011], elastons [Martin et al 2010], and the three-dimensional solid Finite Element Method (FEM) [Twigg and Kačić-Alesić 2010;Lu et al 2011].…”

“…In the context of plant simulation, Stam [1997] used a modal basis to compute noise in the frequency domain, and Diener [2009] used a wind projection basis to increase computation speed. Low-dimensional (three of less) linear modal simulations on individual, fully decoupled, branches modeled as Euler-Bernoulli beams were presented in [Habel et al 2009;Hu et al 2012], as well as methods to tune the models to match recorded real tree motion. These approaches produce quality high-frequency motion of trees, e.g., leaves and branches rapidly fluttering in the wind, and are as such complementary to our nonlinear model reduction simulator.…”

“…Because the interfaces between branches and/or leaves often have small surface areas, it is common to neglect their bending. Often, plant simulators even assume that all the parts (the branches) are completely decoupled [Habel et al 2009;Hu et al 2012]. In our work, the domains are coupled, with the assumption that the interface deformations are small.…”