Online Submission ID: 335

Simulation of Autumn Leaves

Figure 1: Our method for simulating autumn leaves: a singlechinar leaf(left), some maple leaves(right).

1 Introduction

Visual simulation of autumn leaves and their weathering se-quences requires both the convincing geometry shapes andthe reasonable materials for the leaves. This problem canbe solved from two major aspects, the geometric modelingand the material synthesis. With realistic rendering of au-tumn leaves, our system can generate convincing results asis shown in Fig. 1

2 Double Layered Model

The deformation of a leaf is the aggregation of the deforma-tion of all the cells on the leaf. Mesophyll cells and vascularbundle cells have distinctly different degree of rigidity forshrinkage. In order to simulate the deformation of an au-tumn leaf realistically we need the realistic venation distri-bution of the leaf. We modify Runions’s technique [Runionset al. 2005] by increasing the growing speed of the strongestvein or the primary vein on the top growing point. Then,according to the venation, a double layered model (DLM), aphysically-based mechanism, is proposed to simulate the de-formation of autumn leaves. In DLM, the upper layer standsfor the cells in mesophyll which have remarkable shrinkingratio, meanwhile the lower layer stands for the cells in ve-nation which are more rigid to resist the shrinking force, asshown in Fig. 2. The two layers are also inter-connected tohold the mechanical stability. By setting up the mass-springsystem in two interconnecting layers, different kinetic man-ners of mesophyll and veins can be simulated respectively.Meanwhile the double layers affect each other and determinetogether the deformed shape of leaves.

3 Material Model

Differing from Wang et al. [Wang et al. 2006], we find thatonly a single leaf is insufficient to represent all the aging

Figure 2: Double Layered Model: the mass springs in up-per layer(green) denote the deformable leaf blade, while themass-spring on the lower layer (red) denote the leaf veinswhich have relatively rigid property.

Figure 3: Generating the aging degree maps from the com-plete aging space. (Left top)the input samples of leaves ofdifferent ages. (Left bottom)The aging degree of the inputsamples. (Right)The input samples in the material spaceand the related aging curve.

appearances of the leaves. Hence our system extends theconstruction of appearance manifold to the input by mul-tiple leaves, which is called complete aging space. We canthus interpret the relative degrees of aging on all the sam-ple points from the multiple leaves. As shown in Fig. 3,the complete aging space is created by the front sides of sev-eral sample leaves at different aging status. Since the samplepoints in the aging space typically form a dense distribution,the k-means clustering method can be applied to separatethe sample points. And then we can create an aging curveby using a Bezier curve according to the means of the clus-ters. After that, aging degrees of all the sample points canbe easily determined by projecting them onto this curve.

By replacing the appearance values of the sample with de-gree values, we obtain an aging degree map, which displaysspatial variations in aging degree over the leaf sample. Withthe aging degree map, our method synthesizes detailed ap-pearance onto leaf model according to a given distributionof aging degrees over the surface.

References

Runions, A., Fuhrer, M., Lane, B., Federl, P., Rolland-Lagan, A.-

G., and Prusinkiewicz, P. 2005. Modeling and visualization of leaf

venation patterns. ACM Trans. Graph. 24, 3, 702–711.

Wang, J., Tong, X., Lin, S., Pan, M., Wang, C., Bao, H., Guo, B., and

Shum, H.-Y. 2006. Appearance manifolds for modeling time-variant

appearance of materials. ACM Trans. Graph. 25, 3, 754–761.

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