Procedural techniques for simulating the growth of plant leaves and adapting venation patterns

Abstract

This paper presents biologically-motivated a procedural method for the simulation of leaf contour growth and venation development. We use a mathematical model for simulating the growth of a plant leaf. Leaf tissue is regarded as a viscous, incompressible fluid whose 2D expansion is determined by a spatially varying growth rate. Visually realistic development is described by a growth function RERG that reacts to hormone (auxin) sources embedded in the leaf blade. The shape of the leaf is determined by a set of feature points within the leaf contour. The contour is extracted from photos by utilizing a Curvature Scale Space (CSS) Corner Detection Algorithm. Auxin transport is described by an initial auxin flux from an auxin source to an auxin sink that is gradually channelized into cells with high levels of highly polarized transporters. The leaf is presented as a triangulated double layer structure that consists of a Voronoi-Diagram that is discretised along the vein structures.

GeoMaTree : Geometric and Mathematical Model Based Digital Tree Authoring System

“…One such study includes a modeling method that applies the CGA Shape grammar to the growth of digital plants based on the convolution sums of divisor functions [13]. Other examples include a study using hierarchical topology-preserving, blending, and morphing techniques for tree modeling [14,15], another study involving a method for modeling trees using local convolution surface approximation, and yet another study based on simulating the growth of plant leaves that are composed of Voronoi diagrams [17]. However, these studies have shown limitations in the context of effectively generating various digital plants, since they lack in the aspect of intuitiveness from the user's perspective.…”

Topologically consistent leafy tree morphing

“…Later, Pirk et al automatically infer the developmental parameters from one single static tree and then interpolates them to generate the tree growth animations. Environmental factors, including obstacles, lighting, winds, and competition with other trees have been studied to date to realistically animate interactions between trees and the environment. However, none of them is capable of generating fluid morphing between topologically varying trees.…”

“…The transformation of one‐to‐many matched chains is achieved by split or merge operations. The in‐between trunks are interpolated and then reconstructed using the method of Alsweis et al…”