Modelling and Programming Evolutions of Surfaces

Abstract

In recent years, a lot of work has been done on modelling natural phenomena and simulating the evolution of natural objects. For instance, procedural methods have been developed for simulating corpuscular phenomena and tree growth. In this paper we present a new procedural method for simulating evolutions of subdivisions of surfaces (i.e. partitions of surfaces into vertices, edges and faces). The representations of topology, embedding and photometry are clearly distinguished in the geometric model used for the representation of such subdivisions and thus, each of these features may be evolved independently (as in natural metamorphoses). Evolutions are achieved by applying topological and embedding operations on the geometric model. Control of these evolutions is based upon the behaviour concept. Behaviours (i.e. sets of operations) are associated with cells of the modelled subdivision. At each step, and for each cell, the corresponding behaviour is applied to the cell. The definition and computation of parameters have been studied, in order to control such evolutions. The method has been implemented and tested with many examples of surface evolutions (mainly evolutions of vegetal surfaces: leaves, flowers). Based on the method, a language has been defined for programming surface evolutions.