Techniques for Stochastic ImplicitSurface Modelling and Rendering

Abstract

Implicit surfaces are a powerful shape primitive for computer graphics. This thesis focuseson a shape modelling approach which generates synthetic shapes by the specification of animplicit surface generating function that has random properties. This type of graphic objectcan be called a stochastic implicit surface because the surface is perceived as the realisationof a stochastic process. The main contributions of this thesis are in the form of new andimproved modelling and rendering algorithms to deal with stochastic implicit surfaces that canbe complex and feature fractal scaling properties.On the modelling side, a new topological correction algorithm is proposed to detect disconnectedsurface parts that arise as a consequence of the implicit surface representation. A surfacedeformation algorithm, based on advection through a vector field, is also presented.On the rendering side, several algorithms are proposed. First, an improved ray casting methodis presented that guarantees correct intersections between view rays and the surface. Second, anew progressive refinement rendering algorithm is proposed that provides a dynamic renderingenvironment where the image quality steadily increases with time. Third, a distributed renderingmechanism is presented to deal with the long computation times involved in the imagesynthesis of stochastic implicit surfaces.An application of the proposed techniques is given in the context of the procedural modellingof a planet. A procedural planet model must be able to generate synthetic planets showing thecorrect range of geological scales. The planet is generated as a stochastic implicit surface. Thisrepresents an improvement over previous models that generated planets as displacement mapsover a sphere. Terrain features that were previously difficult to model can be achieved throughthe implicit surface approach. This approach is a generalisation over those previous modelssince displacement maps over the sphere can be recast as implicit surfaces.