Geometric Shape Abstraction and Simplification

Abstract

In this thesis we present new insights into the research area of abstraction and simplification of geometric shapes, and to the field of simulation of botanical processes.Abstracting and simplifying 3D shapes is one of the fundamental problems in shape processing research. Many application areas, including architecture, urban modeling, gaming, and movies, require shapes in a reduced form. In the first part of this thesis we introduce three novel approaches, each addressing specific issues in the problem domain of abstraction and simplification of shapes.A new method for the automatic simplification of botanical tree models is presented based on adaptive Billboard Clouds. An iterative optimization is applied to the tree structure to evaluate which geometric parts of the tree are substituted by Billboards. The entire process is guided by a newly developed quality measure that accounts for intrinsic properties of the tree. We evaluate our method by measuring the visual difference between full polygonal tree models and their simplifications. Inspired by non-photorealistic rending methods, we further introduce a novel paradigm for the abstraction of 3D shapes. The idea is to analyze a shape in a semi-automatic way with regard to symmetries and regular patterns to determine important structures. By using this information, the original geometry of a shape is replaced by a number of pre-defined and parameterized geometric fill patterns, which are derived from an initial user study. This allows us to produce abstractions in which the expressiveness of a shape is directly manifested in its geometry, rather than only in its rendering. Another novel method for the abstraction of 3D shapes presented in this thesis allows users to easily convey abstractions with only a few simple strokes. For this we propose, a new user interface that combines perceptual rules defined by Gestalt principles with sketches that capture the user's intent. In particular, we extend the formulation of 2D Gestalt grouping principles to 3D elements. Compared to previous abstraction methods, this allows us to preserve important visual structures perceived by humans. Finally, we validate the effectiveness of our system through two extensive user studies.The second part of this thesis is dedicated to contributions anchored in the field of simulation of botanical processes. Especially in computer graphics, an accurate simulation of such processes is often required to produce plausible results from a biological point of view. In our work we focus on the simulation of botanical tree growth. In particular, we introduce a new method that captures the so-called cambial growth of a tree -- the process that causes individual branches to thicken. Moreover, the simulation is coupled to a physical cracking model to produce plausible bark structures. By applying our method, we can give ordinary objects a tree-like appearance with familiar lignified features and cracked bark textures.