Analysis and Synthesis of Structured Variations in 3D Geometries

In recent years, the use of 3D digital content becomes widespread in various industrial and scientific domains. However, content creation still remains a costly task as extensive manual work is often required. As such, one of the core research topics in computer graphics is to accelerate the content creation process. In this dissertation, we investigate the benefit of utilizing shape structure in creating different categories of digital content. To speed up the design process of 3D geometries, instead of dealing with individual shape separately, we propose to process structured variations, which are different models sharing certain key structural information. A geometry processing framework of structured variations consists of the analysis of structure from a collection of model variations, and the synthesis of novel shapes. We propose algorithms for three common types of digital content in computer graphics, which include facade textures, procedural modeling output, and 3D reconstruction point clouds from multiview stereo or scanning. There is a high demand in high quality and customized facade textures, especially in urban design, 3D cities or games. We introduce a framework to create structured variations of building facades via structure-aware editing. Our framework deals with irregular facade layouts, which are common in practice. To automatically create a large number of structured variations, a suitable technique is procedural modeling, which generates models by means of computer programs or procedures. However, the connection between the procedures and generated models is not explicit and it is usually difficult to modify the underlying procedures to generate a set of models customized to certain design intent. We present a framework which allows a user to interactively manipulate the set of generated models. Finally, a cost-effective method to generate digital content is to digitalize the real world. Nonetheless, the reconstructed point clouds are often noisy and contain missing data. We analyze point clouds of buildings to detect structural relations amongst building elements by means of template fitting. Once detected, these information can be used to improve the reconstruction output or to synthesize novel models via structural-aware editing.