Point primitives for interactive modeling and processing of 3D-geometry

3D geometry has become increasingly popular as a new form of digital media. Similar to other types of media data, i.e., sound, images, and video, this requires tools to acquire, store, process, edit, and transmit 3D geometry. With increasing complexity of 3D geometric models and growing demand for advanced modeling functionality, significant effort is being devoted to the design of efficient, reliable, and scalable algorithms for digital geometry processing. This thesis investigates the use of point primitives for 3D geometry processing and interactive modeling. Representing surfaces by point clouds allows direct processing of 3D scanner data, which avoids the need for surface reconstruction methods. The structural simplicity of point-based representations supports efficient re-sampling for extreme geometric deformations and topology changes. It also leads to concise algorithms that are well suited for hardware implementation. The main focus of this thesis is on algorithms for shape and appearance modeling of surfaces represented by point clouds. This requires methods for local surface analysis and reconstruction, filtering, re-sampling, and estimation of the signed distance function. Local surface analysis is based on a statistical operator applied to local neighborhoods of point samples. This enables efficient estimation of the tangent space of the underlying surface, as well as providing different approximations for surface curvature. To compute local approximations of a surface represented by point samples, an extension of the moving least squares surface model is presented that adapts to the local sampling density. An important geometric processing tool is surface simplification. To reduce the complexity of point-sampled surfaces, various simplification methods are presented, including clustering, iterative point-pair contraction, and particle simulation. These methods are used to build hierarchies of surface approximations for efficient multilevel computations. A multi-scale surface representation is introduced that enables sophisticated editing functionality at different approximation levels. Representing a point-sampled surface at different levels of geometric detail supports advanced filtering methods such as enhancement filters. Multi-scale methods are also applied to implement a feature extraction pipeline for point-sampled surfaces with particular emphasis on robustness and efficiency. The above methods are integrated into a unified framework for point-based shape and appearance modeling. Shape modeling functionality includes boolean operations and free-form deformation, appearance editing comprises painting, texturing, sculpting, and filtering methods. Based on a dynamic sampling paradigm, this system defines a complete and versatile modeling environment for 3D content creation.