Intrinsic point-based surface processing

The need for the processing of surface geometry represents an ubiquitous problem in computer graphics and related disciplines. It arises in numerous important applications such as computer-aided design, reverse engineering, rapid prototyping, medical imaging , cultural heritage acquisition and preservation, video gaming and the movie industry. Existing surface processing techniques predominantly follow an extrinsic approach using combinatorial mesh data structures in the embedding Euclidean space to represent, manipulate and visualise the surfaces. This thesis advocates, firstly, the intrinsic processing of surfaces, i.e. processing directly across the surface rather than in its embedding space. Secondly, it continues the trend towards the use of point primitives for the processing and representation of surfaces. The discussion starts with the design of an intrinsic point sampling algorithm template for surfaces. This is followed by the presentation of a module library of template instanti-ations for surfaces in triangular mesh or point cloud form. The latter is at the heart of the intrinsic meshless surface simplification algorithm also put forward. This is followed by the introduction of intrinsic meshless surface subdivision, the first intrinsic meshless surface subdivision scheme and a new method for the computation of geodesic centroids on manifolds. The meshless subdivision scheme uses an intrinsic neighbourhood concept for point-sampled geometry also presented in this thesis. Its main contributions can therefore be summarised as follows: • An intrinsic neighbourhood concept for point-sampled geometry. • An intrinsic surface sampling algorithm template with sampling density guarantee. • A modular library of template instantiations for the sampling of planar domains and surfaces in triangular mesh or point cloud form. • A new method for the computation of geodesic centroids on manifolds. • An intrinsic meshless surface simplification algorithm. • The introduction of the notion of intrinsic meshless surface subdivision. • The first intrinsic meshless surface subdivision scheme. The overall result is a set of algorithms for the processing of point-sampled geometry centering around a generic sampling template for surfaces in the most widely-used forms of representation. The intrinsic nature of these point-based algorithms helps to overcome limitations associated with the more traditional extrinsic, mesh-based processing of surfaces when dealing with highly complex point-sampled geometry as is typically encountered today.