Meshless Geometric Subdivision

摘要

Point-based surface processing has developed into an attractive alternative to mesh-based processing techniques for a number of geometric modeling applications. By working with point cloud data directly, any processing is based on the given raw data and its underlying geometry rather than any arbitrary intermediate representations and generally artificial connectivity relations. In this paper, we introduce the notion of meshless, or point cloud, subdivision by extending concepts from recursive mesh subdivision to the point cloud case. We are primarily concerned with showing the conceptual viability of this idea and propose a first geometric meshless subdivision framework. By replacing the role of mesh connectivity by intrinsic point proximity information and devising a meshless geodesic subdivision operator, we avoid the costly surface reconstruction, simplification and potential remeshing preprocessing steps typically required for supporting mesh-based subdivision, steps which are in general not directly related to the underlying object geometry. Furthermore, the maintenance of any global combinatorial data structure such as a mesh connectivity graph is not required. This property also makes our approach relatively easily extensible to the processing of point- based representations of higher-dimensional surfaces. Apart from introducing the idea of meshless subdivision, our main contributions are, firstly, a first meshless geodesic subdivision operator. Secondly, we present a new method for the computation of geodesic weighted averages on manifold surfaces, which are at the heart of our point cloud subdivision framework.