Studies On Digital Geometry Processing Of 3D Point-sampled Models

Recently, point primitive enjoyed great attention in computer graphics community. Compared with traditional primitive likes triangular meshes, shape representation with point primitives has shown distinct advantage on rendering efficiency, convenient 3D point data acquirement and data structure maintenance, especially for highly complex objects or dynamically changing shapes. With the more comprehensive and sophisticated investigation in the digital geometry processing of point-sampled geometry, we call for more new algorithms and more technologies to push the point - based surface presentation into practicality. As a new type of medium and surface presentation, compared with the traditional digital image processing, video processing, mesh processing, digital geometry processing of point-sampled geometry is still in its initialization stage.Based on the sound mathematical foundation, this dissertation investigates the use of point primitives for 3D digital geometry processing and interactive modeling. The research scope ranges from the pre-processing such as the denoising, geometry completion, to geometry processing and animation, that is , nearly every important aspects in the digital geometry processing of point set surface. We have presented a nearly complete geometry processing framework for point-sample geometry. Since the there is no connectivity information between point primitives, most the algorithms proposed in this dissertation can be directly extended to the mesh models.The major contributions of the dissertation are:· A dynamic well-balanced flow equation is introduced to filtering the point-sampled geometry. Besides the necessary denoising function, the filtering operator has the following desired properties: feature reservation, anti-shrinkage, anti-point drifting. In order to receive a low frequency geometric signal of the point set surface, we also presented a mean curvature flow operator.· Based on a global optimized approach, direct texture synthesis method on point-sampled surface is achieved by energy minimization. To enhance the roughness appearance of the geometry, we reconstruct the normals of the surfels for rendering according to the texture synthesis result. In addition, based on 3D flow fields, we implement a user controllable texture synthesis algorithm for the point set surface.· Color texture completion and geometry completion algorithm . For blank...