| As 3D digital photographic and scanning devices produce higher resolution images, acquired geometric data sets grow more complex in terms of the modeled objects' size, geometry, and topology. As a consequence, point-sampled geometry is becoming ubiquitous in graphics and geometric information processing, and poses new challenges which have not been fully resolved by the state-of-art graphical techniques.; In this dissertation, we address the challenges by proposing a novel framework for dynamic shape modeling, physical animation, and scientific simulation of point-sampled geometry. We developed the Point-based Modeling, Animation, and Simulation System, or P-MASS, for any scanned point geometry, without the need of converting them to polygonal meshes or higher order spline representations.; This dissertation follows our development of the P-MASS framework. First, we propose to combine point-based geometry with implicit surface representation and integrate the mass-spring-based dynamic implicit volumetric model with the point-based geometry, in order to introduce physics-based modeling and haptics interface to the sculpting and deformation of point set surfaces. We further incorporate scalar-field guided free-form deformation (FFD) into our surface deformation system to further expand local and global surface editing functionality. In addition to the implicit surface approach, we systematically develop a global conformal parameterization method for point-sampled surfaces, which can serve as a foundation for many other graphics applications, such as physical simulation, shape registration, morphing, attribute transfer, and spline surface fitting of point set surfaces, etc. Finally, we develop a meshless computational framework to simulate the elastic deformation and crack propagation of the underlying point-based surface and volumetric physical model.; Our P-MASS framework aims to bridge the gap between the point-sampled geometry with, physics-based modeling governed by partial differential equations. We have employed our methodologies in a wide variety of applications, including surface editing, reverse engineering and model restoration, solid modeling and simulation, attribute transfer and morphing, thin-shell elastic and fracture simulation, haptic rendering, etc. We describe these applications in detail and outline implementation issues pertaining to our framework. |
