Study Of 3D Modeling And Processing Based On Meshes

3D geometry has become increasingly popular as a new form of digital media. Similar to other types of media, i.e., sound, image, and video, this requires tools and theories to model and process 3D geometry freely, robustly and fast in the fields of computer-aided design, computer simulation, computer animation and 3D games. It also has been the hot research topics in computer graphics. To author's knowledge, almost all of research works in computer graphics have been proposed for two main kinds of properties of 3D models: geometric shape and texture property. The main focus of this thesis is on algorithms and theories for shape and texture modeling and processing of surfaces represented by meshes. This includes the techniques for swept volume approximation computation for arbitrary meshes and free-form deformation in geometric and solid modeling, the method for 3D interactive texture painting in appearance modeling and texture design and the theory for geometry image based filtering.In computation of swept volume approximation, an improved technique to generate the swept volume approximation for arbitrary meshes is presented by introducing generator simplification and path resample using Frenet moving frames along the discreted sweeping trajectory. Other steps, such as a directed distance field computation on a uniform grid based on the hardware accelerated computation technique and iso-surface extraction using Marching Cubes algorithm, are also included in this algorithm. In addition, the simplification scheme and smoothing technique are applied to the swept volume generated from iso-surface extraction. A large number of analytical data is extracted from well-designed experiments, with which the influence of the generator simplification and the trajectory resample to the last swept volume is analyzed. It shows that the generator simplification can do improve the sweeping speed of the last swept volume in linear time while preserving its quality, but after reaching a critical point, the quality of the swept volume declines sharply with simplification of the generator. So does the trajectory resample.In free-form deformation, the basic functions are implied to the displacement curve representation to replace the Bezier-shaped displacement reference curves used in our original system. To author's knowledge, it can remedy the fact that the Bezier-shaped displacement reference curves are laid in local hulls in one hand, so that the deformation region can be further and larger; on other hand, it makes the computation and quality more robust and better. In addition, an extended curve constraint is presented to replace the original triangulation and parameterization techniques and instead of the Bezier-shaped displacement reference, the basic function with parameters to control the deformation area and the magnitude are used to surface deformation. Moreover, a nonuniform deformation technique is implemented by controlling the deformation region and magnitude nonuniformly. This technique also shows that it can simulate deformation effects constructed by other geometric primitives, such as ellipsoid and torus.In mesh filtering, the concept of geometry image is introduced into surface filter and a novel filter theory based on geometry images is illustrated, which is completely different in spirit Geometry images are created to represent 3D surfaces after cut and parameterization. Our improvement in resolution and reconstruction algorithms are presented while creating geometry images. These geometry images are then sent to the image processing toolboxes for varaints of filtering effects. 3D filtered models can be created via reconstruction from these filtered images. In our experiements, different and interesing surface filtering effects are achieved, such as blur, sharpen, crystallize, pixelize and variants of color adjustments.In appearance modeling, it is well known that the painting system based on texture mapping is often limited by the model's parameterization into 2D texture space. For models with...