Research On Several Key Algorithms For CAD Modeling

Modeling technology is always one of the hot spots in CAD area. This dissertation focuses on a few related technologies of geometric modeling, include the boundary evaluation of quadric-based models and several algorithms of triangle mesh.This dissertation proposes algebraic algorithms for computing the intersections between torus and natural quadrics. It presents a geometric and intuitive way to identify and compute the conic section intersections, and presents a novel, efficient and robust algorithm to sorting these unordered intersection points to form intersection curves. For torus/sphere intersection, the intersection curves can be explicitly represented by algebraic forms.Chapter 3 introduces some approaches to improve mesh reconstruction based region-growing, such as grid-dividing on point cloud, normal evaluation, and mesh optimization. Furthermore, combined with mesh mergence algorithm, the mesh reconstruction algorithm is good for large-scale point data.Chapter 4 presents a mesh mergence algorithm driven by IPD algorithm, before which the redundant triangles are deleted by backwards approach. It can work well even if the high curvature meshes are being merged.Finally, this dissertation presents a mesh denoising algorithm based on bilateral filter, which doesn't modify the differential property and significantly perverse the features. It is geometric and intuitive.