Framework for Local Restructure of Meshed Surfaces

While the design step should be free from computational related constraints and operations due to its artistic aspect, the modeling phase has to prepare the model for the later stages of the pipeline. This dissertation is concerned with the design and implementation of a framework for local remeshing and optimization. Based on the experience gathered, a full study about mesh quality criteria is also part of this work. The contributions can be highlighted as: (1) a local meshing technique based on a completely novel approach constrained to the preservation of the mesh of non interesting areas. With this concept, designers can work on the design details of specific regions of the model without introducing more polygons elsewhere; (2) a tool capable of recovering the shape of a refined area to its decimated version, enabling details on optimized meshes of detailed models; (3) the integration of novel techniques into a single framework for meshing and smoothing which is constrained to surface structure; (4) the development of a mesh quality criteria priority structure, being able to classify and prioritize according to the application of the mesh. Although efficient meshing techniques have been proposed along the years, most of them lack the possibility to mesh smaller regions of the base mesh, preserving the mesh quality and density of outer areas. Considering this limitation, this dissertation seeks answers to the following research questions: 1. Given that mesh quality is relative to the application it is intended for, is it possible to design a general mesh evaluation plan? 2. How to prioritize specific mesh criteria over others? 3. Given an optimized mesh and its original design, how to improve the representation of single regions of the first, without degrading the mesh quality elsewhere? Four main achievements came from the respective answers: 1. The Application Driven Mesh Quality Criteria Structure: Due to high variation in mesh standards because of various computer aided operations performed for different applications, e.g. animation or stress simulation, a structure for better visualization of mesh quality criteria is proposed. The criteria can be used to guide the mesh optimization, making the task consistent and reliable. This dissertation also proposes a methodology to optimize the criteria values, which is adaptable to the needs of a specific application. 2. Curvature Driven Meshing Algorithm: A novel approach, a local meshing technique, which works on a desired area of the mesh while preserving its boundaries as well as the rest of the topology. It causes a slow growth in the overall amount of polygons by making only small regions denser. The method can also be used to recover the details of a reference mesh to its decimated version while refining it. Moreover, it employs a geometric fast and easy to implement approach representing surface features as simple circles, being used to guide the meshing. It also generates quad-dominant meshes, with triangle count directly dependent on the size of the boundary. 3. Curvature-based Method for Anisotropic Mesh Smoothing: A geometric-based method is extended to 3D space to be able to produce anisotropic elements where needed. It is made possible by mapping the original space to another which embeds the surface curvature. This methodology is used to enhance the smoothing algorithm by making the nearly regularized elements follow the surface features, preserving the original design. The mesh optimization method also preserves mesh topology, while resizing elements according to the local mesh resolution, effectively enhancing the design aspects intended. 4. Framework for Local Restructure of Meshed Surfaces: The combination of both methods creates a complete tool for recovering surface details through mesh refinement and curvature aware mesh smoothing