Simplificação de malhas triangulares baseada em templates

• Ano de defesa: 2015
• Autor(a) principal: Macedo, Diego Chicuta
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Alagoas; Brasil; Programa de Pós-Graduação em Matemática; UFAL
• Palavras-chave em Português: Geometria; Simplificação de malhas; Topologia; Distância geodésica; Principal Components Analysis (PCA); Geometry; Mesh simplification; Topology; Geodesic Distance; Fast Marching Method (FMM); CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://www.repositorio.ufal.br/handle/riufal/6660

Algorithms for mesh simplification can be applied to remove vertices avoiding changes to the topology of the object. In this work we have developed a technique for simplification of 3D meshes based on templates. We present a method that tries to optimize the complexity of a mesh decreasing the number of vertices and faces, so that the geometry and topology of the surface are preserved. Our goal is to define the geometry of the template so that it approximates our original surface. We will use the Principal Components Analysis (PCA) to achieve an initial alignment of the two surfaces. This alignment searches a fit between the two meshes so that we have an alignment of its main directions, which allows proper generation of correspondence between its vertices. With the aim of improving the correspondence between the vertices of both meshes, we added the geodetic distance information of each vertex to the of fixed points of dense mesh, using Fast Marching (FMM). This allows us to discriminate vertices distant in the mesh, but next in the distance euclidean. For the generation of the new mesh that is less dense than the initial we will use a technique based on projections that aims to change the position of the vertices of a dense mesh by their respective correspondences in the template that has quantity of vertices less. As a result of these projections we Will have a mesh resulting much less dense than the initial, which preserves the geometrical and topological properties.