Geodesic-based manifold learning for parameterization of triangular meshes

Reverse Engineering (RE) requires representing with free forms (NURBS, Spline, Bézier) a real surface which has been pointsampled -- To serve this purpose, we have implemented an algorithm that minimizes the accumulated distance between the free form and the (noisy) point sample -- We use a dualdistance calculation point to / from surfaces, which discourages the forming of outliers and artifacts -- This algorithm seeks a minimum in a function that represents the fitting error, by using as tuning variable the control polyhedron for the free form -- The topology (rows, columns) and geometry of the control polyhedron are determined by alternative geodesicbased dimensionality reduction methods: (a) graphapproximated geodesics (Isomap), or (b) PL orthogonal geodesic grids -- We assume the existence of a triangular mesh of the point sample (a reasonable expectation in current RE) -- A bijective composition mapping allows to estimate a size of the control polyhedrons favorable to uniformspeed parameterizations -- Our results show that orthogonal geodesic grids is a direct and intuitive parameterization method, which requires more exploration for irregular triangle meshes -- Isomap gives a usable initial parameterization whenever the graph approximation of geodesics on be faithful -- These initial guesses, in turn, produce efficient free form optimization processes with minimal errors -- Future work is required in further exploiting the usual triangular mesh underlying the point sample for (a) enhancing the segmentation of the point set into faces, and (b) using a more accurate approximation of the geodesic distances within , which would benefit its dimensionality reduction

• Autores: Acosta, Diego A.; Ruíz, Óscar E.; Arroyave, Santiago; Ebratt, Roberto; Cadavid, Carlos; Londono, Juan J.
• Fecha de publicación: 2014
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/9668
• Acceso en línea: http://hdl.handle.net/10784/9668
• Palabra clave: TRIANGULACIÓN; POLIEDRO; ALGORITMOS; SUPERFICIES MÍNIMAS; TOPOLOGÍA; TEORÍA DE GRAFOS; GEODESIA; GENERACIÓN NUMÉRICA DE MALLAS (ANÁLISIS NUMÉRICO); Triangulation; Polyhedra; Algorithms; Minimal surfaces; Topology; Graph theory; Geodesy; Numerical grid generation (Numerical analysis); Triangulation; Polyhedra; Algorithms; Minimal surfaces; Topology; Graph theory; Geodesy; Numerical grid generation (Numerical analysis); Ingeniería inversa; Superficies NURBS; Geometría computacional; Reconstrucción superficial; Triangulación de Delaunay
• License: Acceso abierto