Reconstruction of freeform surfaces for metrology

The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces exhibit enhanced performance especially when they take aspheric forms or more complex forms with multi-undulations. This study is mainly focused on the reconstruction of complex shapes such as freeform optical surfaces, and on the characterization of their form. The computer graphics community has proposed various algorithms for constructing a mesh based on the cloud of sample points. The mesh is a piecewise linear approximation of the surface and an interpolation of the point set. The mesh can further be processed for fitting parametric surfaces (Polyworks® or Geomagic®). The metrology community investigates direct fitting approaches. If the surface mathematical model is given, fitting is a straight forward task. Nonetheless, if the surface model is unknown, fitting is only possible through the association of polynomial Spline parametric surfaces. In this paper, a comparative study carried out on methods proposed by the computer graphics community will be presented to elucidate the advantages of these approaches. We stress the importance of the pre-processing phase as well as the significance of initial conditions. We further emphasize the importance of the meshing phase by stating that a proper mesh has two major advantages. First, it organizes the initially unstructured point set and it provides an insight of orientation, neighbourhood and curvature, and infers information on both its geometry and topology. Second, it conveys a better segmentation of the space, leading to a correct patching and association of parametric surfaces.EMR

Performance comparison of adapted delaunay triangulation method over nurbs for surface optimization problems

Traditionally NURBS (Non-Uniform Rational Basis Spline) are used as the basis for defining free-form surfaces as they can define non-regular surfaces with minimal control points. However, they require parameters such as knot vectors and weights to configure a surface. Similarly, DT (Delaunay Triangulation) is proven and used widely for meshing, rendering and surface reconstruction applications, but its capability in freeform surface design for optimization is untested. Thus, this paper proposes Adapted Delaunay Triangulation (ADT) method which can generate a surface from scattered data points without any parameters. The paper presents a comparison of the performance of ADT method and NURBS fitting method for surface generation from scattered 3D coordinate points. This method was suggested so that the generated surface could be used in Stochastic Optimization Algorithm (SOA) methods and computational fluid dynamics applications (CFD) simultaneously. Data points that other 3D point clouds fitting methods would ignore as outliers are included in ADT method. Small change in each data point during optimization cycle should show a distinctive change in its output as SOA approaches depend on such differences for its optimal performance. Special consideration has been made for fast processing and rendering of the surface with minimum complexity (removing parameters such as knots and weights) and storage requirements as SOA methods demand generation of numerous surfaces to solve any problem

Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x. <br /

On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing

his paper deals with the implementation in 3D of the constrained natural element method (CNEM) in order to simulate material forming involving large strains. The CNEM is a member of the large family of mesh-free methods, but is at the same time very close to the finite element method. The CNEM’s shape function is built using the constrained Voronoï diagram (the dual of the constrained Delaunay tessella- tion) associated with a domain defined by a set of nodes and a description of its border. The use of the CNEM involves three main steps. First, the constrained Voronoï diagram is built. Thus, for each node, a Voronoï cell is geometrically defined, with respect of the boundary of the domain. Then, the Sibson-type CNEM shape functions are computed. Finally, the discretization of a generic variational for- mulation is defined by invoking an ‘‘stabilized conforming nodal integration’’. In this work, we focus especially on the two last points. In order to compute the Sibson shape function, five algorithms are pre- sented, analyzed and compared, two of them are developed. For the integration task, a discretization strategy is proposed to handle domains with strong non-convexities. These approaches are validated on some 3D benchmarks in elasticity under the hypothesis of small transformations. The obtained results are compared with analytical solutions and with finite elements results. Finally, the 3D CNEM is applied for addressing two forming processes: high speed shearing and machining

Reconstruction d'ensembles compacts 3D

Reconstruire un modèle à partir d'échantillons est un problème central se posant en médecine numérique, en ingénierie inverse, en sciences naturelles, etc. Ces applications ont motivé une recherche substantielle pour la reconstruction de surfaces, la question de la reconstruction de modèles plus généraux n'ayant pas été examinée. Ce travail présente an algorithme visant à changer le paradigme de reconstruction en 3D comme suit. Premièrement, l'algorithme reconstruit des formes générales--des ensembles compacts et non plus des surfaces. Sous des hypothèses appropriées, nous montrons que la reconstruction a le type d'homotopie de l'objet de départ. Deuxièmement, l'algorithme ne génère pas une seule reconstruction, mais un ensemble de reconstructions plausibles. Troisièmement, l'algorithme peut être couplé à la persistance topologique, afin de sélectionner les traits les plus stables du modèle reconstruit. Enfin, en cas d'échec de la reconstruction, la méthode permet une identification aisée des régions sous-echantillonnées, afin éventuellement de les enrichir. Ces points clefs sont illustrés sur des modèles difficiles, et devraient permettre de mieux tirer parti de leurs caractéristiques dans les application sus-citées

Object-based classification of photogrammetrically acquired point cloud

This graduation thesis addresses unmanned aerial vehicle for aerial data acquisition - quadrocopter. Data (point cloud), acquired with the vehicle is presented and object-based classification of this point cloud is performed. The thesis describes methodology of data preparation with free open source software SAGA and classification of point cloud in free open source software InterImage. Protocol of producing different data layers from the point cloud is tested and the influence of input data on the segmentation quality is presented. We focused on finding appropriate parameters for classification and studied their impact on classification results based on histogram analysis. We used the knowledge of parameter selections obtained from one point cloud and applied it to another point cloud that represented similar area. We discovered that the classification with the same parameters can be repeated only for certain object classes. For sufficient classification of all object classes new parameter settings are required.\u