IEEE-INDIN 2007, Vienna, Austria
Ruiz O, Vanegas C. (2007) Statistical Assessment of Global and Local Cylinder Wear. Accepted for presentation at the IEEE 5th International Conference on Industrial Informatics, to be held in Vienna, Austria, July 23-27, 2007.

ABSTRACT
Assessment of cylindricity has been traditionally performed on the basis of cylindrical crowns containing a set of points that are supposed to belong to a controlled cylinder. As such, all sampled points must lie within a crown. In contrast, the present paper analyzes the cylindricity for wear applications, in which a statistical trend is assessed, rather than to assure that all points fall within a given tolerance. Principal Component Analysis is used to identify the central axis of the sampled cylinder, allowing to find the actual (expected value of the) radius and axis of the cylinder. Application of k-cluster and transitive closure algorithms allow to identify particular areas of the cylinder which are specially deformed. For both, the local areas and the global cylinder, a quantile analysis allows to numerically grade the degree of deformation of the cylinder. The algorithms implemented are part of the CYLWEAR(c) system and used to assess local and global wear cylinders.
 

ADM-INGEGRAF 2007, Perugia, Italy
Xoan A. Leiceaga, Oscar E. Ruiz, Carlos A. Vanegas, Jose Prieto, Manuel Rodriguez, Eva Soto (2007). Bi-curve and Multi-patch smoothing with Application to the Shipyard Industry. In Proceedings "Congresso Internazionale Congiunto XVI ADM - XIX INGEGRAF", Perugia, Italy, June 6-9, 2007, pp. 415-424.
 
ABSTRACT
Algorithms are proposed and implemented in a commercial system which allow for the C1-continuity matching between adjacent B-spline curves and B-spline patches. These algorithms only manipulate the positions of the control points, therefore respecting the constraint imposed by the sizes of the available commercial steel plates. The application of the algorithms respect the initial hull partition made by the designers and therefore the number and overall shape and position of the constitutive patches remains unchanged. Algorithms were designed and tested for smoothing the union of (a) two B-spline curves sharing a common vertex, (b) two B-spline surfaces sharing a common border, and (c) four B-spline surfaces sharing a common vertex. For this last case, an iterative heuristic degree-of-freedom elimination algorithm was implemented. Very satisfactory results were obtained with the application of the presented algorithms in shipyards in Spain.

TMCE 2006, Ljubljana, Slovenia
Ruiz O, Vanegas C. (2006) Piecewise linear curve reconstruction from point clouds. In I. Horvath, J. Duhovnik (Eds.), Proceedings of the TMCE 2006 Ljubljana, Slovenia: Sixth International Symposium on Tools and Methods of Competitive Engineering pp. 285–298.

ABSTRACT
Surface reconstruction from point samples must take into consideration the stochastic nature of the sample. This means, geometric algorithms reconstructing the surface should not insist in following in literal way each sampled point. Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing for the best possible (in statistical sense) geometric loci that represents the sample. Two meth-ods are presented in this paper, which respond to the stochastic nature of the sampling of a 1-manifold (a wire in 3-D). Both of them reduce the problem of quasi-planar samples to a problem in the XY plane. One of them uses the Voronoi Diagram and Delone Triangulation of the planarized sample to calculate the best possible tape-shaped polygon covering the point set, and then approaching the manifold with the me-dial axis of the polygon. The other method applies Principal Component Analysis to find a Piecewise Lin-ear approximation of the same aforementioned medial Axis. Results are presented in the realm of Computer Vision applications. The authors seek to integrate the two methods in the near future.

Journal of Engineering Design
Ruiz O, Vanegas C, Cadavid C. (2007) Principal Component and Voronoi Skeleton alternatives for curves reconstruction from noisy point sets. Special issue on shape search, reconstruction and optimization.

ABSTRACT
Surface reconstruction from point samples must take into consideration the stochastic nature of the sample. This means, geometric algorithms reconstructing the surface should not insist in following in literal way each sampled point. Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing for the best possible (in statistical sense) geometric loci that represents the sample. Two methods are presented in this paper, which respond to the stochastic nature of the sampling of a quasi-planar 1-manifold (a wire in 3-D). One of them uses the Voronoi Diagram and Delaunay Triangulation of the planarized sample to calculate the best possible tape-shaped polygon covering the point set, and then approaching the manifold with the medial axis of such a polygon. The other method applies Principal Component Analysis to find a Piecewise Linear approximation of the same aforementioned medial Axis. A comparative discussion of the methods is presented for Nyquist-compliant samples. Principal Component Analysis is simpler and more robust for non-self intersecting curves. For self-intersecting curves the Voronoi-Delaunay medial axis is more robust, at the price of higher computational complexity. An application is presented in Integration of meshes originated in Range Pictures of an artistic object. Such an application reaches the point of complete reconstruction of a unified mesh.