Examinando por Autor "Ruiz, OE"

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    Ítem
    PL-geodesics on PL-continuous partial meshes
    (VYDAVATELSTVI ZAPADOCESKE UNIVERZITY, 2001-01-01) Ruiz, OE; Carlos, A; Cadavid, M; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Geometric characteristics of 2-manifolds embedded in R-3 space have been analyzed from the point of view of differential geometry and topology. In the past, results relevant to these areas have been Pound for C-infinity curves and surfaces. However, current scientific, industrial, entertainment and medical applications, and availability of more powerful point sampling systems, press for characterization of discrete counterparts for the continuous properties and characteristics evaluated previously in C-infinity curves and surfaces. Recent works have presented estimation methods for properties such as the principal and rotated quadrics of point sampled surfaces. The present article uses the findings of previous investigations to propose and implement a method for evaluation of planarity of surfaces. It is based on: (i) Estimation of a CO partial mesh fitting sets of planar or grid sample points. (ii) Evaluation of the piecewise – linear (PL) version of families of geodesic curves on the mesh. (iii) Diagnostic of the property of planarity based on the behavior of the families of geodesic curves. The present work can be applied in the area of design and manufacturing of products based on sheet materials, such as apparel, metal stamping, thin structures, etc.
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    Ítem
    Principal component analysis -PCA- and delone triangulations for PL approximation C-1-continuous 1-manifolds in R-N
    (ACTA PRESS, 2004-01-01) Ruiz, OE; Cadavid, CA; Garcia, MJ; Martinod, R; Ruiz, OE; Cadavid, CA; Garcia, MJ; Martinod, R; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecánica Aplicada
    A Method is presented which combines statistical (Principal Component Analysis) and deterministic (Voronoi-Delone) methods to find Piecewise Linear approximations of curves C-i(u) in R-3 sampled with statistical noise. If the curves are self-intersecting, there are a finite number of points in which they are not 1-manifolds. Otherwise, they are 1-manifolds in all extents. The combination presented, of PCA and V-D methods, allows the recovery of 1-manifold approximations for C-i(u) for self-intersecting quasi-planar and non self-intersecting curves. In the later case the PCA alone succeeds in finding 1-manifold PL approximations for them. The algorithm implemented finds applications in contour and shape reconstruction from noisy data, subject to sampling errors or blockage.
  • No hay miniatura disponible
    Ítem
    Principal component analysis -PCA- and delone triangulations for PL approximation C-1-continuous 1-manifolds in R-N
    (ACTA PRESS, 2004-01-01) Ruiz, OE; Cadavid, CA; Garcia, MJ; Martinod, R; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    A Method is presented which combines statistical (Principal Component Analysis) and deterministic (Voronoi-Delone) methods to find Piecewise Linear approximations of curves C-i(u) in R-3 sampled with statistical noise. If the curves are self-intersecting, there are a finite number of points in which they are not 1-manifolds. Otherwise, they are 1-manifolds in all extents. The combination presented, of PCA and V-D methods, allows the recovery of 1-manifold approximations for C-i(u) for self-intersecting quasi-planar and non self-intersecting curves. In the later case the PCA alone succeeds in finding 1-manifold PL approximations for them. The algorithm implemented finds applications in contour and shape reconstruction from noisy data, subject to sampling errors or blockage.