PL-geodesics on PL-continuous partial meshes
Por:
Ruiz, OE, Carlos, A, Cadavid, M
Publicada:
1 ene 2001
Resumen:
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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