PL-Geodesics on PL-continuous partial meshes
Ruíz, Óscar E.
Cadavid M., Carlos A.
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Geometric characteristics of 2-manifolds embedded in R3 space have been analyzed from the point of view of differential geometry and topology -- In the past, results relevant to these areas have been found for C∞ 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∞ 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 C0 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