Reconstruction approximating method by biquadratic splines of offset surfaces holes
Metadatos
Mostrar el registro completo del ítemEditorial
Springer
Materia
Spline approximation Hole filling Offset surface
Fecha
2022-01-08Referencia bibliográfica
Kouibia, A., Pasadas, M. Reconstruction approximating method by biquadratic splines of offset surfaces holes. J Math Chem (2022). [https://doi.org/10.1007/s10910-021-01322-7]
Patrocinador
Universidad de Granada / CBUAResumen
Standard Offset surfaces are defined as locus of the points which are at constant distance
along the unit normal direction from the generator surfaces. Offset are widely
used in various practical applications, such as tolerance analysis, geometric optics
and robot path-planning. In some of the engineering applications, we need to extend
the concept of standard offset to the generalized offset where distance offset is not
necessarily constant and offset direction are not necessarily along the normal direction.
Normally, a generalized offset is functionally more complex than its progenitor
because of the square root appears in the expression of the unit normal vector. For
this, an approximation method of its construction is necessary. In many situation it
is necessary to fill or reconstruct certain function defined in a domain in which there
is a lack of information inside one or several sub-domains (holes). In some practical
cases, we may have some specific geometrical constrains, of industrial or design
type, for example, the case of a specified volume inside each one of these holes. The
problem of filling holes or completing a 3D surface arises in all sorts of computational
graphics areas, like CAGD, CAD-CAM, Earth Sciences, computer vision in
robotics, image reconstruction from satellite and radar information, etc. In this work
we present an approximation method of filling holes of the generalized offset of a
surface when there is a lack information in a sub-domain of the function that define
it. We prove the existence and uniqueness of solution of this problem, we show how
to compute it and we establish a convergence result of this approximation method.
Finally, we give some graphical and numerical examples.