Details of some methods for approximating discontinuous surfaces
DOI:
https://doi.org/10.70577/asce.v5i1.640Keywords:
Non-regular functions, Approximation, Approximation methods, Rapidly varying data, Approximation of discontinuous surfaces.Abstract
The approximation of functions (surfaces) that present strong (or large) variations or vary rapidly (non-regular functions) from a set of data known (sparse and/or regularly distributed) of Lagrange-type, de , with , for an explicitly defined function (approximate) for , is a specific problem that has a significant number of applications, such as: approximation of maritime fronts from bathymetric data; approximation of surfaces with faults in the field of Geosciences; among other. Within this context, the purpose of the study is to review and present the details, in the sense of: structure, requirements, processes, functionality and results; of some of the approximation methods of non-regular functions, with emphasis on those useful for discontinuous surfaces which are caused by rapid variation in the data set. In this sense, the research was approached under a non-iterative qualitative approach, of a descriptive type, with a documentary research design; based on documents (books and articles) of a scientific nature related to the approximation methods of explicit surfaces from a set of data that present strong variations. As a result, an overview of the general processes used in the application of some of the most notable approximation methods for discontinuous surfaces was obtained. In conclusion, knowing the details of certain standard methods for approximating discontinuous surfaces allows you to choose the most appropriate approach, either by applying existing ones or by designing your own methodologies to optimize the expected results.
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