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Tolerance for barycentric coordinates in georrefered attribute interpolations

Ivanildo Barbosa, Flávio Luís de Mello, Luiz Felipe Coutinho Ferreira da Silva

Abstract


To apply the linear model to interpolate attributes for 2D points, the
attributes of three points ware weighted with their respective barycentric
coordinates. However, the finite arithmetic effects at the computation returns
barycentric coordinates contaminated with numerical residuals that, despite
their irrelevant dimensions that face the representable objects, it may influence
the system to make decisions involving values comparisons. In order to fix
this problem, tolerance limits were established around the theorical value, and
the processed values are attuned. This paper analyzes the influence from
attributes interpolation numerical precision over a computational environment.
The limits for residuals produced by computational barycentric coordinates
calculus were defined. Those limits were chosen so that data imprecision did
not exceed it original cartographical documents precision limits, according to
the Padrão de Exatidão Cartográfica (PEC), under the most rigid
classification. The residuals found in tests were quite smaller than the
precision assured by the cartographic document used. This way, the
established limits were reliable references to solve the purposed problem.

Keywords


Rede Triangular Irregular; Interpolação; Padrão de Exatidão Cartográfica; Triangular Irregular Network (TIN); Interpolation; Cartographical Exactness Standard