Front tracking with moving-least-squares surfaces

Hermite Interpolation of Implicit Surfaces with Radial Basis Functions

“…In fact, HRBF implicits have the good properties shared by previous RBF methods, as being able to deal with quite irregular datasets, while experiments indicate it is also superior to related approaches [2], [4], [7] when dealing with close sheets [2], [7] (Fig. 2).…”

“…In particular, the interpolation of scattered data sets is frequently desired in various specific applications, e.g., modeling [1], tracking of timedependent surfaces [2] and polygon soup interpolation [3]. In this work we tackle the problem of computing an implicit function interpolating Hermite scattered data defined as a set P of unorganized points with their corresponding normal vectors.…”

“…normal clustering), or even statistical inference to select points belonging to the same sheet before evaluating the implicit function [8], [9]. In this aspect, HRBF implicits are most similar to methods which build into the interpolation/approximation scheme a capability of identifying and handling close sheets without the need of additional information [2], [4], [5], [7]. Figure 2.…”

“…Figure 2. The issue of close sheets (see [2], [7]): when two parts of the surface are very close, many interpolation/approximation techniques behave poorly. Case (a) is an example of undesired interpolation, whereas case (b) is an example of undesired approximation.…”

Métodos implícitos para a reconstrução de superfícies a partir de nuvens de pontos

“…Por exemplo, o trabalho de Gois et al (2008) propõe o uso de técnicas baseadas em MLS (Moving Least Squares) para a representação das fronteiras de fluidos. A Figura 1.2 mostra a fronteira de um fluido sendo representada através de MLS conforme são realizadas deformações.…”