@Article{icces.2024.012260,
AUTHOR = {Taku Itoh},
TITLE = {Implicit Surfaces Generated from Field Values Directly-Obtained from Scattered Points},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {31},
YEAR = {2024},
NUMBER = {4},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v31n4/58832},
ISSN = {1933-2815},
ABSTRACT = {In meshless methods, although elements constructing an analysis domain are not required, the domain should be represented in some way, instead. A scalar field g(x), that contains the analysis domain, is sometimes employed, and the boundary of analysis domain is represented as an implicit surface, g(x) = 0. In this study, we consider generating an implicit surface from scattered points on the surface of an object. The scattered points are obtained by a three-dimensional scanning device. To generate g(x), field values f<sub>ijk</sub> on N3 uniform grid points x<sub>ijk</sub> are required. Although the field values f<sub>ijk</sub> have been originally obtained from another scalar field f(x) [1], they can be obtained from a set of scattered points directly by a method described in [2]. After field values f<sub>ijk</sub> are obtained, the scalar field g(x) is often constructed as a set of piecewise polynomials based on B-spline functions [1]. Note that, to represent the piecewise polynomial in each of cells in the grid, some coefficients of the piecewise polynomial must be stored on a device memory. For this reason, when N becomes large, the memory cost tends to be large. If the field values f<sub>ijk</sub> can be interpolated without piecewise polynomial, the memory cost may be decreased. In this study, to directly interpolate the field values f<sub>ijk</sub>, we focus on the isoparametric elements that have been employed in the finite element analysis. The purpose of this study is to present a method for generating implicit surface employing the isoparametric elements from field values directly-obtained from scattered points. Some kinds of isoparametric elements will be applied, the performance of each of them is compared. Results and discussions will be presented at the conference.},
DOI = {10.32604/icces.2024.012260}
}