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Implicit Surfaces Generated from Field Values Directly-Obtained from Scattered Points

Taku Itoh^1,*

1 College of Industrial Technology, Nihon University, 1-2-1 Izumi-cho, Narashino, Chiba, 275-8575, Japan

* Corresponding Author: Taku Itoh. Email:

The International Conference on Computational & Experimental Engineering and Sciences 2024, 31(4), 1-1. https://doi.org/10.32604/icces.2024.012260

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_ijk on N3 uniform grid points x_ijk are required. Although the field values f_ijk 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_ijk 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_ijk can be interpolated without piecewise polynomial, the memory cost may be decreased. In this study, to directly interpolate the field values f_ijk, 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.

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Keywords

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