IMPLICIT CURVES AND SURFACES MODELING WITH PSEUDOGAUSSIAN INTERPOLATION
DOI:
https://doi.org/10.15588/1607-3274-2025-1-3Keywords:
surface representation, curve representation, implicit representation, pseudo-Gaussian function, regular grid, implicit surface modeling, implicit surface data formatAbstract
Context. With the contemporary development of topological optimization, and parametric and AI-guided design, the problem of implicit surface representation became prominent in additive manufacturing. Although more and more software packages use implicit modeling for design, there is no common standard way of writing, storing, or passing a set of implicit surfaces or curves over the network. The object of the study is one of the possible ways of such representation, specifically: modeling implicit curves and surfaces using pseudo-Gaussian interpolation.
Objective. The goal of the work is the development of a modeling method that improved the accuracy of the implicit object representation wothout significant increase in memory used or processing time spent.
Method. One of the conventional ways to model an implicit surface would be to represent its signed distance function (SDF) with its values defined on a regular grid. Then a continuous SDF could be obtained from the grid values by means of interpolation.
What we propose instead is to store not SDF values but the coefficients of a pseudo-Gaussian interpolating function in the grid, which would enable picking the exact interpolation points before the SDF model is written. In this way we achieve better accuracy in the regions we’re interested the most in with no additional memory overhead.
Results. The developed method was implemented in software for curves in 2D and validated against several primitive implicit curves of different nanture: circles, sqaures, rectangles with different parameters of the model. The method has shown improved accuaracy in general, but there were several classes of corner cases found for which it deserves further development.
Conclusions. Pseudo-Gaussian interpolation defined as a sum of radial basis functions on a regular grid with points of interpolation defined in the proximity of the grid points generally allows to model an implicit surface more accurately than a voxel model interpolation does. The memory intake or computational toll isn’t much different in these two approaches. However, the interpolating points selection strategy and the choice of the best modeling parameters for each particular modeling problem remain an open quesition.
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Copyright (c) 2025 N. M Ausheva, Iu. V. Sydorenko, O. S. Kaleniuk, O. V. Kardashov, M. V. Horodetskyi
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