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Fast Generation of Smooth Implicit Surface Based on Piecewise Polynomial

Taku Itoh1, Susumu Nakata2
Nihon University, Narashino, Chiba, Japan.
Ritsumeikan University, Kusatsu, Siga, Japan.

Computer Modeling in Engineering & Sciences 2015, 107(3), 187-199.


To speed up generating a scalar field g(x) based on a piecewise polynomial, a new method for determining field values that are indispensable to generate g(x) has been proposed. In the proposed method, an intermediate for generating g(x) does not required, i.e., the field values can directly be determined from given point data. Numerical experiments show that the computation time for determining the field values by the proposed method is about 10.4–12.7 times less than that of the conventional method. In addition, on the given points, the accuracy of g(x) obtained by using the proposed method is almost the same as that of the conventional method. Furthermore, the computation time of the proposed method is almost not affected by the number of given points for the case where the number of all cells is large.


Implicit Surface, Piecewise Polynomial, Meshless Methods, Computer Graphics, B-spline, Surface Reconstruction

Cite This Article

Itoh, T., Nakata, S. (2015). Fast Generation of Smooth Implicit Surface Based on Piecewise Polynomial. CMES-Computer Modeling in Engineering & Sciences, 107(3), 187–199.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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