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Contouring Discrete Indicator Functions
Author(s) -
Manson J.,
Smith J.,
Schaefer S.
Publication year - 2011
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2011.01869.x
Subject(s) - contouring , marching cubes , fast marching method , isosurface , computer science , aliasing , boundary (topology) , simple (philosophy) , algorithm , surface (topology) , function (biology) , mathematics , computer graphics (images) , computer vision , visualization , artificial intelligence , mathematical analysis , geometry , philosophy , epistemology , evolutionary biology , undersampling , biology
We present a method for calculating the boundary of objects from Discrete Indicator Functions that store 2‐material volume fractions with a high degree of accuracy. Although Marching Cubes and its derivatives are effective methods for calculating contours of functions sampled over discrete grids, these methods perform poorly when contouring non‐smooth functions such as Discrete Indicator Functions. In particular, Marching Cubes will generate surfaces that exhibit aliasing and oscillations around the exact surface. We derive a simple solution to remove these problems by using a new function to calculate the positions of vertices along cell edges that is efficient, easy to implement, and does not require any optimization or iteration. Finally, we provide empirical evidence that the error introduced by our contouring method is significantly less than is introduced by Marching Cubes.