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Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic
Author(s) -
Figueiredo Luiz Henrique,
Stolfi Jorge
Publication year - 1996
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 - 10.1111/1467-8659.1550287
Subject(s) - affine arithmetic , rendering (computer graphics) , affine transformation , operand , interval arithmetic , computer science , enumeration , arithmetic , saturation arithmetic , mathematics , algorithm , arbitrary precision arithmetic , computer graphics (images) , discrete mathematics , geometry , bounded function , mathematical analysis
We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub‐formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster.