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Normal Computation for Discrete Surfaces in 3D Space
Author(s) -
Thürmer Grit,
Wüthrich Charles A.
Publication year - 1997
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 - 10.1111/1467-8659.00138
Subject(s) - computation , rendering (computer graphics) , disjoint sets , surface (topology) , discrete space , normal , normal space , mathematics , neighbourhood (mathematics) , space (punctuation) , computer science , point (geometry) , algorithm , geometry , mathematical analysis , computer graphics (images) , discrete mathematics , topological space , topological vector space , operating system
Associating normal vectors to surfaces is essential for many rendering algorithms. We introduce a new method to compute normals on discrete surfaces in object space. Assuming that the surface separates space locally into two disjoint subsets, each of these subsets contains implicitly information about the surface inclination. Considering one of these subsets in a small neighbourhood of a surface point enables us to derive the surface normal from this set. We show that this leads to exact results for C 1 continuous surfaces in R 3 . Furthermore, we show that good approximations can be obtained numerically by sampling the considered area. Finally, we derive a method for normal computation on surfaces in discrete space.