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Quad-Edge Data Structures in Two and Three Dimensions

Because Clifford algebra abstracts beyond absolute position, its elements cannot be directly drawn. They need to be supplemented by a coordinate system. Because numbers, both in such a coordinate system and in the coefficients for the Clifford elements are subject to round-off or truncation errors in the computer, both coordinates and Clifford elements also need complementary topological information. Coordinates and topology make up a data structure representing spatial data, supplemented by Clifford algebra to quantify angles. We start in two dimensions with the quad-edge data structure [GS85, MBC + 02].