Finite Point Sets and Oriented Matroids Combinatorics in Geometry

Many algorithms in computational geometry deal with finite point sets represented by matrices over the reals. The set of oriented matroids can be considered as a set of topological invariants of matrices over the reals together with a natural set of such topological objects making the set complete. One main advantage of these topological invariants is its possible representation as signed vectors allowing computational investigations easily. Various systems of axioms exist for oriented matroids. We try to illustrate basic ideas in the theory of oriented matroids by using various interesting example classes.

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