Reducing the Time Complexity of Minkowski-Sum Based Similarity Calculations by Using Geometric Inequalities
نویسندگان
چکیده
The similarity of two convex polyhedra A and B may be calculated by evaluating the volume or mixed volume of their Minkowski sum over a specific set of relative orientations. The relative orientations are characterized by the fact that faces and edges of A and B are parallel as much as possible. For one of these relative orientations the similarity measure is optimal. In this article we propose and test a method to reduce the number of relative orientations to be considered by using geometric inequalities in the slope diagrams of A and B. In this way the time complexity of O(n) is reduced to O(n). This is derived, and verified experimentally.
منابع مشابه
University of Groningen Reducing the time complexity of Minkowski-sum based similarity calculations by using geometric inequalities
The similarity of two convex polyhedra A and B may be calculated by evaluating the volume or mixed volume of their Minkowski sum over a specific set of relative orientations. The relative orientations are characterized by the fact that faces and edges of A and B are parallel as much as possible. For one of these relative orientations the similarity measure is optimal. In this article we propose...
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