Closed-form characterization of the Minkowski sum and difference of two ellipsoids
نویسندگان
چکیده
This paper makes three original contributions: (1) Explicit closed-form parametric formulas for the boundary of the Minkowski sum and difference of two arbitrarily oriented solid ellipsoids in n-dimensional Euclidean space are presented; (2) Based on this, new closed-form lower and upper bounds for the volume contained in these Minkowski sums and differences are derived in the 2D and 3D cases and these bounds are shown to be better than those in the existing literature; (3) A demonstration of how these ideas can be applied to problems in computational geometry and robotics is provided, and a relationship to the Principal Kinematic Formula from the fields of integral geometry and geometric probability is uncovered.
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