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| Content Provider | Springer Nature Link |
|---|---|
| Author | Yan, Yan Chirikjian, Gregory S. |
| Copyright Year | 2014 |
| Abstract | 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. |
| Starting Page | 103 |
| Ending Page | 128 |
| Page Count | 26 |
| File Format | |
| ISSN | 00465755 |
| Journal | Geometriae Dedicata |
| Volume Number | 177 |
| Issue Number | 1 |
| e-ISSN | 15729168 |
| Language | English |
| Publisher | Springer Netherlands |
| Publisher Date | 2014-04-22 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Minkowski sum Ellipsoid Integral geometry Steiner’s formula Mean curvature Numerical approximation and computational geometry (primarily algorithms) Geometry |
| Content Type | Text |
| Resource Type | Article |
| Subject | Geometry and Topology |
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