Abstract
We study the oriented bounding box on a set of continuously moving points.
The smallest oriented bounding box is the smallest bounding box, oriented to minimize the area. This optimal orientation may be very unstable as the points are moving, which is undesirable in many practical scenarios. Alternatively, we can bound the speed with which the orientation of the bounding box may change. However, this can increase the area of the resulting bounding box. In this paper we study the trade-off between stability and quality of the oriented bounding box.
We define a "chasing" algorithm that attempts to follow the optimal orientation with bounded speed. Under mild conditions, we show that chasing algorithms with sufficient speed approximate the optimal area at every time step for oriented bounding boxes. The analysis of such chasing algorithms is challenging and has received little attention in literature. Hence we believe that our methods used to perform this analysis are of independent interest.
The smallest oriented bounding box is the smallest bounding box, oriented to minimize the area. This optimal orientation may be very unstable as the points are moving, which is undesirable in many practical scenarios. Alternatively, we can bound the speed with which the orientation of the bounding box may change. However, this can increase the area of the resulting bounding box. In this paper we study the trade-off between stability and quality of the oriented bounding box.
We define a "chasing" algorithm that attempts to follow the optimal orientation with bounded speed. Under mild conditions, we show that chasing algorithms with sufficient speed approximate the optimal area at every time step for oriented bounding boxes. The analysis of such chasing algorithms is challenging and has received little attention in literature. Hence we believe that our methods used to perform this analysis are of independent interest.
| Original language | English |
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| Pages | 39:1-39:7 |
| Number of pages | 7 |
| Publication status | Published - 2019 |
| Event | 35th European Workshop on Computational Geometry (EuroCG 2019) - Utrecht, Netherlands Duration: 18 Mar 2019 → 20 Mar 2019 Conference number: 35 http://www.eurocg2019.uu.nl/ |
Workshop
| Workshop | 35th European Workshop on Computational Geometry (EuroCG 2019) |
|---|---|
| Abbreviated title | EuroCG |
| Country/Territory | Netherlands |
| City | Utrecht |
| Period | 18/03/19 → 20/03/19 |
| Internet address |