Abstract
We study accuracy guaranteed solutions of geometric problems define on convex region under an assumption that input points are known only up to a limited accuracy, that is, each input point is given by a convex region that represents the possible locations of the point. We show how to compute tight error bounds for basic problems such as convex hull, Minkowski sum of convex polygons, diameter of points, and so on. To compute tight error bound from imprecise coordinates, we represent a convex region by a set of half-planes whose intersection gives the region. Error bounds are computed by applying rotating calipers paradigm to this representation.
This work is supported by the Grant in Aid for Scientific Research of the Ministry of Education, Science and Cultures of Japan.
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© 2001 Springer-Verlag Berlin Heidelberg
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Nagai, T., Tokura, N. (2001). Tight Error Bound of Goemetric Problems on Convex Objects with Imprecise Coordinates. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_24
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DOI: https://doi.org/10.1007/3-540-47738-1_24
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