Abstract
Let S be a set of points in IRd, each with a weight that is not known precisely, only known to fall within some range. What is the locus of the centroid of S? We prove that this locus is a convex polytope, the projection of a zonotope in IRd+1. We derive complexity bounds and algorithms for the construction of these "centroid polytopes".
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CITATION STYLE
Bern, M., Eppstein, D., Guibas, L., Hershberger, J., Suri, S., & Wolter, J. (1995). The centroid of points with approximate weights. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 979, pp. 460–472). Springer Verlag. https://doi.org/10.1007/3-540-60313-1_163
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