Stacking Monotone Polytopes

This paper addresses the problem of computing the optimal stacking of two monotone polytopes P and Q in Rd. A monotone polytope in Rd is defined as a polytope whose intersection with any line parallel to the last coordinate axis xd is connected, and the stacking of P and Q is defined as a translatio...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-09, Vol.16 (9), p.1246
Main Authors: Ahn, Hee-Kap, Lee, Seung Joon, Yoon, Sang Duk
Format: Article
Language:English
Subjects:
Algorithms
computational geometry
exact algorithm
monotone polytope
Polytopes
stacking problem
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Summary:This paper addresses the problem of computing the optimal stacking of two monotone polytopes P and Q in Rd. A monotone polytope in Rd is defined as a polytope whose intersection with any line parallel to the last coordinate axis xd is connected, and the stacking of P and Q is defined as a translation of Q, such that “Q touches P from above”. To evaluate the stack, we use three different scoring criteria: (1) the height of the stack, (2) the maximum pointwise distance along the xd-axis, and (3) the volume between P and Q. We propose exact algorithms to compute the optimal stacking for each scoring criterion.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16091246