منابع مشابه
Area-constrained planar elastica.
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties; not only can the Euler-Lagrange equation be integrated to provide a quadrature for ...
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A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. These layouts are used as rectangular cartograms in cartography, as floorplans in building architecture and VLSI design, and as graph drawings. Often areas are associated with the rectangles of a rectangular layout and it is desirable for one rectangular layout to represent several area assignm...
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It is known that for any set V of n ≥ 4 points in the plane, not in convex position, there is a 3-connected planar straight line graph G = (V, E) with at most 2n− 2 edges, and this bound is the best possible. We show that the upper bound |E| ≤ 2n continues to hold if G is constrained to contain a given graph G0 = (V,E0), which is either a 1-factor (i.e., disjoint line segments) or a 2-factor (i...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2002
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.65.031801