Positive Center Sets of Convex Curves

Autor: Yunlong Yang, Pingliang Huang, Shengliang Pan
Rok vydání: 2015
Předmět:
Zdroj: Discrete & Computational Geometry. 54:728-740
ISSN: 1432-0444
0179-5376
DOI: 10.1007/s00454-015-9715-9
Popis: In this paper we shall investigate the positive center set $${\mathfrak {P}}(\gamma )$$P(?) of a convex curve $$\gamma $$? and show that $${\mathfrak {P}}(\gamma )$$P(?) has only one point if and only if $$\gamma $$? is a circle; $${\mathfrak {P}}(\gamma )$$P(?) is a segment if and only if $$\gamma $$? is a sausage curve; if $$\gamma $$? is a strictly convex non-circular curve, then $${\mathfrak {P}}(\gamma )$$P(?) is a domain of positive area; and furthermore, if $$\gamma $$? is a constant width curve, then $${\mathfrak {P}}(\gamma )$$P(?) is its inner parallel body $$K_{-r_1}$$K-r1.
Databáze: OpenAIRE
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