The santalo point of a planar convex set

✍ Scribed by M.J. Kaiser

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 505 KB
• Volume: 6
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/0893-9659(93)90011-b

✦ Synopsis

An algorithm is described to determine the minimum area polar set of a planar convex polygon described in terms of its vertices. We adopt a result due to Santalo to verify our minimizing solution, and then demonstrate the search procedure on a few examples. 'For triangular (and centrally symmetric) regions the center-of-gravity of P3 will coincide with the center-ofgravity of Pi, or more simply, g(P3) = g(P:;g(Ps)). In th8 's case the minimal area occurs for the initial duality point and thus there is no need to search for the solution; generally speaking, since simplice~ HIT "self-dud" [3],

this is true in any dimension.