Centers of convex bodies
Abstract
This dissertation investigates general center points of polygons and convex bodies and some of their applications to engineering science. A general definition of center points is given and two dual representations are characterized. Solution points that solve similar minimization problems are shown to have similar characterizations. Zero-, one-, and two-dimensional analytic centers are defined, and a zero-dimensional analytic center is shown to approach a two-dimensional analytic center under an appropriate limit. A one-dimensional analytic center of a polygonal system is extended to convex bodies. A family of analytic curvature centroids is examined and characterized. The zero-dimensional analytic center is shown to be equivalent to the solution of the complex moment problem, and is then applied to obnoxious facility location problems. Center points are used to categorize the out-of-roundness measures of industrial metrology. It is shown that a linear (limacon) approximation to the Minimum Zone Circle (MZC) problem (due to Chetwynd and obtained using duality theory of linear programming) has a characterization originally due to Bonnesen, and a result on the equivalence between the MAD (Minimum Area Difference), MIC (Maximum Inscribed Circle), and MCC (Minimum Circumscribed Circle) problem is demonstrated for a centrally symmetric convex body.
Degree
Ph.D.
Advisors
Morin, Purdue University.
Subject Area
Industrial engineering
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