acase@tulane.edu / We study the problem of computing the minimum homotopy area of a planar normal curve. The area of a homotopy is the area swept by the homotopy on the plane. First, we consider a specific class of curves, namely self-overlapping curves, and show that the minimum homotopy area of a self-overlapping curve is equal to its winding area. For an arbitrary normal curve, we show that there is a decomposition of the curve into the self-overlapping subcurves such that the minimum homotopy area can be computed as the sum of winding areas of each self-overlapping subcurve in the decomposition. / 1 / Karakoc, Selcuk
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_76399 |
| Date | January 2017 |
| Contributors | Karakoc, Selcuk (author), Tipler, Frank (Thesis advisor), School of Science & Engineering Mathematics (Degree granting institution) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | electronic, 108 |
| Rights | No embargo, Copyright is in accordance with U.S. Copyright law. |
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