Volume 7 Number 6 (Jun. 2012)
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JSW 2012 Vol.7(6): 1219-1226 ISSN: 1796-217X
doi: 10.4304/jsw.7.6.1219-1226

Convexity Conditions for Parameterized Surfaces

Kui Fang1, Lu-Ming Shen2, Xiang-Yang Xu3, and Jing Song1
1Institute of Information Science & Technology, Hunan Agricultural University, Changsha, P. R. China
2Science College, Hunan Agricultural University, Changsha, P. R. China
3Institute of Computer Science ,Changsha University, Changsha, P. R. China

Abstract—Based on a geometrical method, the internal relationships between locally parameterized curves and the local parameterized surfaces are analyzed. A necessary and sufficient condition is derived for the local convexity of parameterized surfaces and functional surfaces. A criterion for local convexity (concavity) of parameterized surfaces is found, also, the criterion condition of binary function convex surfaces is obtained. Finally, the relationships between a globally parameterized curves surfaces is discussed, a necessary condition is presented for the global convexity of parameterized surfaces , and it is proved that locally convex parameterized surfaces are also globally convex.

Index Terms—local convexity, global convexity, gauss curvature, the second fundamental form


Cite: Kui Fang, Lu-Ming Shen, Xiang-Yang Xu, and Jing Song, "Convexity Conditions for Parameterized Surfaces," Journal of Software vol. 7, no. 6, pp. 1219-1226, 2012.

General Information

ISSN: 1796-217X (Online)
Frequency:  Bimonthly (Since 2020)
Editor-in-Chief: Prof. Antanas Verikas
Executive Editor: Ms. Yoyo Y. Zhou
Abstracting/ Indexing: DBLP, EBSCO, Google Scholar, ProQuest, INSPEC(IET), ULRICH's Periodicals Directory, WorldCat, etc
E-mail: jsw@iap.org
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