Characterization of polyhedron monotonicity

Authors:
J. S. Ha;K. H. Yoo;J. K. Hahn
Affiliations:
Department of Computer Engineering, Woosuk University 490 Hujongri, Samrae-Up, Wanju-Kun, Chonbuk 565-701, South Korea;Department of Computer Education and Information Industrial Engineering, Chungbuk National University, 48 Gaesin-Dong, Cheongju, Chungbuk 361-763, South Korea;Department of Computer Science, The George Washington University, 801 22nd Street, NW Phillips Hall Suite 720B, Washington, DC 20052, USA
Venue:
Computer-Aided Design
Year:
2006

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Abstract

The notion of polygon monotonicity has been well researched to be used as an important property for various geometric problems. This notion can be more extended for categorizing the boundary shapes of polyhedrons, but it has not been explored enough yet. This paper characterizes three types of polyhedron monotonicity: strong-, weak-, and directional-monotonicity: (Toussaint, 1985). We reexamine the three types of polyhedron monotonicity by relating them with 3D manufacturing problems, and present their formulation with geometric problems on the sphere.