Restricted-orientation convexity

Eugene Fink and Derick Wood

Springer-Verlag, Berlin, Germany, 2004. ISBN 3-540-66815-2.

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Contents

1.  Introduction
.   1.1  Standard convexity
.   1.2  Ortho-convexity
.   1.3  Strong ortho-convexity
.   1.4  Convexity spaces
.   1.5  Book outline
.
2.  Two dimensions
.   2.1  O-convex sets
.   2.2  O-halfplanes
.   2.3  Strongly O-convex sets

3.  Computational problems
.   3.1  Visibility and convexity testing
.   3.2  Strong O-hull
.   3.3  Strong O-kernel
.   3.4  Visibility from a point

4.  Higher dimensions
.   4.1  Orientation sets
.   4.2  O-convexity and O-connectedness
.   4.3  O-connected curves
.   4.4  Visibility

5.  Generalized halfspaces
.   5.1  O-halfspaces
.   5.2  Directed O-halfspaces
.   5.3  Boundary convexity
.   5.4  Complementation

6.  Strong convexity
.   6.1  Strongly O-convex sets
.   6.2  Strongly O-convex flats
.   6.3  Strongly O-convex halfspaces

7.  Closing remarks
.   7.1  Main results
.   7.2  Conjectures
.   7.3  Future work

References
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