Angle counts for isothetic polygons and polyhedra

Authors:
Ben Yip;Reinhard Klette
Affiliations:
Microsoft Corporation, Room 4113675, 1 Microsoft Way, Redmond, WA;CITR, University of Auckland, Tamaki Campus, Building 731, Auckland, New Zealand
Venue:
Pattern Recognition Letters
Year:
2003

Citing 3
Cited 0

Optimal binary space partitions for orthogonal objects

Journal of Algorithms
On the optimal binary plane partition for sets of isothetic rectangles

Information Processing Letters
Illuminating rectangles and triangles in the plane

Journal of Combinatorial Theory Series B

Quantified Score

Hi-index	0.10

Visualization

Abstract

In the case of isothetic simple polyhedra there are only six different types of 3D angles. This article states and proofs a formula about counts of these angles. This complements formulas in combinatorial topology such as Euler's polyhedron formula, or the previously known formula on angle counts for isothetic polygons. The latter formula and the shown equality for angle counts of isothetic simple polyhedra are useful formulas for analyzing isothetic boundaries in 2D digital images (e.g. classification into inner (boundary of a hole) or outer boundaries, see Voss [Discrete Images, Objects, and Functions in Zn Springer, Berlin, 1993]) and isothetic surfaces in 3D digital images (e.g. necessary condition for a complete surface scan).