In a polyhedron, it is observed that line segments arranged in a certain fashion preserve the intersection property: if intersection occurs with the polyhedron, the same also takes place with the line segments, and vice versa. Such line segments are said to be spanning the polyhedron which can be non-convex and non-simply connected. The properties of the spanning line segments in a polyhedron are introduced and an algorithm is presented based on “building blocks” with known solutions.

Issue Section:
Research Papers
Topics:
Algorithms, Blocks (Building materials)
1.
Blum, H., 1967, “A Transformation for Extracting New Descriptors of Shape,” Models for the Perceptions of Speech and Visual Form, Whaten-Dunn, ed., MIT Press, Cambridge, MA, pp. 362–380.
2.
Blum
H.
, and
Nagel
R.
,
1978
, “
Shape Description using Weighted Symmetric Axis Features
,”
Pattern Recognition
, Vol.
10
, pp.
167
–
180
.
3.
Preparata, F., and Shamos, M., 1985, Computational Geometry, Springer Verlag, New York.
4.
Ratschek
H.
, and
Rokne
J.
,
1993
, “
Test for Intersection Between Plane and Box
,”
Computer Aided Design
, Vol.
25
, No.
4
, April, pp.
249
–
250
.
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