A fast algorithm to compute the -line through points inside a helix cylinder

Author:
Steven H. Izen

Journal:
Proc. Amer. Math. Soc. **135** (2007), 269-276

MSC (2000):
Primary 65H05; Secondary 51N05, 65R10

Published electronically:
July 28, 2006

MathSciNet review:
2280195

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Abstract | References | Similar Articles | Additional Information

Abstract: In the context of helical cone-beam CT, Danielsson et al. discovered that for each point interior to the cylindrical surface containing a given helix, there is exactly one line segment passing through the point which intersects two points less than one turn apart on the helix. This segment is called a -line. A new constructive algebraic proof of this result is presented along with a fast algorithm to compute the endpoints of the -line through an arbitrary point in the interior of the helix cylinder. This proof exposes the geometry of the decomposition of a cylinder interior as a disjoint union of -lines.

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Additional Information

**Steven H. Izen**

Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106

Email:
shi@cwru.edu

DOI:
https://doi.org/10.1090/S0002-9939-06-08449-8

Received by editor(s):
February 26, 2004

Received by editor(s) in revised form:
July 25, 2005

Published electronically:
July 28, 2006

Communicated by:
M. Gregory Forest

Article copyright:
© Copyright 2006
American Mathematical Society