A fast algorithm to compute the $\pi$-line through points inside a helix cylinder
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- by Steven H. Izen PDF
- Proc. Amer. Math. Soc. 135 (2007), 269-276 Request permission
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 $\pi$-line. A new constructive algebraic proof of this result is presented along with a fast algorithm to compute the endpoints of the $\pi$-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 $\pi$-lines.References
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Additional Information
- Steven H. Izen
- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
- Email: shi@cwru.edu
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 269-276
- MSC (2000): Primary 65H05; Secondary 51N05, 65R10
- DOI: https://doi.org/10.1090/S0002-9939-06-08449-8
- MathSciNet review: 2280195