Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Computing the Lines Piercing Four Lines

Seth J. Teller and Michael E. Hohmeyer

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-92-665
January 1991

http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/CSD-92-665.pdf

Given four distinct lines in R^3 there exist zero, one, two, or various infinities of lines incident on the given lines. We wish to characterize and compute the set of incident lines in a numerically stable way. We use the Plucker coordinatization of lines to cast this problem as a null-space computation in R^5, and show how the singular value decomposition (SVD) yields a simple, stable characterization of the incident lines. Finally, we enumerate the types of input degeneracies that may arise, and describe the solution set of lines in each case.


BibTeX citation:

@techreport{Teller:CSD-92-665,
    Author = {Teller, Seth J. and Hohmeyer, Michael E.},
    Title = {Computing the Lines Piercing Four Lines},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1991},
    Month = {Jan},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/6126.html},
    Number = {UCB/CSD-92-665},
    Abstract = {Given four distinct lines in R^3 there exist zero, one, two, or various infinities of lines incident on the given lines. We wish to characterize and compute the set of incident lines in a numerically stable way. We use the Plucker coordinatization of lines to cast this problem as a null-space computation in R^5, and show how the singular value decomposition (SVD) yields a simple, stable characterization of the incident lines. Finally, we enumerate the types of input degeneracies that may arise, and describe the solution set of lines in each case.}
}

EndNote citation:

%0 Report
%A Teller, Seth J.
%A Hohmeyer, Michael E.
%T Computing the Lines Piercing Four Lines
%I EECS Department, University of California, Berkeley
%D 1991
%@ UCB/CSD-92-665
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/6126.html
%F Teller:CSD-92-665