# 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