Computing the Lines Piercing Four Lines

Authors:
Seth J Teller;Michael E Hohmeyer
Affiliations:
-;-
Venue:
Computing the Lines Piercing Four Lines
Year:
1992

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Abstract

Given four distinct lines in R3 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 R5, 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.