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BibTeX entry
@Article{Teller:1999:DLT,
author = "Seth Teller and Michael Hohmeyer",
title = "Determining the Lines Through Four Lines",
journal = j-J-GRAPHICS-TOOLS,
volume = "4",
number = "3",
pages = "11--22",
year = "1999",
CODEN = "JGTOFD",
ISSN = "1086-7651",
ISSN-L = "1086-7651",
bibdate = "Thu Oct 12 17:08:13 2000",
bibsource = "http://www.acm.org/jgt/issues.html;
http://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
URL = "http://www.acm.org/jgt/papers/TellerHohmeyer99/",
abstract = "This paper describes how to compute the line or lines
which intersect four given lines in three dimensions.
This intersection computation arises in computer
graphics (for visibility computations), computational
geometry (for line traversals), and computer vision
(for object recognition).\par
Given four distinct lines in three dimensions, there
exist zero, one, two, or various infinities of lines
intersecting the given lines. We use Pl{\"u}cker
coordinatization of lines to cast this problem as a
null-space computation in five dimensions, and show how
the singular value decomposition (SVD) yields a simple,
stable characterization of the incident lines, and an
efficient algorithm to determine them.\par
Finally, we enumerate the types of input degeneracies
that may arise, show how to detect each type in
practice, and describe for each case the solution set
of lines that arises.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
}
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