> >Hello,

> > I'm writing some routines for 2D polygons and I'd like some

> >pointer to where I can learn how to determine the endpoints of an

> >intersection of two line segments when they segments are colinear

> >(coincident) over some length.

> If two line segments are colinear and overlapping, the endpoints of the

> intersection(overlap) must be 2 of their 4 endpoints. You should

> create a 1D parameterization. Pretend one of the endpoints is the

> origin. Calculate the _signed_ distance of each of the other points

> from this origin. Now you have reduced the problem of determining if 2

> intervals overlap in 1D, which you can do simply by comparing these new

> coordinates.

> Jon

> (sorry if that wasn't terriby clear, but I'm in a rush just now)

If you've already determined that the lines are collinear, you can just

compare the X coordinates of the endpoints (or Y, of course, if the lines

have large or infinite slope) to determine whether the segments overlap

and if so how. The coordinates *are* a 1D parameterisation, after all.

I'm sure this is Joe's book, anyway.

Patrick

--

, author = "J. O'Rourke"

, title = "Computational Geometry in {C}"

, publisher = "Cambridge University Press"

, year = 1994

, note = "ISBN 0-521-44592-2/Pb \$24.95,

ISBN 0-521-44034-3/Hc \$49.95.

Cambridge University Press

40 West 20th Street

New York, NY 10011-4211

1-800-872-7423

346+xi pages, 228 exercises, 200 figures, 219 references.

C code and errata available by anonymous ftp from

grendel.csc.smith.edu (131.229.222.23),

in the directory /pub/compgeom; Third Printing: Dec. 1995"

Quote:}