[Octave-bug-tracker] [bug #60818] delaunayn - 2D code path vectorization doesn't match nD algorithm

[Nicholas Jankowski]

Follow-up Comment #36, bug #60818 (project octave):

and now looking at the geometric alternative of doing the volume comparison
for the LU code, and I'm realizing we may be calculating volume wrong in the
Laplace expansion code. the simple orthogonal cases may have just masked it.

volume of a triangle, tetragonal, etc., is 1/n! * volume of the
parallelogram/parallelepiped, etc., defined by the vector product. but that
requires use of a coterminated vectors.  (p21, p31, p41, etc.) not (p21, p32,
p43) like we have there.  I was just following the 2D code which used p12 and
p23, since they're co-terminated except for a sign. But using p12, p23, p34,
... for higher dims uses vectors not part of the parallelepiped to calculate
it's volume, which i suspect is very wrong.

It's a trivial switch in the Laplace expansion determinant code.  will make
that change and update the patch after check on the effect of leaving q out or
changing it to q in the LU code.

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