I was aware in the beginning that the signs were probably incorrect, but
I had left them as I wasn't sure how they worked. Thanks to enki
(bivector community), I was pointed in the right direction for getting
the calculations right: the product of a basis blade with its dual
(x !x) must product the positive pseudo-scalar.
I guess I had forgotten that new_mv() does *NOT* initialize the
components. Things just happened to work (usually) because memory was
not getting recycled.
Currently only PGA(3) is supported, but that's because the parser is
rather simple (recursive descent with a lame lexer), but it works well
enough for playing with geometric algebra without having to recompile
every time.
This gives the resultant point the correct sign. Though the projective
divide would take care of the sign, this makes reading the point a
little less confusing (still need to sort out automatic blade reversals
for the likes of e31).
As the dot product is a metric product, using the metric is vital to
getting the correct results. This fixes the calculation of the closest
point on a line to a point other than the origin (and a whole pile of
other issues, I imagine).
