Re: gEDA-user: pcb GL can't render stretched arcs

[karl@xxxxxxxxxxx (Karl Hammar)]

Igor:
> 2011/7/14 Karl Hammar <karl@xxxxxxxxxxx>:
> > Looking at pcb.pdf, page 64, section 8.8.1 Arc...
...
> > And there is no way to specify a "slanted" ellipse in the file format
> > either, so if we really want ellipses, the file format is incomplete
> > and should be changed.
> >
> > Why not just give a warning if width and height is not equal, saying
> > that we don't really support ellipses for the moment, and be done with
> > it.
...
> I just liked the challenge with rotated ellipses especially checking for
> intersection between them.

Well, one could add a

 int slant = 0; // TODO: add support for rotated ellipses

and start debugging.

Or why not add full support for slantet/rotated ellipses. It would
affect documentation (file format), gui, src/search.c and possible
other places.

In your code, you translate to ellipse center, why not rotate so the
ellipse is with the foci on the x-axis, wouldn't that make the calc.
easier? You already have the a/b ((semi-)width/height above) and the
slant (or what should we call the ellipse rotation), so it is only
the test point (X,Y) we are rotating, and the ellipse would then be
in the normal form (simpler to visualize), one could also mirror the
system so X and Y > 0:

 x^2/a^2 + y^2/b^2 = 1, a >= b > 0
 with foci at (0,c) and (0,-c) where c = sqrt(a^2 - b^2)

One could possible use:

. a normal to the ellipse bisects the rays from the foci

. if
    P = (x,y) is on the perimeter, x > 0, y > 0
    F = (0,c) a focus
    Q = (a/e, y), where e = c/a, y = the y of P
  then

  PF / PQ = e, PF = length P to F, dito. PQ

///

And while we are at it, shouldn't we use a sane geometry where
positive y's are up and zero angle is alinged with positive x-axis...

Regards,
/Karl Hammar

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