[cairo] arc_to patch version 0.0.0

[Carl Worth]

On Wed, 27 Jul 2005 18:13:49 -0400 (EDT), Behdad Esfahbod wrote:
> That's what my implementation does too, because that's what you
> get with no extra consideration.  If both of the points (x0,y0)
> (current point), and (x2,y2) are near enough to (x1,y1) such that
> both lines go backward, then a better solution is to draw the
> other arc on the same circle which is more than pi.

I don't think it's a "better" solution. It's just different, and
that's not necessarily good.

>                                                     That's quite
> consistent with the definition of arc_to, that draws an arc with
> two tangent lines ...,

It's inconsistent in that the tangents of the arc are pi radians
different from the tangents specified by the 3 points.

The biggest problem with this approach is that it creates a boundary
condition with drastically different visual results on either side.

Imagine an interactive application that allowed the user to set the
parameters for arc_to. With the above approach, as the user adjusted
the radius the would suddenly "jump" to the other side of the circle.

The principle we don't want to violate here is that small changes in
the input should result in small changes in the visual output.

-Carl
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