Ronaldo Persiano rcmpersiano at gmail.com
Tue May 28 21:04:15 EDT 2019

```Thank you for your interest in the solution I proposed.

> Does the boundary of your tripatch have an order 4 bezier representation?
> It
> sounds like you constructed the match to match up with such a curve?  What
> are the order 4 control points for the patch you posted?
>

Yes, the border of the standard 5th degree tripatch is indeed 4th degree
Bezier curve like the ones we considered for 2D cases with curvature
continuity. Its degree was elevated to 5 in order to have more freedom in
the internal control points of the patch. The control points of the 3
border curves of the standard 5th degree tripatch are:

[[1, 1, 0], [1, 0.6, 0], [1, 0, 0], [1, 0, 0.6], [1, 0, 1]]

[[0, 1, 1], [0, 1, 0.6], [0, 1, 0], [0.6, 1, 0], [1, 1, 0]]

[[1, 0, 1], [0.6, 0, 1], [0, 0, 1], [0, 0.6, 1], [0, 1, 1]]

They correspond to 4th degree curves with a form factor of r0=0.4.
Another possible form factor appeared in the development of the tripatch.
Its effect is restricted to the interior of the patch and do not affect its
border. That form factor were arbitrated to be 1 in the standard 5th degree
tripatch I proposed before.

> My FDM printed models are inconclusive because the shape of the roundovers
> is not similar enough.  The case I did with spheres does seem worse,
> despite
> the limited resolution of my layer thickness---I printed with 0.15mm
> layers.
> I might try another test with 0.05 layers after a better effort to match
> the
> shape of the roundovers.  But ultimately there's a problem that the limited
> z resolution makes this less important.  I suppose someone with SLS or some
> other higher resolution output device would notice the difference more
> clearly.
>

It seems to me that to compare the standard tripatch with the degenerated
rectangular one, this last one should be generated with the same form
factor 0.4. Otherwise, the corner border curves (and the edge roundover)
may be very different.
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