The answer kinda depends on whether the part of the surface in question
exhibits positive or negative curvature. On the outside of your spring,
which has positive curvature, it's clear which diagonal looks better, but
for the negative curvature inside, the answer is less clear. In some cases,
what looks "right" depends more on which direction you're viewing from than
which diagonal is shorter.

The best solution actually comes from staggering your points. I wrote code
for generating mathematical surfaces in the form of z = f(x, y), and I
recently rewrote it to sample points on an equilateral triangular grid
rather than a square grid to solve this problem. By choosing the shorter
diagonal across a quad, you're soft of approximating this solution.

There can still be spots that don't look perfectly smooth (usually because
the function has a high second derivative), but it generally handles these
things a lot better than the square grid. The next step in complexity would
be to write code to use a variable mesh density (or at least one that
remains constant relative to the face's orientation, rather than just
relative to the x/y plane), but without true variables, that would be very
difficult to implement. Even with true variables, I'm sure thesis papers in
topology have been written on the subject, some of which likely resulted in
some of the re-meshing algorithms in Meshlab.

On January 24, 2019 at 11:13:36, nop head (nop.head@gmail.com) wrote:

No its the shorter diagonal, not the longer.  I am pretty sure it isn't a
general solution for any quad patch on a 3D surface. It might be for a
sweep where the quads are always in rings, but I don't know. Seems to work
with helical springs.

The spring machines I have seen feed wire though a nozzle against an anvil
that forces it to turn into a helix . The anvil moves allowing it to vary
the pitch and diameter continuously if necessary. Then it cuts it off and
starts a new one.

On Thu, 24 Jan 2019 at 17:47, NateTG nate-openscadforum@pedantic.org
wrote:

OpenSCAD mailing list
Discuss@lists.openscad.org
http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org

This is an ancient story.  The bottom line is that quads lead to all sorts of problems.

Best (if you can manage it) is to deal with purely triangular meshes.

Second best is to be exceedingly careful with non-planar quads.  Again - a good approach is
often to subdivide by producing a good point on your intended surface at the center of the
quad to produce FOUR triangles instead of trying to make do with only TWO.

Finally, when forced to choose a diagonal,  you can evaluate the error at the center of the
quad - or you can blindly choose the smaller of the two diagonals.

--
Kenneth Sloan
KennethRSloan@gmail.com
Vision is the art of seeing what is invisible to others.

On Wed, Jan 23, 2019 at 10:05:58PM +0000, nop head wrote:

The current rendering uses a single shade that depends on the normal
of the triangle.

If the length of the diagonals are not equal, chosing the shorter
triangle reduces the "aspect ratio" (longest possible line segment
divided by the largest perpendicular segment). As an example: imagine
two equilateral triangles joined to a rhombus.

Split them into the two original triangles and the aspect ratio is
almost one (sqrt(3)/2 iirc). Split it the other way and you get a much
larger aspect ratio. Something like sqrt(3) or even more.

The aspect ratio being small means that the points of that triangle
will be colored the same to "close" points. A pointy triangle has
points far away that will be colored the same due to having the same
normal.

For presentation (i.e. not 3D printing) you can do "phong
shading". This has something to do with averaging colors close to an
edge between two triangles. An object shaded that way will look
"perfectly round" until you start examining the image at the pixel
scale. This would be great for quick rendering realistic
representation of an object where you're working with a low $fn during
development but are going to increase $fn for final rendering to be
printed.

That sounds like a plan.

The inside of the spring is concave (in one direction) (I'm guessing that
this is exaclty the "partially convex" that you say :-) ).

Roger. 

--
** R.E.Wolff@BitWizard.nl ** https://www.BitWizard.nl/ ** +31-15-2049110 **
**    Delftechpark 11 2628 XJ  Delft, The Netherlands.  KVK: 27239233    **
The plan was simple, like my brother-in-law Phil. But unlike
Phil, this plan just might work.

I didn't get that in the sense of the general case with n slices. Can you
show linear_extrusion code that has this problem?

Obviously, when you do a twisted linear_extrusion say with 5 slices and the
result is exactly what you want, you are better of.

Whosawhatsis wrote

--
Sent from: http://forum.openscad.org/

No what I mean't was no shape can be totally concave on the outside, it
must curve back to meet itself and be convex as it does so.

Even on the inside of the spring, a quad oriented along it should still be
folded to be convex. Locally the surface is more convex around the ring and
less concave along it. So perhaps you would look the four neighbouring
quads on its sides and pick the most curved direction to decide it
should be convex or concave.

On Fri, 25 Jan 2019 at 12:18, Rogier Wolff R.E.Wolff@bitwizard.nl wrote:

Kenneth Sloan wrote

This is not practicable for linear_extrude in a general sense, since it uses
an integral slices variable. And even then it is not trivial as it would
imply to also subdivide the polygon, i.e. getting 8 vertices for a square.
So multiplying slices by 2 will multiply the number of triags by four.

--
Sent from: http://forum.openscad.org/

Actually linear extrude seems to chose the longest diagonal. It definitely
looks bad for negative twists but less so for positive ones. I wonder what
it would look like if it choose the shortest on positive twists.

On Fri, 25 Jan 2019 at 13:43, Parkinbot rudolf@digitaldocument.de wrote:

I think the asymmetry is due to the lighting direction. Even with positive
twist it looks to have concave dimples.  My guess is it would look better
in both case if it chose the shortest diagonal to make the quads convex.

On Fri, 25 Jan 2019 at 14:01, nop head nop.head@gmail.com wrote: