Hi Peer,

re:
> Understood, though I haven't tried SVG export. It's not available in v4, right?

Correct, SVG import/export is new in the v5 beta.


> My understanding is that you're generating densely-spaced streamlines (or vector
> fields) along lines of curvature in object space and then using these to guide the
> growth of visible lines in image space, but that while what happens in image space
> is guided by the projected streamlines, the visible lines can deviate from the projected
> streamlines because the procedure is something like an optimization or curve fitting.

Yup, that's more or less what's going on.


> I worry that getting this right is a difficult problem. I'd rather receive hatch lines that are
> evenly spaced in object space, even if they become dense to an unsightly degree in some
> areas, than the result of trying to maintain even tone in image space if that leads to
> geometric inaccuracies.

The thing is there's a similar issue in object space as well. Except in special cases there is not
such a thing as an exact line of curvature that is equidistant at all points from another
line of curvature. There is with cylinders but not on just any arbitrary curved surface.

What I mean is If you make a line of curvature and then pick a point on that curve and move
a certain distance away from it in and then make a second line of curvature going through
that new point the new line of curvature can easily converge towards or diverge away from
the previous one.

So kind of the whole general idea of "evenly spaced lines of curvature" is rather ill defined.


> Another reason that I'm arguing for even spacing in object space is that curvature lines that
> have automatically been broken in a random way to give even tone will limit what I can do with
> those lines. But, if I get lines that are continuous from edge to edge, then I can decide how or
> where I want to end them.

I guess it could be possible also in image space to have an option to allow a line being traced to
have free rein to go where it wants to become a more accurate line of curvature but it will probably
be pretty messy looking with a lot of density and converging pieces. Something like a torus
could also be prone to them going on and on but I guess they could terminate after some
kind of winding threshold.


> In the example scene that you've been posting since the start, what determines the direction
> of hatching on planar surfaces? Does it have something to do with the lines of curvature on
> adjacent areas (i.e. a continuity condition), some conditions about how hatch lines interact
> with ridges, or is it purely decided by UV of planes used in construction?

It's just the UV directions of the NURBS surface.


re:
> Regarding smoothly varying width, that is done in woodcut, but I can't think of a nice way to do it
> digitally that would still be reasonably editable. Do you have an idea regarding smoothly varying width?

Well it's not supported as a regular line stroke property so it would have to be formed by a filled
outline rather than as a stroked curve.


Thanks,
- Michael