Hi Peer, I've always admired these types of illustrations but have not ever really deeply researched them so your docs are very informative and helpful for me, thanks.

Unfortunately I can't really spend a huge amount of time developing every detail of this area. Probably the cutoff point at least for now will be on things that require supplementary object selections or guiding strokes. With those sorts of things it will probably require some kind of interactive preview along with it and although that would definitely be cool it overall adds up to a pretty large package of work.

re:
> In case I wasn’t clear before: I don’t want to either render min curvature lines OR max
> curvature lines; I want both to be rendered but in separate groups or line styles so that I can
> choose which ones I want on a patch-by-patch basis.

Yeah I didn't realize that. When generating both directions I can put them inside groups for AI and SVG format exports. PDF format does not have a grouping operator in it for graphics content streams so it may not be viable to do it for PDF format.


Question - is there a specific rule for these types of breaks like should they always occur nearby a line that has been terminated because it is entering a brightly lit area?



re:
> I want still more accurate curvature lines. I know you can do this since your N-gon mesher
> makes quads with vertices that lie exactly along curvature lines

Well not quite exactly - the N-gon mesher makes quads in the UV parameter space of the NURBS surface. For conic sections they are the same but for more general surfaces it won't be.


> Any visible squiggle will spoil the effect, as will errors in line orientation, such as min curvature
> lines on a cone that are erroneously parallel in image space when they should in fact converge
> to the point:

Yeah I noticed that on the cone. So what happens there is that there is a conflict between tracing an accurate curvature line and simultaneously keeping regular spacing in image/page space. Basically the min curvature cone line wants to travel towards the point but previous lines have already taken claim to that area and so the new one can't quite follow the accurate line of curvature that it would like to.

One thing that I've tinkered with to mitigate that somewhat is to generate lines more sparsely instead of being tightly packed one after another, that gives a result like this instead (at the expense of having more shorter pieces):






I think I could get more accuracy on the curvature lines if they were allowed to approach closer to each other instead of maintaining even spacing...

Do you have some examples on what cones should look like?


re:
> I would like an option to choose whether lines are spaced evenly in image space or whether
> they're spaced evenly in object space.

The mechanism is currently pretty heavily based on image space but I'll try some experiments for this.


re:
> For example, where 3 fillets meet at a
> spherical corner I’d probably want the drawn curvature lines to be continuous with lines of min
> curvature on the fillets:

Hmmm, I'm pretty doubtful that I could get it to do that.


re:
> If there’s an option to use lines of curvature to show both shape and shading then I would like to
> be able to select whether shading is accomplished by line spacing or whether it’s accomplished
> with variable line weight. <...>

This might be feasible... I didn't realize that these were done using just one heavier line weight I kind of thought they were gradually increasing and decreasing like one long paint brush stroke.

Would you expect for the lightweight line to run the full length underneath the heavier segment or should it be trimmed out where the heavier one starts and ends?

Thanks, - Michael