This is what I'm trying to create in Illustrator. (for those interested, it's a graph of a Mexican hat potential function)
Here's what I've done so far, using Illustrator's 3D->Revolve and Map Art.
I drew a curve simliar to the shape first. (I know this is not the exact shape, the top should be curve a bit. I'm just using this curve for a proof of concept for now.)
then I drew a grid(expanded) and made it to a symbol.
While having the curve selected, I picked 3D->Revolve. I checked the "Invisible Geometry" option. I used the grid symbol I made to map the 2 surfaces. Illustrator divided the 3d shape to 6 surfaces. But only 2 are needed. Basically the "cone" and the "bowl".
This is what I got.(I'm showing the perspective at a different angle from the original to better present my problems) At the first glance it wasn't too bad. But looking closely:
- The grid lines don't connect seamlessly between the cone and the bowl surfaces.
- The lines at the edge of the bowl are too thick. I want all the lines to be the same width.
- I need to hide the lines of the bowl behind the cone, so the cone doesn't look like it's transparent.
For problem (1) my guess is that I need to create different grid symbols and scale them differently. It may be a painful process through trial and error. I wish I could somehow make Illustrator see this whole thing as 2 surfaces(top and bottom), then I'd only have to map art to the top surface and ignore the bottom surface.
For problem (2) I'm not sure if there's anyway to get around this at all, since mapping to a circular surface will no doubt skew the mapped pattern.
For problem (3) I guess a work-around would be to expand the 3D shape and then manually clip off those paths. Still this will be painful.