For compensating light fall-off you'll need an equal distance from the pinhole to each place on the negative. Thus you'll need a bowl instead of a funnel !!
This would be doable with a glass salad bowl (shape = 1/2 of a ball) with coating on the inside and placing the pinhole in the center of the circle of the top of the bowl.
This would also eliminate all the anamorphic effect if you look inside the developed bowl. Placing this glass bowl-negative inside a photopaper cylinder would create an
anamorphic image on the photopaper when lying flat again.

I wonder: If I put the glass funnel-negative in the photopaper cylinder, would the print be less anamorphic or more anamorphic?? I suppose lesser than the negative itself.

A practical problem would be to concentrate the light source in one small point to avoid distortions. Would be a very nice experiment ;-)

An orthographic projection is what you'll get with the original camera obscura, a 3D image converted into a 2D image:


A stereographic projection seems very difficult, if not impossible to do with a pinhole camera? I'm not sure if I understand the concept of stereographic projection. My bowl suggestion above could be considered a (inverted) stereographic projection?

By stereographic projection I was just thinking of a coherent mapping between the 360-degree photographic view and its projection onto the 2-dimensional photo paper. I didn't mean a stereographic projection literally, like used in astrolabes and star charts, but just some way to take the 3-d view of a half-sphere and map it onto a flat 2-d surface in a way that would make sense to look at. It seems to me that by having two steps ( 1st into a vase or funnel or cone, and then projecting that onto paper ) it might be possible to create a 360-degree image that is more "comprehensible" and less anamorphic. But that was pure speculation and I haven't really thought about it!

As for compensating for light falloff, yes a bowl or hemisphere will compensate falloff. But what I was getting at was that the "squint" of the pinhole tends to "compensate" the light falloff in a cylindrical anamorphic camera... so I wonder if there is a way to take advantage and play them against each other and come up with a shape that would have even illumination all over?? Since the equations for light falls off ( roughly an inverse square ) and the squint of the pinhole ( the area of the visible ellipse at each point ) are not too bad, there ought to be a way to solve them simultaneously and see what that shape looks like. I'll think about this!

Just an other thought:
1) Coat a glass bowl (= half of a ball) on the inside with liquid emulsion, place it inside the pinhole camera with the opening facing toward the pinhole, make exposure & develop.
2) Place the bowl upside down over a lamp (in the darkroom!!), place a cylinder of photopaper over it, make exposure by turning on lamp & develop paper.

Seems simple enough to do and will give nice anamorphic effects. And all kind of variations are possible:
- place flat horizontal paper above the bowl/sphere
- place flat diagonal paper above the bowl/sphere
- place paper curved "as a rainbow" over the sphere
- coat an other larger glass bowl on the inside, turn it upside down and place it over the negative bowl, make exposure & create a positive bowl ;-)
- etc ....

And if you want to do it again with a whole other set of ananmorphic effects, start over with a second glass bowl at 1) but this time put the coated bowl
inside the pinhole camera with the opening facing away from the pinhole, make exposure & develop. Then repeat all the same steps for printing and
compare the anamorphic results.

That should keep you busy during the holidays (and make you an anamorphic expert by empirical testing). Wish I had a science class to test with ....

Exactly! By having two "projection" stages all sorts of things are possible. I think the first one you mentioned is probably similar to some kind of stereographic projection. It would be fun to know how all of these work out! Now you've got me thinking about liquid light....

Yesterday I did try the new method of pounding the aluminum flat to make pinholes. It did not work very well, the aluminum that I used got brittle and started splitting before it got very thin. I did make a few new pinholes by the usual "dimple and sand" method, and for the first time I put them in my enlarger and measured them. They are all perfectly round as far as I can tell, and I really think if you hold the pinhole up close to your eye you can see the roundness just as well as in an enlarger. The main use of the enlarger, I think, is to get an accurate diameter measurement.

I normally use the aluminum from Cola cans and it works perfectly for me. I bought an old manual microscope (about $30) to view my pinholes.
I recently also ordered some tubes with perfect pinholes (several sizes), officially used for large electron microscopes. Perfect round holes.
I had to order rather a large quantity so will put some up for cost price at APUG later, if someone can use it.
I have to look up what sizes I have. I didn't have time to test these yet, but I want to use it in my 360 degrees pinhole cam with 8 holes,
to make sure all the holes are the same size.

I have an old microscope...should have thought of that! I've found different kinds of aluminum drink cans work differently. The best one so far was a mexican soda that had thin, soft metal. I've worked a little bit on the anamorphic curve that has uniform EV... it is roughly an hourglass shape. This is the curve that equalizes the drop in light due to the profile of the pinhole and the increase in light due to decreasing the distance from it. I need to do some more math and then I'll post it. I have not computed yet whether the smaller radius needed at the top will block the rays to lower sections. ( For a cylindrical anamorphic pinhole and the idea of painting liquid light inside a vase-shaped glass... )

Oops. I forgot about the vase shape calculation. There is a spreadsheet sitting here that I need to fill in more before I can plot the shape.

Update on camera building:

Well not so much an update as a change in thinking. I'm coming to realize that I don't like pinhole photos as much at normal "focal" lengths. So at least for the time being I am abandoning the idea of swapping pinholes and lenses on the same fixed-focal length cameras. The pinhole cameras are going to be wide and the lensed cameras will be made to fit the lens.

Went to "Michaels" ( a chain art store here in the U.S. ) yesterday to get some black foamcore and the only sheets they had left were damaged too much. I need to go to a proper art supply store, but the good one is about a 40 minute drive from here.

-Ned