Imagine this:
A person enclosed in a perfect sphere that is mirrored on the inside. This person is hovering such that his belly button is in the exact center of the sphere. He turns on a light and looks straight ahead. What does he see?
To be a little more definite, make the person six feet tall, and the sphere with a radius of twelve feet. For the metrically inclined, try a two meter person and 4 meter sphere radius. The position, size, and direction of the light probably will have a large influence on what can be seen.
Any Dopers with access to Lightwave or Maxon 4D or POVRay or something along those lines want to give it a try? I asked this question of the Maxon guys at the CeBIT in Hannover this year, and they told me that it would probably take an hour to compute, so they didn’t try it.
I first saw this question in “Callahan’s Secret” from Spider Robinson, and have always wondered about it.
I’ve just tried pretty much what you described with caligari’s truespace 4.1, and the results are…weird. I tried with spheres of different diameters. With small spheres, it’s just a mass of scrambled, magnified reflections. But with big spheres, it breaks up into many individual, well-defined reflections of the guy in the middle. I think this is due to the facets that make up the sphere in the program, though. You could keep subdividing the sphere into smaller and smaller facets, but that’s going to make rendering it really slow.
I’d post images, if I could find a free server space place that didn’t require me to fill out a bunch of advertising fodder.
Insufficient data, the problem has not been adequately defined. I don’t see what the belly button has to do with it, a person could be any height so that his eyes could be almost any distance from the center. And how big is the sphere?
But it doesn’t matter, because no rendering or ray tracing software will ever render this scene faithfully. Most of them have limits to how many reflections it will trace, and what you’ve got here is an “optical cavity” which has an infinite number of reflections of both the light source and the man. Essentially the man has an infinite number of light sources and makes an infinite number of reflections.
But there is a solution. I have a book on perspective drawing, it describes variations on “spherical perspective” that sound like what you are after. It is almost impossible to describe the technique, and the artist is admonished to only calculate and draw one reflection. It is an anamorphic perspective trick, which were quite common at one time. Think about that famous Escher self-portrait holding a mirrored sphere, and you see his face in the sphere, curved. Anyway, I’d go dig up this book and scan you an example but it is locked away in storage and would take days to locate. Perhaps you can find examples on the web if you search for “spherical perspective” or “anamorphosis.”
What part of “sphere with a radius of 12 feet” was unclear? The bit about the belly button IS relevant. This is simply to place our test subject with a clear refence point. If you move him so that his belly button is a couple of feet to the left then it won’t look the same as when he is in the center of the sphere.
Quite correct about the raytracing programs having a limit to the trace depth, but in reality the reflections would die off after a certain number bounces so that you just need to estimate how many bounces it would take for the image to fade using a reflection efficiency of, say, 90%. 90% may be kind of high, but even so twenty five reflections get you down to less than 1% the original brightness.
Weird. Some kinda’ look like a Georgia O’Keefe painting, huh?
Depending on when he can grab some computer time, my friend and I are going to try the same thing using Cray 3-D RenderRay, supposedly a much more true-to-life program.
You should try a program like Radiance, I’d be curious to see how a true radiosity algorithm would handle this. I’d also like to see different placement of the light source, see how that affects things.
This is an interesting question, and what it makes me wonder is if it would be possible to put the light source outside the sphere, in such a way that it comes equally from all directions. Otherwise, one of the things (besides the person) that would be reflected would be the lightbulb (or whatever you’re using). At first, I was thinking of using one-way mirror material for the sphere, but I’m not sure if that would work very well…would be funky though. I always wanted to mirror a room: all walls, floor, and ceiling. That would be disorienting, to say the least. But a sphere? Makes me dizzy to think of it. Looking forward to further results. Short of nouns for subjects in my sentences.
One way mirrors will probably be kind of hard to do. They also don’t reflect very well, so that the images would probably fade out after relatively few reflections. A better bet might be to use “ambient lighting.” This has no source, and no direction. Don’t know how it would effect the reflections, though.
Sorry, Cranky. I didn’t mean to disturb your domestic bliss. Hope things get back to normal soon.
