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The Radon transform is used to take 2d projections of an object and create a 3d representation.

It seems like it would be possible to apply such a transform in 3d graphics in games (although possibly too slow to be practical).

For example, a very simple way to display an object is to use a 3d rectangle and texture map each side. This is relatively fast but the 3d detail is limited. When a side is parallel with the visual plane it will represent the detail 100% (so the visual detail would be limited to that of the texture map). Of course it won't represent external 3d effects properly, like lighting.

But by using the Radon transform one could gain a true 3d approximation of the object from the six textures/projections used. By increasing the number of textures/projections the approximation is better.

I'm curious if the idea has potential. Possibly for high-quality 3d models it might pay off in performance and size. Of course 3d models can be optimized to limit their size which also increases speed but visually doesn't change much.

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I've been studying the use of OpenGL and DirectX and even though I am at an intermediate level, I believe this is where the use of bump maps, light maps etc comes into play. These are encapsulated in the idea of a Shader. The hardest part about the shader and lighting to work correctly with the 3D object with respect to the angle of the camera view directly depends if your normals are defined correctly. As for what you are describing it does make sense using 3D approximation, however my linear algebra is a little rusty, I am not sure if the conventional 4x4 matrices will work, and when it comes to motion with rotations you might have to redefine your quaternions too.

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Well, I imagine the transform will have to be used in hardware. The radon transform is what is used in things like MRI's(the difference is they use xrays so they can peak inside the object). Bump maps are not the same as they don't create 3d geometry but just give the illusion that the texture is not flat(so the illusion of 3d geometry). The radon transform can actually produce the 3d geometry. For example, suppose you have a human and take pictures of all angles. You can use the transform to generate a 3d model(except for occlusions unless you use xrays or something). –  Archival Oct 19 '12 at 23:21
    
I imagine it would be way to slow for real time use for 3d games unless the algorithms were built into the gpu. (since you would be having many transforms being done simultaneously). One can sorta think about it as texture maps-> 3d geometry. Just upload your texture maps to the gpu, tell the gpu how to use them for it's radon tranform... and get a 3d model that then can be used as any normal model... or even possibly just animate the textures first. The issue is one of performance and memory. Maybe too many angles needed for the radon transform to be useful for 3d games. –  Archival Oct 19 '12 at 23:25
    
Rather than use a radon transform(which use different types of textures) you can use photo's directly: en.wikipedia.org/wiki/3D_reconstruction_from_multiple_images. (this is really what I mean rather than the radon transform) –  Archival Oct 19 '12 at 23:33
    
Well with the advance in hardware technology, and the fact that 90% of all new processors that are sold either it be Intel or AMD are a multi-core and multi-thread, And most motherboards are now all sata for drives and pci-express for video cards. And some of these cards are 2GB in video ram and im sure there are some that have more. With a 64bit win7+ os using directx 11 you can have up to I believe it is 24GB system ram. It might be plausable to use the radon. I would suggest having atleast a dual video card setup with each card using 2GB video ram.... more on next comment –  Francis Cugler Oct 20 '12 at 11:38
    
However if the mother board supports an an extra pci-express slot that is .1 or the real short one, a very good physics card could help doing the process. You might have to write directly to the hardware though, so you would be pretty much redesigning the graphics pipepline that DirectX and OpenGL uses. I do believe it can be done. For a system like this I would also suggest that it be refridgerated cooled. You would probably want the Intel i7 extreme with 24mb L3 cache 4Ghz proccessor that can be overclocked. And the video card either being AMD/ATI or NVIDIA be overclocked as well... –  Francis Cugler Oct 20 '12 at 11:45
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