3 ms·

A bit of more information: with global illumination (GI) a point is shaded by considering the light coming in from all directions to that point. It is the integ

A bit of more information: with global illumination (GI) a point is shaded by considering the light coming in from all directions to that point. It is the integral over Omega in the rendering equation [1]. This is expensive to compute. Especially since it is recursive to infinity, if the incoming light was reflected by a surface. The author uses pre-computation and keeps the geometry static, which is quite a common approach. [1]: https://en.wikipedia.org/wiki/Rendering_equation https://en.wikipedia.org/wiki/Rendering_equation

conceit 11y ago
> It is the integral over Omega in the rendering equation [1]. This is expensive to compute. The approach would be just exhaustive summation, I suppose. Would symbolic integration be equally expansive for simple enough geometry? Simplified approximations to the geometry, i.e. bounding boxes, would probably not look real enough. I get, there are all kinds of approaches. I heard Monte Carlo method used to limit the search space to a random subset.
- CyberDildonics 11y ago
  Although I don't know what exactly symbolic integration is, I'm guessing it is a direct mathematical solution. The problem is that even with simple scene geometry, the geometry of the search space in the domain of the integral becomes non trivial probably after the first bounce of light, but definitely after the second. A path of light can bounce of a sphere and be occluded by another sphere. Then there are BRDF that could be modified by textures, emission textures, diffuse and specular modulation textures, etc. Old school radiosity was an attempt at a more contained solution, you might be able to look at that for something similar.
- hiker 11y ago
  Monte Carlo integration is what's used by most (all?) offline production renderers. The standard book on the subject is "Physically Based Rendering" [http://pbrt.org/ http://pbrt.org/] if you want to learn more.
- dahart 11y ago
  Symbolic integration, or more often called "analytic integration" (as opposed to numeric integration or sampling) is usually much more expensive. But the benefit is that you can get a much more accurate result, if you need an accurate result. There is no known analytic / symbolic integral for arbitrary geometry like curved surfaces, but I believe it can be done with purely polygonal scenes. A lot of work has been done on using analytic integration techniques, as well as higher quality numeric approximations, for global illumination, in particular with radiosity methods. https://en.m.wikipedia.org/wiki/Radiosity_(computer_graphics) https://en.m.wikipedia.org/wiki/Radiosity_(computer_graphics... http://www.mi.uni-koeln.de/c/mirror/www.cs.curtin.edu.au/units/cg351-551/notes/restricted/lect13e1.html http://www.mi.uni-koeln.de/c/mirror/www.cs.curtin.edu.au/uni... http://dl.acm.org/citation.cfm?id=74367 http://dl.acm.org/citation.cfm?id=74367
- corysama 11y ago
  Square-Enix has experimented with using textured discs that approximate the scene geometry. Imperfect Ray-Bundle Tracing for Interactive Multi-Bounce Global Illumination http://www.jp.square-enix.com/info/library/ http://www.jp.square-enix.com/info/library/

conceit 11y ago

> It is the integral over Omega in the rendering equation [1]. This is expensive to compute. The approach would be just exhaustive summation, I suppose. Would symbolic integration be equally expansive for simple enough geometry? Simplified approximations to the geometry, i.e. bounding boxes, would probably not look real enough. I get, there are all kinds of approaches. I heard Monte Carlo method used to limit the search space to a random subset.

CyberDildonics 11y ago
Although I don't know what exactly symbolic integration is, I'm guessing it is a direct mathematical solution. The problem is that even with simple scene geometry, the geometry of the search space in the domain of the integral becomes non trivial probably after the first bounce of light, but definitely after the second. A path of light can bounce of a sphere and be occluded by another sphere. Then there are BRDF that could be modified by textures, emission textures, diffuse and specular modulation textures, etc. Old school radiosity was an attempt at a more contained solution, you might be able to look at that for something similar.
hiker 11y ago
Monte Carlo integration is what's used by most (all?) offline production renderers. The standard book on the subject is "Physically Based Rendering" [http://pbrt.org/ http://pbrt.org/] if you want to learn more.
dahart 11y ago
Symbolic integration, or more often called "analytic integration" (as opposed to numeric integration or sampling) is usually much more expensive. But the benefit is that you can get a much more accurate result, if you need an accurate result. There is no known analytic / symbolic integral for arbitrary geometry like curved surfaces, but I believe it can be done with purely polygonal scenes. A lot of work has been done on using analytic integration techniques, as well as higher quality numeric approximations, for global illumination, in particular with radiosity methods. https://en.m.wikipedia.org/wiki/Radiosity_(computer_graphics) https://en.m.wikipedia.org/wiki/Radiosity_(computer_graphics... http://www.mi.uni-koeln.de/c/mirror/www.cs.curtin.edu.au/units/cg351-551/notes/restricted/lect13e1.html http://www.mi.uni-koeln.de/c/mirror/www.cs.curtin.edu.au/uni... http://dl.acm.org/citation.cfm?id=74367 http://dl.acm.org/citation.cfm?id=74367
corysama 11y ago
Square-Enix has experimented with using textured discs that approximate the scene geometry. Imperfect Ray-Bundle Tracing for Interactive Multi-Bounce Global Illumination http://www.jp.square-enix.com/info/library/ http://www.jp.square-enix.com/info/library/