How to simulate mathimatically correct shadows of transparent objects?

Question

I want to simulate shadows casted by complex and composite transparent objects. This shadows must be mathematically correct for particular light source (at least for point light). I think this is true for any graphical library, is it? Than, there must NOT be any refraction at all.

This image is not what I actually want to get of course.

Does OpenGL can do this? If it can not then what should I use instead?

UPD. So I need some path tracer. Is there some wich I could use programmatically: give it file of 3d-scene with objects and get the result of tracing?

Answer 1

This shadows must be mathematically correct

There's no such thing as a mathematically correct or wrong illumination. What you mean is physically correct.

Images like you want to create them rely on light propagation. The only way to properly simulate light propagation is to shoot virtual photons into a scene and follow their path. This is called path tracing.

Does OpenGL can do this?

OpenGL just draws points, lines and triangles… one at a time, without any concept of a scene or models.

Old, fixed function pipeline OpenGL had a simple Blinn illumination model built in, but this did just calculate a "light" value per vertex based on surface orientation (normal) and position relative to a light source.

Modern OpenGL does not even do that. Instead it relies on the programmer to provide programs that are executed for every vertex to decide where in the picture it goes and for every fragment (roughly a pixel) drawn to determine which color to give it.

In this programs, called shaders you can do just about anything. So if you want to implement a path tracer using OpenGL shaders, you can most certainly do this. But this path tracer will not interact with the points, lines and triangles you draw. Instead these will just serve to define the boundaries within which the shaders do their computations.

If it can not then what should I use instead?

It's not so much a question of if it is possible, but how easy it is to implement. In your case OpenGL is certainly not the right programming environment, because you'd be essentially starting from scratch. Instead you should use one of the existing path tracers around. There are also some, that are GPU accelerated.