texture minification filter in raytracing?

Question

can someone point me to a paper/algorithm/resource/whatever that tells me how to implement a texture minification filter (applies when texels are smaller than pixels) in a raytracer?

thanks!

Answer 1

thank you guys for your answers, but since I didn't find any appropriate techinque i created something myself which turned out to work very well:

i assume my ray to be a cone with a coneradius of half a pixel on the imageplane. when the ray hits a surface, i calculate the ellipse which is projected onto the surface (the ellipse from the plane-cone intersection). Then, using the texturecoordinate derivatives at the intersection point, i project this ellipse into texturespace. now i know which part of the texture lies under my pixel and can subsample this area

I Also use RipMaps to improve the quality - and i chose the RipMap level based on the size of the ellipse in Texturespace

Answer 2

Since you are using ray tracing I suspect you are looking for a high quality filtering that changes sampling dynamically based on the amount of "error". Based on this assumption I would say take a look at "ray differentials". There's a nice paper on this here: http://graphics.stanford.edu/papers/trd/ and it takes effects like refraction and reflection into account.

Answer 3

Your answer to yourself sounds like the right approach, but since others may stumble across the page I'll add a resource link as requested. In addition to discussing mipmapping (ripmapping is basically more advanced mipmapping), they discuss the effects of reflection and refraction on derivatives and mip-level selection.

Homan Igehy. "Tracing Ray Differentials." 1999. Proceedings of SIGGRAPH. http://graphics.stanford.edu/papers/trd/

Upon closer reading I see that Rehno Lindeque mentioned this paper. At first didn't realize that it was the right reference because he says that the method samples dynamically based on the error of the sampling, which is incorrect. Filtering is done based on the size of the pixel's footprint and uses only one ray, just as you described.

Edit: Another reference that might be useful ( http://www.cs.unc.edu/~awilson/class/238/#challenges ). Scroll to the section "Derivatives of Texture Coordinates." He suggests backward mapping of texture derivatives from the surface to the screen. I think this would be incorrect for reflected and refracted rays, but is possibly easier to implement and should be okay for primary rays.

Answer 4

I think you mean mipmap'ing.

Here is an article talking about using them.

But nether say how to chose which mipmap to use, but they are often blended (the bigger and smaller mipmap).

Here's a one more article about how Google Earth works, and it talks about how they mipmapping the earth.