## Archive for June, 2009

### Dispersion, Spectral Filtering, Subpixel Sampling

Bunny model available here. Ajax bust available here (thanks jotero!). Bunny scene was under 3 hours, Ajax scene was 8 hours.

The Cubo prism model is available here. For comparison, here is a proper rendering by luxrender. The prism shows off a new feature, spectral rendering. I used 20,000,000 photons which took about 1h20m to emit, and another 10 hours for rendering. (Without diffuse final gather it renders in about 2.5 hours.)

Dispersion in the glass is computed using Cauchy’s equation with dense flint glass (SF10) coefficients. Spectral computations are done in a way similar to this project, but with support for arbitrary wavelengths. I sample a wavelength from the visible spectrum and compute a “wavelength filter”, which is just an RGB color. I convert the CIE XYZ response for that wavelength to RGB and normalize such that a uniform sampling of the entire spectrum produces white (1, 1, 1) instead of (0.387463, 0.258293, 0.240652). Then I scale the emitted photon color and primary rays’ radiance by the normalized color. I sample the wavelengths with importance sampling according to the average CIE XYZ response.

With this spectral filtering I have to take more samples to eliminate the chromatic noise, but the result is consistent with the non-spectral result, provided there is no wavelength dependent reflection such as dispersion. That is, without dispersion, the spectral and non-spectral results match. If there *is* wavelength dependent reflection, then you get results like the prism image.

Finally, the cubo prism image and the last batch of sphere BRDF tests use subpixel sampling (similar to what’s done in smallpt). I divide each pixel up into 4×4 subpixels. Basically I scale the image resolution by 4, render, do all the tone mapping, and then shrink the image back down to the desired resolution using averaging. This produces much sharper results at the cost of increased memory usage. This is partially based on what Sunflow does, whose source I used as a guide, but without the adaptive anti-aliasing.

6 comments### Multiple Importance Sampling

Fixed lots of bugs in my Ashikhmin & Shirley and Schlick BRDF’s. Schlick anisotropic is still not 100% correct. Added explicit BRDF calculation for both BRDF’s, allowing for light sampling in addition to BRDF importance sampling. This helped a great deal with small light sources like the sun. To incorporate the benefits of both sampling strategies (light and BRDF), I also added Multiple Importance Sampling (MIS) using the one-sample model and balance heuristic as described in section 9.2.4 of Eric Veach’s dissertation. This solves the glossy highlights problem (section 9.3.1).

The MIS is actually incredibly simple to do, once you can compute the BRDF for an arbitrary direction. Choose weights for two sampling strategies (light sampling or brdf sampling). I do .5 and .5. Then select one of the sampling techniques according to its weight. Trace the ray and compute the BRDF. Then divide by the PDF as done for regular importance sampling, but now the PDF is weight1*pdf1+weight2*pdf2 (regardless of technique chosen). Done. Well… actually, it took some refactoring and debugging in lots of places to add MIS everywhere.

I was hung up for a long time because I tried to be cheap and only compute the simplified BRDF/PDF ratio when importance sampling the BRDF. Pointless. Just compute both the BRDF and PDF, since you’ll need both for MIS.

Also added direct lighting computation for emissive spheres.

Times are about 42 minutes with 1024 samples per pixel (spp), on a Q6600 quad core cpu.

5 comments### Distance Field Experiments

Here are the results from some distance field intersection experiments.

Inspired by slisesix by Inigo Quilez. A better explanation is on my reading list.

I also posted these on ompf. A single sample at 1024×768 takes about 6 seconds on a 2.4GHz Q6600 quad core CPU. Intersection works by stepping the field distance with a minimum step until the isosurface is intersected, and then the distance is refined with bisection method.