Soft shadows, depth of field, and diffuse global illumination are common distribution effects, usually rendered by Monte Carlo ray tracing. Physically correct, noise-free images can require hundreds or thousands of ray samples per pixel, and take a long time to compute. Recent approaches have exploited sparse sampling and filtering; the filtering is either fast (axis-aligned), but requires more input samples, or needs fewer input samples but is very slow (sheared). We present a new approach for fast sheared filtering on the GPU. Our algorithm factors the 4D sheared filter into four 1D filters. We derive complexity bounds for our method, showing that the per-pixel complexity is reduced from O ( n 2 l 2 ) to O ( nl ), where n is the linear filter width (filter size is O ( n 2 )) and l is the (usually very small) number of samples for each dimension of the light or lens per pixel (spp is l 2 ). We thus reduce sheared filtering overhead dramatically. We demonstrate rendering of depth of field, soft shadows and diffuse global illumination at interactive speeds. We reduce the number of samples needed by 5-8×, compared to axis-aligned filtering, and framerates are 4× faster for equal quality.

Monte Carlo (MC) ray-tracing for photo-realistic rendering often requires hours to render a single image due to the large sampling rates needed for convergence. Previous methods have attempted to filter sparsely sampled MC renders but these methods have high reconstruction overheads. Recent work has shown fast performance for individual effects, like soft shadows and indirect illumination, using axis-aligned filtering. While some components of light transport such as indirect or area illumination are smooth, they are often multiplied by high-frequency components such as texture, which prevents their sparse sampling and reconstruction. We propose an approach to adaptively sample and filter for simultaneously rendering primary (defocus blur) and secondary (soft shadows and indirect illumination) distribution effects, based on a multi-dimensional frequency analysis of the direct and indirect illumination light fields. We describe a novel approach of factoring texture and irradiance in the presence of defocus blur, which allows for pre-filtering noisy irradiance when the texture is not noisy. Our approach naturally allows for different sampling rates for primary and secondary effects, further reducing the overall ray count. While the theory considers only Lambertian surfaces, we obtain promising results for moderately glossy surfaces. We demonstrate 30x sampling rate reduction compared to equal quality noise-free MC. Combined with a GPU implementation and low filtering over-head, we can render scenes with complex geometry and diffuse and glossy BRDFs in a few seconds.

We introduce an algorithm for interactive rendering of physically-based global illumination, based on a novel frequency analysis of indirect lighting. Our method combines adaptive sampling by Monte Carlo ray or path tracing, using a standard GPU-accelerated raytracer, with real-time reconstruction of the resulting noisy images. Our theoretical analysis assumes diffuse indirect lighting, with general Lambertian and specular receivers. In practice, we demonstrate accurate interactive global illumination with diffuse and moderately glossy objects, at 1-3 fps. We show mathematically that indirect illumination is a structured signal in the Fourier domain, with inherent band-limiting due to the BRDF and geometry terms. We extend previous work on sheared and axis-aligned filtering for motion blur and shadows, to develop an image-space filtering method for interreflections. Our method enables 5--8X reduced sampling rates and wall clock times, and converges to ground truth as more samples are added. To develop our theory, we overcome important technical challenges---unlike previous work, there is no light source to serve as a band-limit in indirect lighting, and we also consider non-parallel geometry of receiver and reflecting surfaces, without first-order approximations.

Abstract Environment‐mapped rendering of Lambertian isotropic surfaces is common, and a popular technique is to use a quadratic spherical harmonic expansion. This compact irradiance map representation is widely adopted in interactive applications like video games. However, many materials are anisotropic, and shading is determined by the local tangent direction, rather than the surface normal. Even for visualization and illustration, it is increasingly common to define a tangent vector field, and use anisotropic shading. In this paper, we extend spherical harmonic irradiance maps to anisotropic surfaces, replacing Lambertian reflectance with the diffuse term of the popular Kajiya‐Kay model. We show that there is a direct analogy, with the surface normal replaced by the tangent. Our main contribution is an analytic formula for the diffuse Kajiya‐Kay BRDF in terms of spherical harmonics; this derivation is more complicated than for the standard diffuse lobe. We show that the terms decay even more rapidly than for Lambertian reflectance, going as l–3, where l is the spherical harmonic order, and with only 6 terms (l = 0 and l = 2) capturing 99.8% of the energy. Existing code for irradiance environment maps can be trivially adapted for real‐time rendering with tangent irradiance maps. We also demonstrate an application to offline rendering of the diffuse component of fibers, using our formula as a control variate for Monte Carlo sampling.

We develop a simple and efficient method for soft shadows from planar area light sources, based on explicit occlusion calculation by raytracing, followed by adaptive image-space filtering. Since the method is based on Monte Carlo sampling, it is accurate. Since the filtering is in image-space, it adds minimal overhead and can be performed at real-time frame rates. We obtain interactive speeds, using the Optix GPU raytracing framework. Our technical approach derives from recent work on frequency analysis and sheared pixel-light filtering for offline soft shadows. While sample counts can be reduced dramatically, the sheared filtering step is slow, adding minutes of overhead. We develop the theoretical analysis to instead consider axis-aligned filtering, deriving the sampling rates and filter sizes. We also show how the filter size can be reduced as the number of samples increases, ensuring a consistent result that converges to ground truth as in standard Monte Carlo rendering.