We present an area-preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1] 2 and range in a region included in the unit-radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1] 2 onto the spherical rectangle. This allows for easily incorporating stratified, quasi-Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square [0, 1] 2 to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low-variance stratified sampling of direct illumination from disk-shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.

Figure 1: Simple BSSRDF without (a) and with (b) axis MIS (25 spp). Complex BSSRDF without (c) and with (d) weight MIS (16 spp).Light propagation within translucent materials can be described by a BSSRDF [Jensen et al. 2001]. The main difficulty in integrating this effect lies in the generation of well-distributed samples on the surface within the support of the rapidly decaying BSSRDF profile. Jensen suggested that these points could be importance sampled but did not provide implementation details. More recently, Walter et al. [2012] and Christensen et al. [2012] proposed other sampling methods which can still suffer from excessive variance. P N Rm r P hitFigure 2: Geometric setup for Equation 1.Disk based sampling Our approach uses a disk distribution of samples which we project against the surface geometry using probe rays. We bound the radial term of the BSSRDF with a maximum distance Rm to define a bounding sphere around the shading point P. We cast probe rays against this sphere along an axis V perpendicular to the disk and compute the incoming irradiance at all intersection points we find inside the sphere. The contribution of each point is modulated by:which accounts for the probability of generating the point, the change in differential area measure and the BSSRDF itself. We omit the view-dependent terms here for simplicity. We choose the pdf to be proportional to R d , as for flat surfaces this results in perfect importance sampling. We have developed equations for both cubic and gaussian profiles. For a single planar gaussian defined as R d (r) = (2πv) −1 e −r 2 /2v , we use the following normalized pdf and warping equation to get r ∈ [0, Rm) from a random sample ξ ∈ [0, 1):pdf disk (r) = R d (r) / 1 − e −R 2 m /2v r(ξ) = −2v log 1 − ξ 1 − e −R 2 m /2v

Arnold is a physically based renderer for feature-length animation and visual effects. Conceived in an era of complex multi-pass rasterization-based workflows struggling to keep up with growing demands for complexity and realism, Arnold was created to take on the challenge of making the simple and elegant approach of brute-force Monte Carlo path tracing practical for production rendering. Achieving this required building a robust piece of ray-tracing software that can ingest large amounts of geometry with detailed shading and lighting and produce images with high fidelity, while scaling well with the available memory and processing power. Arnold’s guiding principles are to expose as few controls as possible, provide rapid feedback to artists, and adapt to various production workflows. In this article, we describe its architecture with a focus on the design and implementation choices made during its evolutionary development to meet the aforementioned requirements and goals. Arnold’s workhorse is a unidirectional path tracer that avoids the use of hard-to-manage and artifact-prone caching and sits on top of a ray-tracing engine optimized to shoot and shade billions of spatially incoherent rays throughout a scene. A comprehensive API provides the means to configure and extend the system’s functionality, to describe a scene, render it, and save the results.

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