Abstract We introduce a Monte Carlo importance sampling method for integrands composed of products and show its application to rendering where direct sampling of the product is often difficult. Our method is based on warp functions that operate on the primary samples in [0,1)n, where each warp approximates sampling a single factor of the product distribution. Our key insight is that individual factors are often well‐behaved and inexpensive to fit and sample in primary sample space, which leads to a practical, efficient sampling algorithm. Our sampling approach is unbiased, easy to implement, and compatible with multiple importance sampling. We show the results of applying our warps to projected solid angle sampling of spherical triangles, to sampling bilinear patch light sources, and to sampling glossy BSDFs and area light sources, with efficiency improvements of over 1.6× on real‐world scenes.

Diffusion-weighted magnetic resonance imaging is a relatively new modality capable of elucidating the fibrous structure of certain types of tissue, such as the white matter within the brain. One tool for interpreting this data is volume rendering because it permits the visualization of three dimensional structure without a prior segmentation process. In order to use volume rendering, however, we must develop methods for assigning opacity and color to the data, and create a method to shade the data to improve the legibility of the rendering. Previous work introduced three such methods: barycentric opacity maps, hue-balls (for color), and lit-tensors (for shading). The paper expands on and generalizes these methods, describing and demonstrating further means of generating opacity, color, and shading from the tensor information. We also propose anisotropic reaction-diffusion volume textures as an additional tool for visualizing the structure of diffusion data. The patterns generated by this process can be visualized on their own or they can be used to supplement the volume rendering strategies described in the rest of the paper. Finally, because interpolation between data points is a fundamental issue in volume rendering, we conclude with a discussion and evaluation of three distinct interpolation methods suitable for diffusion tensor MRI data.

In this paper we present a technique for computing the direct lighting in a three-dimensional scene containing area light sources.Our method correctly handles partial visibility between luminaires and receivers, and is able to efficiently generate accurate soft shadows in scenes modeled with general bidirectional reflectance distribution functions.In most current algorithms, the form factor between a light source and receiver is computed using a stochastic ray casting approach which evaluates partial visibility.Such an approach often leads to noisy artifacts or aliasing problems.Generating significantly more rays is often the only solution to improving image quality.Our approach first stores visibility information in the image plane, using lazy evaluation of the visibility function.In a second phase, illumination values for each pixel are generated, using analytic or stochastic integration.Soft shadows and other shading effects are generated with high accuracy in less time than with existing shading algorithms.Coherence in specific blockerlight source relationships across the image plane is exploited to amortize the cost of analytic form factor calculations.By storing information in the image plane, our method is currently designed for generating a single image, and is thus view-dependent.