Visibility Silhouettes for Semi-Analytic Spherical Integration

1Université de Montréal 2Disney Research Zürich 3Belmont Technology, Inc.

In Computer Graphics Forum, 2014

We compute spherical integrals of visibility-masked functions commonly found in rendering, e.g. in ambient occlusion and all-frequency direct illumination. This scene (123.2k triangles) took ~5 minutes to render on a 4-core CPU, independent of the lighting. These results render at 84% to 106% the speed of a noise-free ray-traced image, depending on the lighting.


At each shade point, the spherical visibility function encodes occlusion from surrounding geometry, in all directions. Computing this function is difficult and point-sampling approaches, such as ray-tracing or hardware shadow mapping, are traditionally used to efficiently approximate it. We propose a semi-analytic solution to the problem where the spherical silhouette of the visibility is computed using a search over a 4D dual mesh of the scene. Once computed, we are able to semi-analytically integrate visibility-masked spherical functions along the visibility silhouette, instead of over the entire hemisphere. In this way, we avoid the artifacts that arise from using point-sampling strategies to integrate visibility, a function with unbounded frequency content. We demonstrate our approach on several applications, including direct illumination from realistic lighting and computation of PRT data. Additionally, we present a new frequency-space method for exactly computing all-frequency shadows on diffuse surfaces. Our results match ground truth computed using importance-sampled stratified Monte Carlo ray-tracing, with comparable performance on scenes with low-to-moderate geometric complexity.


Supplemental Video

Text Reference

Derek Nowrouzezahrai, Ilya Baran, Kenny Mitchell, Wojciech Jarosz. Visibility Silhouettes for Semi-Analytic Spherical Integration. Computer Graphics Forum, 33(1):105–117, February 2014.

BibTex Reference

    author = "Nowrouzezahrai, Derek and Baran, Ilya and Mitchell, Kenny and Jarosz, Wojciech",
    title = "Visibility Silhouettes for Semi-Analytic Spherical Integration",
    journal = "Computer Graphics Forum",
    volume = "33",
    number = "1",
    month = "February",
    year = "2014",
    pages = "105–117",
    doi = "10.1111/cgf.12257",
    keywords = "all-frequency shadowing, image-based rendering, spherical visibility"

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