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In the presence of shadows, rendering these effects can be prohibitively expensive: current algorithms are based on ray marching, i.e., integrating the illumination scattered towards the camera along each view ray, modulated by visibility to the light source at each sample. Visibility must be determined for each sample using shadow rays or shadow-map lookups. We observe that in a suitably chosen coordinate system, the visibility function has a regular structure that we can exploit for significant acceleration compared to brute force sampling. We propose an efficient algorithm based on partial sum trees for computing the scattering integrals in a single-scattering homogeneous medium. On a CPU, we achieve speedups of 17--120x over ray marching.<\/jats:p>","DOI":"10.1145\/1882261.1866200","type":"journal-article","created":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T20:18:10Z","timestamp":1291234690000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["A hierarchical volumetric shadow algorithm for single scattering"],"prefix":"10.1145","volume":"29","author":[{"given":"Ilya","family":"Baran","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiawen","family":"Chen","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Ragan-Kelley","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fr\u00e9do","family":"Durand","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jaakko","family":"Lehtinen","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,12,15]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1572769.1572792"},{"key":"e_1_2_2_2_1","volume-title":"Proc. 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