乐胖代购免代理版

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Graph."],"published-print":{"date-parts":[[2018,4,30]]},"abstract":"Many applications in rendering rely on integrating functions over spherical polygons. We present a new numerical solution for computing the integral of spherical harmonics (SH) expansions clipped to polygonal domains. Our solution, based on zonal decompositions of spherical integrands and discrete contour integration, introduces an important numerical operating for SH expansions in rendering applications. Our method is simple, efficient, and scales linearly in the bandlimited integrand\u2019s harmonic expansion. We apply our technique to problems in rendering, including surface and volume shading, hierarchical product importance sampling, and fast basis projection for interactive rendering. Moreover, we show how to handle general, nonpolynomial integrands in a Monte Carlo setting using control variates. Our technique computes the integral of bandlimited spherical functions with performance competitive to (or faster than) more general numerical integration methods for a broad class of problems, both in offline and interactive rendering contexts. Our implementation is simple, relying only on self-contained SH evaluation and discrete contour integration routines, and we release a full source CPU-only and shader-based implementations (<750 lines of commented code).<\/jats:p>","DOI":"10.1145\/3015459","type":"journal-article","created":{"date-parts":[[2018,3,23]],"date-time":"2018-03-23T12:29:49Z","timestamp":1521808189000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["Integrating Clipped Spherical Harmonics Expansions"],"prefix":"10.1145","volume":"37","author":[{"given":"Laurent","family":"Belcour","sequence":"first","affiliation":[{"name":"University of Montreal"}]},{"given":"Guofu","family":"Xie","sequence":"additional","affiliation":[{"name":"University of Montreal"}]},{"given":"Christophe","family":"Hery","sequence":"additional","affiliation":[{"name":"Pixar Animation Studios"}]},{"given":"Mark","family":"Meyer","sequence":"additional","affiliation":[{"name":"Pixar Animation Studios"}]},{"given":"Wojciech","family":"Jarosz","sequence":"additional","affiliation":[{"name":"Dartmouth College, Hanover, NH"}]},{"given":"Derek","family":"Nowrouzezahrai","sequence":"additional","affiliation":[{"name":"McGill University"}]}],"member":"320","published-online":{"date-parts":[[2018,3,23]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Proceedings of the 15th Eurographics Conference on Rendering Techniques (EGSR\u201904)","author":"Annen Thomas","year":"2004","unstructured":"Thomas Annen , Jan Kautz , Fr\u00e9do Durand , and Hans-Peter Seidel . 2004 . Spherical harmonic gradients for mid-range illumination . In Proceedings of the 15th Eurographics Conference on Rendering Techniques (EGSR\u201904) . 331--336. Thomas Annen, Jan Kautz, Fr\u00e9do Durand, and Hans-Peter Seidel. 2004. Spherical harmonic gradients for mid-range illumination. In Proceedings of the 15th Eurographics Conference on Rendering Techniques (EGSR\u201904). 331--336."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218467"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13137-012-0035-4"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s13137-014-0065-1"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12674"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383696.2383700"},{"key":"e_1_2_2_7_1","volume-title":"Arvo","author":"Chen Min","year":"2000","unstructured":"Min Chen and James R . Arvo . 2000 . 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