{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T08:17:00Z","timestamp":1774599420265,"version":"3.50.1"},"reference-count":27,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2006,7,1]],"date-time":"2006-07-01T00:00:00Z","timestamp":1151712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2006,7]]},"abstract":"<jats:p>\n            We consider real-time rendering of dynamic glossy objects with realistic shadows under distant all-frequency environment lighting. Previous PRT approaches pre-compute light transport for a fixed scene and cannot account for cast shadows on high-glossy objects occluded by dynamic neighbors. In this paper, we extend double\/triple product integral to\n            <jats:italic>generalized multi-function product integral<\/jats:italic>\n            . We represent shading integral at each vertex as the product integral of multiple functions, involving the lighting, BRDF, local visibility and dynamic occlusions. Our main contribution is a new mathematical representation and analysis of multi-function product integral in the wavelet domain. We show that multi-function product integral in the primal corresponds to the summation of the product of basis coefficients and integral coefficients. We propose a novel\n            <jats:italic>generalized Haar integral coefficient theorem<\/jats:italic>\n            to evaluate arbitrary Haar integral coefficients. We present an efficient sub-linear algorithm to render dynamic glossy objects under time-variant all-frequency lighting and arbitrary view conditions in a few seconds on a commodity CPU, orders of magnitude faster than previous techniques. To further accelerate shadow computation, we propose a Just-in-time Radiance Transfer (JRT) technique. JRT is a new generalization to PRT for dynamic scenes. It is compact and flexible, and supports glossy materials. By pre-computing radiance transfer vectors at runtime, we demonstrate rendering dynamic view-dependent all-frequency shadows in real-time.\n          <\/jats:p>","DOI":"10.1145\/1141911.1141980","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"955-966","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":30,"title":["Generalized wavelet product integral for rendering dynamic glossy objects"],"prefix":"10.1145","volume":"25","author":[{"given":"Weifeng","family":"Sun","sequence":"first","affiliation":[{"name":"University of Central Florida"}]},{"given":"Amar","family":"Mukherjee","sequence":"additional","affiliation":[{"name":"University of Central Florida"}]}],"member":"320","published-online":{"date-parts":[[2006,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192181"},{"key":"e_1_2_2_2_1","unstructured":"Biedenharn L. C. and Louck J. D. 1981. Angualr Momentum in Quantum Physics theory and application. Addison-Wesley Publishing Company.  Biedenharn L. C. and Louck J. D. 1981. Angualr Momentum in Quantum Physics theory and application. Addison-Wesley Publishing Company."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/360349.360353"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073328"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258884"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.365003"},{"key":"e_1_2_2_7_1","unstructured":"Dutre P. Bekaert P. and Bala K. 2003. Advanced Global Illumination. AK Peters Limited.   Dutre P. Bekaert P. and Bala K. 2003. Advanced Global Illumination. 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S."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073214"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/78.258085"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566612"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882281"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882279"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073335"},{"key":"e_1_2_2_25_1","unstructured":"Stollnitz E. J. DeRose T. D. and Salesin D. H. 1996. Wavelets for Computer Graphics: Theory and Applications. Morgan-Kaufmann.   Stollnitz E. J. DeRose T. D. and Salesin D. H. 1996. Wavelets for Computer Graphics: Theory and Applications. Morgan-Kaufmann."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383533.2383580"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073332"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1141911.1141980","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1141911.1141980","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:14:24Z","timestamp":1750259664000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1141911.1141980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["10.1145\/1141911.1141980"],"URL":"https:\/\/doi.org\/10.1145\/1141911.1141980","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7]]},"assertion":[{"value":"2006-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}