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Building upon moment shadow mapping, we present a moment-based method for compact storage and fast reconstruction of this depth-dependent function per pixel. We work with the logarithm of the transmittance such that the function may be accumulated additively rather than multiplicatively. Then an additive rendering pass for all transparent surfaces yields moments. Moment-based reconstruction algorithms provide approximations to the original function, which are used for compositing in a second additive pass. We utilize existing algorithms with four or six power moments and develop new algorithms using eight power moments or up to four trigonometric moments. The resulting techniques are completely order-independent, work well for participating media as well as transparent surfaces and come in many variants providing different tradeoffs. We also utilize the same approach for the closely related problem of computing shadows for transparent surfaces.<\/jats:p>","DOI":"10.1145\/3203206","type":"journal-article","created":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T11:58:04Z","timestamp":1532606284000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":19,"title":["Moment-Based Order-Independent Transparency"],"prefix":"10.1145","volume":"1","author":[{"given":"Cedrick","family":"M\u00fcnstermann","sequence":"first","affiliation":[{"name":"University of Bonn, Endenicher Allee 19a, Bonn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Krumpen","sequence":"additional","affiliation":[{"name":"University of Bonn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reinhard","family":"Klein","sequence":"additional","affiliation":[{"name":"University of Bonn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christoph","family":"Peters","sequence":"additional","affiliation":[{"name":"Karlsruhe Institute of Technology, Karlsruhe, Germany and University of Bonn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,7,25]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"EGSR07:18th Eurographics Symposium on Rendering","author":"Annen Thomas"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1230100.1230117"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2007.60"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/964965.808585"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1944745.1944751"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.123"},{"key":"e_1_2_2_7_1","unstructured":"Cass Everitt. 2001. 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