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Our method is based on warp functions that operate on the primary samples in [0,1)<\/jats:italic>n<\/jats:italic><\/jats:sup>, where each warp approximates sampling a single factor of the product distribution. Our key insight is that individual factors are often well\u2010behaved and inexpensive to fit and sample in primary sample space, which leads to a practical, efficient sampling algorithm. Our sampling approach is unbiased, easy to implement, and compatible with multiple importance sampling. We show the results of applying our warps to projected solid angle sampling of spherical triangles, to sampling bilinear patch light sources, and to sampling glossy BSDFs and area light sources, with efficiency improvements of over 1.6\u00d7<\/jats:italic> on real\u2010world scenes.<\/jats:p>","DOI":"10.1111\/cgf.14060","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T19:56:20Z","timestamp":1595274980000},"page":"149-158","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Practical Product Sampling by Fitting and Composing Warps"],"prefix":"10.1111","volume":"39","author":[{"given":"D.","family":"Hart","sequence":"first","affiliation":[{"name":"NVIDIA"}]},{"given":"M.","family":"Pharr","sequence":"additional","affiliation":[{"name":"NVIDIA"}]},{"given":"T.","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"NVIDIA"}]},{"given":"W.","family":"Lopes","sequence":"additional","affiliation":[{"name":"NVIDIA"}]},{"given":"M.","family":"McGuire","sequence":"additional","affiliation":[{"name":"NVIDIA"}]},{"given":"P.","family":"Shirley","sequence":"additional","affiliation":[{"name":"NVIDIA"}]}],"member":"311","published-online":{"date-parts":[[2020,7,20]]},"reference":[{"issue":"2","key":"e_1_2_7_2_2","first-page":"1","article-title":"Stratified sampling of convex quadrilaterals","volume":"12","author":"Arvo James","year":"2007","journal-title":"JGT"},{"key":"e_1_2_7_3_2","doi-asserted-by":"crossref","unstructured":"J.Arvo. 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