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We present an algorithm that combines these two kinds of estimates to produce a new surface that approximates both. Our formulation is linear, allowing it to operate efficiently on complex meshes commonly used in graphics. It also treats high-and low-frequency components separately, allowing it to optimally combine outputs from data sources such as stereo triangulation and photometric stereo, which have different error-vs.-frequency characteristics. We demonstrate the ability of our technique to both recover high-frequency details and avoid low-frequency bias, producing surfaces that are more widely applicable than position or orientation data alone.<\/jats:p>","DOI":"10.1145\/1073204.1073226","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"536-543","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":305,"title":["Efficiently combining positions and normals for precise 3D geometry"],"prefix":"10.1145","volume":"24","author":[{"given":"Diego","family":"Nehab","sequence":"first","affiliation":[{"name":"Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Szymon","family":"Rusinkiewicz","sequence":"additional","affiliation":[{"name":"Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James","family":"Davis","sequence":"additional","affiliation":[{"name":"University of California at Santa Cruz"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"Columbia University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2005,7]]},"reference":[{"key":"e_1_2_2_1_1","first-page":"141","volume-title":"IAPR","volume":"1","author":"Banerjee S.","unstructured":"Banerjee , S. , Sastry , P. , and Venkatesh , Y . 1992. 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