{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T18:54:23Z","timestamp":1780512863159,"version":"3.54.1"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2005,7,1]],"date-time":"2005-07-01T00:00:00Z","timestamp":1120176000000},"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":[[2005,7]]},"abstract":"<jats:p>\n                    Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics. Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed polygons, mean value coordinates have been proven to be an excellent method for constructing such an interpolant. In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh\n                    <jats:italic>P<\/jats:italic>\n                    , we show that these coordinates are continuous everywhere and smooth on the interior of\n                    <jats:italic>P<\/jats:italic>\n                    . The coordinates are linear on the triangles of\n                    <jats:italic>P<\/jats:italic>\n                    and can reproduce linear functions on the interior of\n                    <jats:italic>P<\/jats:italic>\n                    . To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.\n                  <\/jats:p>","DOI":"10.1145\/1073204.1073229","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T11:00:45Z","timestamp":1131361245000},"page":"561-566","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":380,"title":["Mean value coordinates for closed triangular meshes"],"prefix":"10.1145","volume":"24","author":[{"given":"Tao","family":"Ju","sequence":"first","affiliation":[{"name":"Rice University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Scott","family":"Schaefer","sequence":"additional","affiliation":[{"name":"Rice University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joe","family":"Warren","sequence":"additional","affiliation":[{"name":"Rice University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2005,7]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"CRC Standard Mathematical Tables","author":"Beyer W. 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S. and Hormann K. 2005. Surface parameterization: a tutorial and survey. In Advances in Multiresolution for Geometric Modelling N. A. Dodgson M. S. Floater and M. A. Sabin Eds. Mathematics and Visualization. Springer Berlin Heidelberg 157--186.","DOI":"10.1007\/3-540-26808-1_9"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/1122905.1648459"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(96)00031-3"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021865439800012X"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(02)00002-5"},{"key":"e_1_2_2_10_1","volume-title":"MIPS - An Efficient Global Parametrization Method. In Curves and Surfaces Proceedings","author":"Hormann K.","unstructured":"Hormann , K. , and Greiner , G . 2000 . MIPS - An Efficient Global Parametrization Method. In Curves and Surfaces Proceedings ( Saint Malo, France), 152--163. Hormann, K., and Greiner, G. 2000. 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Tech. rep., Clausthal University of Technology, September. http:\/\/www.in.tuclausthal.de\/ hormann\/papers\/barycentric.pdf."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882275"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/781606.781641"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/77055.77059"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/237170.237247"},{"key":"e_1_2_2_16_1","volume-title":"Proceedings of the 5th International Mathematica Symposium.","author":"Malsch E.","unstructured":"Malsch , E. , and Dasgupta , G . 2003. Algebraic construction of smooth interpolants on polygonal domains . In Proceedings of the 5th International Mathematica Symposium. Malsch, E., and Dasgupta, G. 2003. Algebraic construction of smooth interpolants on polygonal domains. 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