{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T12:00:32Z","timestamp":1791115232475,"version":"4.1.0"},"reference-count":43,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T00:00:00Z","timestamp":1291161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee, Hong Kong","doi-asserted-by":"publisher","award":["6.19E+11"],"award-info":[{"award-number":["6.19E+11"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:p>\n            Blue noise sampling is widely employed for a variety of imaging, geometry, and rendering applications. However, existing research so far has focused mainly on isotropic sampling, and challenges remain for the anisotropic scenario both in sample generation and quality verification. We present\n            <jats:italic>anisotropic blue noise sampling<\/jats:italic>\n            to address these issues. On the generation side, we extend dart throwing and relaxation, the two classical methods for isotropic blue noise sampling, for the anisotropic setting, while ensuring both high-quality results and efficient computation. On the verification side, although Fourier spectrum analysis has been one of the most powerful and widely adopted tools, so far it has been applied only to uniform isotropic samples. We introduce approaches based on warping and sphere sampling that allow us to extend Fourier spectrum analysis for adaptive and\/or anisotropic samples; thus, we can detect problems in alternative anisotropic sampling techniques that were not yet found via prior verification. We present several applications of our technique, including stippling, visualization, surface texturing, and object distribution.\n          <\/jats:p>","DOI":"10.1145\/1882261.1866189","type":"journal-article","created":{"date-parts":[[2010,12,1]],"date-time":"2010-12-01T20:18:10Z","timestamp":1291234690000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":43,"title":["Anisotropic blue noise sampling"],"prefix":"10.1145","volume":"29","author":[{"given":"Hongwei","family":"Li","sequence":"first","affiliation":[{"name":"Hong Kong UST"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li-Yi","family":"Wei","sequence":"additional","affiliation":[{"name":"Microsoft Research"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pedro V.","family":"Sander","sequence":"additional","affiliation":[{"name":"Hong Kong UST"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Wing","family":"Fu","sequence":"additional","affiliation":[{"name":"Nanyang Tech. Univ."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2010,12,15]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566588"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1201775.882296"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1576246.1531392"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISVD.2009.28"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1866158.1866188"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166151"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01499.x"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/7529.8927"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00580"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1179352.1141915"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70434"},{"key":"e_1_2_2_12_1","volume-title":"In Proc. 2nd International Symposium on Voronoi Diagrams in Science and Engineering, 1--11","author":"Fritzsche L.-P.","unstructured":"Fritzsche , L.-P. , Hellwig , H. , Hiller , S. , and Deussen , O . 2005. Interactive design of authentic looking mosaics using Voronoi structures . In In Proc. 2nd International Symposium on Voronoi Diagrams in Science and Engineering, 1--11 . Fritzsche, L.-P., Hellwig, H., Hiller, S., and Deussen, O. 2005. Interactive design of authentic looking mosaics using Voronoi structures. In In Proc. 2nd International Symposium on Voronoi Diagrams in Science and Engineering, 1--11."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1364901.1364919"},{"key":"e_1_2_2_14_1","volume-title":"Geometric Applications of Fourier Series and Spherical Harmonics","author":"Groemer H.","unstructured":"Groemer , H. 1996. Geometric Applications of Fourier Series and Spherical Harmonics . Cambridge University Press . Groemer, H. 1996. Geometric Applications of Fourier Series and Spherical Harmonics. 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In Proceedings of Eurographics 2003, vol. 22, 515--522."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01259.x"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1179352.1141916"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/777792.777822"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1095878.1095888"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1183287.1183296"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01100.x"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2005.4"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778856"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2008.53"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1730804.1730985"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/0262-8856(83)90046-X"},{"key":"e_1_2_2_27_1","volume-title":"Proceedings of the conference on Graphics interface '92","author":"McCool M.","unstructured":"McCool , M. , and Fiume , E . 1992. Hierarchical Poisson disk sampling distributions . In Proceedings of the conference on Graphics interface '92 , 94--105. McCool, M., and Fiume, E. 1992. Hierarchical Poisson disk sampling distributions. 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