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Our contribution is a novel, efficient way to perform this computation, using a sum of precomputed complex-valued hyperplanar wave-functions, oriented in random directions. We show that using suitable wave profiles and combination operators, our model is able to extend to 3D a number of Gaussian and non-Gaussian noises, including Gabor, by-example and Phasor noises, as well as generate novel cellular noises. Our versatile and controllable solid noise model is very compact, a key feature for complex power spectrum and animated noises. We illustrate this through the design of 2D, 3D, and 3D+t materials using color, transparency and style transfer functions.<\/jats:p>","DOI":"10.1145\/3730928","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T04:02:22Z","timestamp":1753588942000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Multi-Dimensional Procedural Wave Noise"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6387-6355","authenticated-orcid":false,"given":"Pascal","family":"Guehl","sequence":"first","affiliation":[{"name":"LIX, Ecole Polytechnique\/CNRS, Palaiseau, France"},{"name":"Institut Polytechnique de Paris, Palaiseau, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7780-9284","authenticated-orcid":false,"given":"R\u00e9mi","family":"All\u00e8gre","sequence":"additional","affiliation":[{"name":"ICube, Universit\u00e9 de Strasbourg, Strasbourg, France"},{"name":"CNRS, Strasbourg, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9973-1772","authenticated-orcid":false,"given":"Guillaume","family":"Gilet","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Sherbrooke, Sherbrooke, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1004-744X","authenticated-orcid":false,"given":"Basile","family":"Sauvage","sequence":"additional","affiliation":[{"name":"ICube, Universit\u00e9 de Strasbourg, Strasbourg, France"},{"name":"CNRS, Strasbourg, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7752-9031","authenticated-orcid":false,"given":"Marie-Paule","family":"Cani","sequence":"additional","affiliation":[{"name":"LIX, Ecole Polytechnique\/CNRS, Palaiseau, France"},{"name":"Institut Polytechnique de Paris, Palaiseau, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4444-2719","authenticated-orcid":false,"given":"Jean-Michel","family":"Dischler","sequence":"additional","affiliation":[{"name":"ICube, Universit\u00e9 de Strasbourg, Strasbourg, France"},{"name":"CNRS, Strasbourg, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cviu.2018.04.001"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14449"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2023.04.004"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s41095-016-0064-2"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276435"},{"key":"e_1_2_2_6_1","volume-title":"Style transfer functions for illustrative","author":"Bruckner Stefan","unstructured":"Stefan Bruckner and M Eduard Gr\u00f6ller. 2007. 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