{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:18:07Z","timestamp":1760242687979,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2016,2,6]],"date-time":"2016-02-06T00:00:00Z","timestamp":1454716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A new orthogonal projection method for computing the minimum distance between a point and a spatial parametric curve is presented. It consists of a geometric iteration which converges faster than the existing Newton\u2019s method, and it is insensitive to the choice of initial values. We prove that projecting a point onto a spatial parametric curve under the method is globally second-order convergence.<\/jats:p>","DOI":"10.3390\/a9010015","type":"journal-article","created":{"date-parts":[[2016,2,9]],"date-time":"2016-02-09T13:45:23Z","timestamp":1455025523000},"page":"15","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Geometric Orthogonal Projection Strategy for Computing the Minimum Distance Between a Point and a Spatial Parametric Curve"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9923-0011","authenticated-orcid":false,"given":"Xiaowu","family":"Li","sequence":"first","affiliation":[{"name":"College of Information Engineering, Guizhou Minzu University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhinan","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Yichun University, Yichun 336000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linke","family":"Hou","sequence":"additional","affiliation":[{"name":"Center for Economic Research, Shandong University, Jinan 250100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Guizhou Minzu University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunguang","family":"Yue","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Guizhou Minzu University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiao","family":"Xin","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Yili Normal University, Yining 835000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0167-8396(03)00021-9","article-title":"Point inversion and projection for NURBS curve and surface: Control polygon approach","volume":"20","author":"Ma","year":"2003","journal-title":"Comput. 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