{"id":35,"date":"2020-11-25T17:58:31","date_gmt":"2020-11-25T17:58:31","guid":{"rendered":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/?page_id=35"},"modified":"2021-07-15T19:42:01","modified_gmt":"2021-07-15T19:42:01","slug":"research","status":"publish","type":"page","link":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/research\/","title":{"rendered":"Research Interests"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"35\" class=\"elementor elementor-35\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-662e9a79 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"662e9a79\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5911656b\" data-id=\"5911656b\" data-element_type=\"column\" data-e-type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7f502f93 elementor-widget elementor-widget-page-title\" data-id=\"7f502f93\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"page-title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\n\t\t<div class=\"hfe-page-title hfe-page-title-wrapper elementor-widget-heading\">\n\n\t\t\t\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\n\t\t\t\t\t\t\t\t\n\t\t\t\tResearch Interests  \n\t\t\t<\/h2 > \n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-66cc0bb3 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"66cc0bb3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a535095 elementor-widget elementor-widget-text-editor\" data-id=\"6a535095\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>Research expertise<\/h3><ul><li>Computer aided design and manufacturing<\/li><li>Geometrical algorithms and representations<\/li><li>Numerical methods and scientific computing<\/li><\/ul><p>\u00a0<\/p><h3>PDF files of various presentations<\/h3><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Bernstein-polynomial-basis.pdf\">Bernstein polynomial basis<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Computer-numerical-control-algorithms.pdf\">Computer numerical control algorithms<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Helical-curves-and-double-Pythagorean-hodographs.pdf\">Helical curves and double Pythagorean hodographs<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/History-of-mathematics-and-PH-curves.pdf\">History of mathematics and PH curves<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Interpolation-with-PH-curves.pdf\">Interpolation with PH curves<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Introduction-to-PH-curves.pdf\">Introduction to PH curves<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Minkowski-geometric-algebra-of-complex-sets.pdf\">Minkowski geometric algebra of complex sets<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Quaternions-and-spatial-rotations.pdf\">Quaternions and spatial rotations<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Rational-rotation-minimizing-frames.pdf\">Rational rotation-minimizing frames<\/a><\/p><p><a href=\"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-content\/uploads\/sites\/51\/2021\/07\/Time-optimal-control-of-CNC-machines.pdf\">Time-optimal control of CNC machines<\/a><\/p><p>\u00a0<\/p><h3>Involvement with various conferences<\/h3><ul><li><a href=\"http:\/\/smart2014.diism.unisi.it\/\">SMART 2014 Conference<\/a>, Pontignano, Siena, ITALY, September 28-October 1, 2014<\/li><li><a href=\"http:\/\/www.imacs2013.it\/\">IMACS 2013 World Congress<\/a>, Real Centro Universitario El Escorial \u2013 Maria Cristina, San Lorenzo de El Escorial, SPAIN, August 26-30, 2013<\/li><li><a href=\"http:\/\/www.mmrc.iss.ac.cn\/cnc\/cnc2011\/\">International Workshop on Mathematics and Algorithms for Computer-Aided Manufacturing, Engineering, and Numerical Control<\/a>, Chinese Academy of Sciences, Beijing, CHINA, October 24-26, 2011<\/li><li><a href=\"http:\/\/www.math.upatras.gr\/~geomconf11\">10th Panhellenic Geometry Conference<\/a>, University of Patras, GREECE, May 27-29, 2011<\/li><li><a href=\"http:\/\/www.dmmm.uniroma1.it\/~pitolli\/CAGD2010\/\">New Frontiers in CAGD Conference<\/a>,\u00a0Bertinoro, ITALY, May 17-21, 2010<\/li><li><a href=\"http:\/\/math.ustc.edu.cn\/Conference\/AGGM\/\">Algebraic Geometry and Geometric Modeling Conference<\/a>,\u00a0Lijiang, China, July 21-26, 2009<\/li><li><a href=\"http:\/\/www.math.zju.edu.cn\/gmp2008\">Geometric Modeling and Processing 2008 Conference<\/a>,\u00a0Hangzhou, China, April 23-25, 2008<\/li><li><a href=\"http:\/\/www.comp.nus.edu.sg\/~ascm2007\/\">Asian Symposium on Computer Mathematics<\/a>,\u00a0Singapore, December 15-17, 2007<\/li><li><a href=\"http:\/\/www.ig.jku.at\/2007-09stroblcompass.htm\">Workshop on Computational Methods for Algebraic Spline Surfaces<\/a>,\u00a0Strobl, Austria, September 10-14, 2007<\/li><li><a href=\"http:\/\/cs.nyu.edu\/yap\/zero\/\">Zero 2007 Workshop<\/a>, Korea Institute for Advanced Study,\u00a0Seoul, Korea, July 19-21, 2007<\/li><li>Algebraic Geometry and Geometric Modeling Conference,\u00a0Universitat de Barcelona, Spain, September 4-7, 2006<\/li><li>Australian Mathematical Society 49th Annual Meeting,\u00a0University of Western Australia, Perth, Australia, September 27-30, 2005<\/li><li>11th IMA Conference on the Mathematics of Surfaces,\u00a0University of Loughborough, England, September 5-7, 2005<\/li><li>Fifth International AFA-SMAI Conference on Curves and Surfaces,\u00a0Saint-Malo, France, June 27 \u2013 July 3, 2002<\/li><li>Mathematics and Visualization 2002 Workshop, Berlin, Germany,\u00a0May 22-25, 2002<\/li><li>Surface Approximation and Visualization II, Westport, New Zealand,\u00a0February 19-22, 2002<\/li><li>SIAM Conference on Geometric Design and Computing,\u00a0Sacramento, CA, Nov. 5-8, 2001<\/li><li>EuroConference on CAE Integration \u2013 Tools, Trends, and Technologies,\u00a0Cambridge, England, March 29 \u2013 April 1, 2001<\/li><li>Geometric Modeling and Processing 2000, Univerity of Hong Kong,\u00a0China, April 10-12, 2000<\/li><li>SIAM Conference on Geometric Design,\u00a0Albuquerque, NM, Nov. 2-5, 1999<\/li><li>Fourth International AFA Conference on Curves and Surfaces,\u00a0Saint-Malo, France, July 1-7, 1999<\/li><li>Workshop on Mathematical Foundations of Computer Aided Design,\u00a0Mathematical Sciences Research Institute, Berkeley, CA, June 4-5, 1999<\/li><li>SIAM Workshop on Integration of CAD and CFD,\u00a0University of California, Davis, April 12-13, 1999 (<a href=\"http:\/\/www.siam.org\/news\/news.php?id=743\">report<\/a>)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Research Interests Research expertise Computer aided design and manufacturing Geometrical algorithms and representations Numerical methods and scientific computing \u00a0 PDF files of various presentations Bernstein polynomial basis Computer numerical control algorithms Helical curves and double Pythagorean hodographs History of mathematics and PH curves Interpolation with PH curves Introduction to PH curves Minkowski geometric algebra of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-35","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":27,"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":1046,"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/pages\/35\/revisions\/1046"}],"wp:attachment":[{"href":"https:\/\/faculty.engineering.ucdavis.edu\/farouki\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}