{"title":"Rational Bézier Guarding","year":"2022","date_updated":"2025-07-14T12:46:58Z","language":[{"iso":"eng"}],"publication_status":"published","user_id":"117512","publication":"Computer Graphics Forum","publisher":"Wiley","_id":"60368","status":"public","type":"journal_article","page":"89-99","intvolume":"        41","volume":41,"issue":"5","publication_identifier":{"issn":["0167-7055","1467-8659"]},"citation":{"bibtex":"@article{Khanteimouri_Mandad_Campen_2022, title={Rational Bézier Guarding}, volume={41}, DOI={<a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>}, number={5}, journal={Computer Graphics Forum}, publisher={Wiley}, author={Khanteimouri, Payam and Mandad, Manish and Campen, Marcel}, year={2022}, pages={89–99} }","ieee":"P. Khanteimouri, M. Mandad, and M. Campen, “Rational Bézier Guarding,” <i>Computer Graphics Forum</i>, vol. 41, no. 5, pp. 89–99, 2022, doi: <a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>.","chicago":"Khanteimouri, Payam, Manish Mandad, and Marcel Campen. “Rational Bézier Guarding.” <i>Computer Graphics Forum</i> 41, no. 5 (2022): 89–99. <a href=\"https://doi.org/10.1111/cgf.14605\">https://doi.org/10.1111/cgf.14605</a>.","short":"P. Khanteimouri, M. Mandad, M. Campen, Computer Graphics Forum 41 (2022) 89–99.","ama":"Khanteimouri P, Mandad M, Campen M. Rational Bézier Guarding. <i>Computer Graphics Forum</i>. 2022;41(5):89-99. doi:<a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>","mla":"Khanteimouri, Payam, et al. “Rational Bézier Guarding.” <i>Computer Graphics Forum</i>, vol. 41, no. 5, Wiley, 2022, pp. 89–99, doi:<a href=\"https://doi.org/10.1111/cgf.14605\">10.1111/cgf.14605</a>.","apa":"Khanteimouri, P., Mandad, M., &#38; Campen, M. (2022). Rational Bézier Guarding. <i>Computer Graphics Forum</i>, <i>41</i>(5), 89–99. <a href=\"https://doi.org/10.1111/cgf.14605\">https://doi.org/10.1111/cgf.14605</a>"},"abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We present a reliable method to generate planar meshes of nonlinear rational triangular elements. The elements are guaranteed to be valid, i.e. defined by injective rational functions. The mesh is guaranteed to conform exactly, without geometric error, to arbitrary rational domain boundary and feature curves. The method generalizes the recent Bézier Guarding technique, which is applicable only to polynomial curves and elements. This generalization enables the accurate handling of practically important cases involving, for instance, circular or elliptic arcs and NURBS curves, which cannot be matched by polynomial elements. Furthermore, although many practical scenarios are concerned with rational functions of quadratic and cubic degree only, our method is fully general and supports arbitrary degree. We demonstrate the method on a variety of test cases.</jats:p>","lang":"eng"}],"doi":"10.1111/cgf.14605","author":[{"last_name":"Khanteimouri","first_name":"Payam","full_name":"Khanteimouri, Payam"},{"last_name":"Mandad","first_name":"Manish","full_name":"Mandad, Manish"},{"full_name":"Campen, Marcel","first_name":"Marcel","last_name":"Campen","id":"114904","orcid":"0000-0003-2340-3462"}],"extern":"1","department":[{"_id":"969"}],"date_created":"2025-06-25T08:56:35Z"}