{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T23:56:39Z","timestamp":1740182199898,"version":"3.37.3"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,11,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We propose a new method for approximating log-aesthetic curves ${\\boldsymbol C}_{\\mathrm{LA}}$ using high-degree B\u00e9zier curves. By leveraging the property that higher order derivatives are more sensitive to the quality of approximation, the method minimizes an objective function based on the fourth-order derivative; consequently, ${\\boldsymbol C}_{\\mathrm{LA}}$ is approximated with high accuracy. In addition, the proposed method is composed of two steps to ensure stable optimization so as not to be negatively affected because of a local minimum and to evaluate the fourth-order derivative. Furthermore, we reveal the difficulty in sufficiently approximating ${\\boldsymbol C}_{\\mathrm{LA}}$ with B\u00e9zier curves from two aspects. One aspect entails the uncertainty of how accurately the low-degree B\u00e9zier curves can approximate ${\\boldsymbol C}_{\\mathrm{LA}}$. The other aspect is the existence of a subset of ${\\boldsymbol C}_{\\mathrm{LA}}$ that is inherently difficult to approximate with such conventional parametric curves. The experimental results and comparisons demonstrated the validity of the proposed method.<\/jats:p>","DOI":"10.1093\/jcde\/qwac117","type":"journal-article","created":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T16:18:22Z","timestamp":1667319502000},"page":"2439-2451","source":"Crossref","is-referenced-by-count":2,"title":["High-quality approximation of log-aesthetic curves based on the fourth-order derivative"],"prefix":"10.1093","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9991-5635","authenticated-orcid":false,"given":"Shoichi","family":"Tsuchie","sequence":"first","affiliation":[{"name":"Technology Research & Innovation, BIPROGY Inc. , 1-1-1 Toyosu, Koto-ku, Tokyo 135-8560, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Norimasa","family":"Yoshida","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, College of Industrial Technology, Nihon University , 1-2-1 Izumi-cho Narashino, Chiba 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