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We extend this representation to control the magnitudes of local maximum curvature in a new scheme called <jats:italic>extended-<\/jats:italic> or <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\epsilon \\kappa $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03f5<\/mml:mi>\n                    <mml:mi>\u03ba<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-curves.<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\kappa $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03ba<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-curves have been implemented as the curvature tool in Adobe Illustrator<jats:sup>\u00ae<\/jats:sup> and Photoshop<jats:sup>\u00ae<\/jats:sup> and are highly valued by professional designers. However, because of the limited degrees of freedom of quadratic B\u00e9zier curves, it provides no control over the curvature distribution. We propose new methods that enable the modification of local curvature at the interpolation points by degree elevation of the Bernstein basis as well as application of generalized trigonometric basis functions. By using <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\epsilon \\kappa $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03f5<\/mml:mi>\n                    <mml:mi>\u03ba<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-curves, designers acquire much more ability to produce a variety of expressions, as illustrated by our examples.<\/jats:p>","DOI":"10.1007\/s00371-021-02149-8","type":"journal-article","created":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T20:02:26Z","timestamp":1621368146000},"page":"2723-2738","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["$$\\epsilon \\kappa $$-Curves: controlled local curvature extrema"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9326-3130","authenticated-orcid":false,"given":"Kenjiro T.","family":"Miura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3077-8772","authenticated-orcid":false,"given":"R. 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