Miura, Kenjiro T, Gobithaasan, R. U, Salvi, Péter, Wang, Dan, Sekine, Tadatoshi, Usuki, Shin, Inoguchi, Jun-ichi, Kajiwara, Kenji
The Visual Computer Springer 38 (8) 2723 - 2738 0178-2789 2021/05
[Refereed] The kappa-curve is a recently published interpolating spline which consists of quadratic Bezier segments passing through input points at the loci of local curvature extrema. We extend this representation to control the magnitudes of local maximum curvature in a new scheme called extended- or is an element of kappa-curves. kappa-curves have been implemented as the curvature tool in Adobe Illustrator (R) and Photoshop (R) and are highly valued by professional designers. However, because of the limited degrees of freedom of quadratic Bezier 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 is an element of kappa-curves, designers acquire much more ability to produce a variety of expressions, as illustrated by our examples.