It is important to consider curvature properties around the control points to produce natural-looking results in the vector illustration. C2 interpolating splines satisfy point interpolation with local support. Unfortunately, they cannot control the sharpness of the segment because it utilizes trigonometric function as blending function that has no degree of freedom. In this paper, we alternate the definition of C2 interpolating splines in both interpolation curve and blending function. For the interpolation curve, we adopt a rational Bézier curve that enables the user to tune the shape of curve around the control point. For the blending function, we generalize the weighting scheme of C2 interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-C2 features, such as cusps and fillets, without losing generality. In our experiment, we provide both quantitative and qualitative comparisons to existing parametric curve models and discuss the difference among them.
Seung-Tak NOH
University of Tokyo
Hiroki HARADA
University of Tokyo
Xi YANG
University of Tokyo
Tsukasa FUKUSATO
University of Tokyo
Takeo IGARASHI
University of Tokyo
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Seung-Tak NOH, Hiroki HARADA, Xi YANG, Tsukasa FUKUSATO, Takeo IGARASHI, "PPW Curves: a C2 Interpolating Spline with Hyperbolic Blending of Rational Bézier Curves" in IEICE TRANSACTIONS on Information,
vol. E105-D, no. 10, pp. 1704-1711, October 2022, doi: 10.1587/transinf.2022PCP0006.
Abstract: It is important to consider curvature properties around the control points to produce natural-looking results in the vector illustration. C2 interpolating splines satisfy point interpolation with local support. Unfortunately, they cannot control the sharpness of the segment because it utilizes trigonometric function as blending function that has no degree of freedom. In this paper, we alternate the definition of C2 interpolating splines in both interpolation curve and blending function. For the interpolation curve, we adopt a rational Bézier curve that enables the user to tune the shape of curve around the control point. For the blending function, we generalize the weighting scheme of C2 interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-C2 features, such as cusps and fillets, without losing generality. In our experiment, we provide both quantitative and qualitative comparisons to existing parametric curve models and discuss the difference among them.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2022PCP0006/_p
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@ARTICLE{e105-d_10_1704,
author={Seung-Tak NOH, Hiroki HARADA, Xi YANG, Tsukasa FUKUSATO, Takeo IGARASHI, },
journal={IEICE TRANSACTIONS on Information},
title={PPW Curves: a C2 Interpolating Spline with Hyperbolic Blending of Rational Bézier Curves},
year={2022},
volume={E105-D},
number={10},
pages={1704-1711},
abstract={It is important to consider curvature properties around the control points to produce natural-looking results in the vector illustration. C2 interpolating splines satisfy point interpolation with local support. Unfortunately, they cannot control the sharpness of the segment because it utilizes trigonometric function as blending function that has no degree of freedom. In this paper, we alternate the definition of C2 interpolating splines in both interpolation curve and blending function. For the interpolation curve, we adopt a rational Bézier curve that enables the user to tune the shape of curve around the control point. For the blending function, we generalize the weighting scheme of C2 interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-C2 features, such as cusps and fillets, without losing generality. In our experiment, we provide both quantitative and qualitative comparisons to existing parametric curve models and discuss the difference among them.},
keywords={},
doi={10.1587/transinf.2022PCP0006},
ISSN={1745-1361},
month={October},}
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TY - JOUR
TI - PPW Curves: a C2 Interpolating Spline with Hyperbolic Blending of Rational Bézier Curves
T2 - IEICE TRANSACTIONS on Information
SP - 1704
EP - 1711
AU - Seung-Tak NOH
AU - Hiroki HARADA
AU - Xi YANG
AU - Tsukasa FUKUSATO
AU - Takeo IGARASHI
PY - 2022
DO - 10.1587/transinf.2022PCP0006
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E105-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 2022
AB - It is important to consider curvature properties around the control points to produce natural-looking results in the vector illustration. C2 interpolating splines satisfy point interpolation with local support. Unfortunately, they cannot control the sharpness of the segment because it utilizes trigonometric function as blending function that has no degree of freedom. In this paper, we alternate the definition of C2 interpolating splines in both interpolation curve and blending function. For the interpolation curve, we adopt a rational Bézier curve that enables the user to tune the shape of curve around the control point. For the blending function, we generalize the weighting scheme of C2 interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-C2 features, such as cusps and fillets, without losing generality. In our experiment, we provide both quantitative and qualitative comparisons to existing parametric curve models and discuss the difference among them.
ER -