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It is important to consider curvature properties around the control points to produce natural-looking results in the vector illustration. *C*^{2} 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 *C*^{2} 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 *C*^{2} interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-*C*^{2} 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.

- Publication
- IEICE TRANSACTIONS on Information Vol.E105-D No.10 pp.1704-1711

- Publication Date
- 2022/10/01

- Publicized
- 2022/05/26

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.2022PCP0006

- Type of Manuscript
- Special Section PAPER (Special Section on Picture Coding and Image Media Processing)

- Category

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

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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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. *C*^{2} 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 *C*^{2} 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 *C*^{2} interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-*C*^{2} 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. *C*^{2} 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 *C*^{2} 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 *C*^{2} interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-*C*^{2} 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. *C*^{2} 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 *C*^{2} 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 *C*^{2} interpolating splines and replace the trigonometric weight to our novel hyperbolic blending function. By extending this basic definition, we can also handle exact non-*C*^{2} 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 -