The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
É importante considerar as propriedades de curvatura em torno dos pontos de controle para produzir resultados de aparência natural na ilustração vetorial. C2 splines interpolantes satisfazem a interpolação de pontos com suporte local. Infelizmente, eles não podem controlar o agudeza do segmento porque utiliza função trigonométrica como função de mistura que não possui grau de liberdade. Neste artigo, alternamos a definição de C2 interpolando splines na curva de interpolação e na função de mesclagem. Para a curva de interpolação, adotamos uma curva de Bézier racional que permite ao usuário ajustar o formato da curva em torno do ponto de controle. Para a função de combinação, generalizamos o esquema de ponderação de C2 interpolando splines e substituindo o peso trigonométrico por nossa nova função de mistura hiperbólica. Ao estender esta definição básica, também podemos lidar comC2 características, como cúspides e filetes, sem perder generalidade. Em nosso experimento, fornecemos comparações quantitativas e qualitativas com modelos de curvas paramétricas existentes e discutimos a diferença entre eles.
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.
Copiar
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
Copiar
@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},}
Copiar
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 -