Curvatures of the quadratic rational Bezier curves

被引：20
|
作者：
Ahn, YJ [1 ]
Kim, HO [1 ]
机构：
[1] KAIST, Dept Math, Taejon, South Korea
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 1998年 / 36卷 / 09期
关键词：
quadratic rational Bezier curves; monotone curvature; local extrema of curvature; fairing curves; offset curves;
D O I：
10.1016/S0898-1221(98)00193-X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find necessary and sufficient conditions for the curvature of a quadratic rational Bezier curve to be monotone in [0, 1], to have a unique local minimum, to have a unique local maximum, and to have both extrema in (0, 1), and we also visualize them in figures. As an application, we present a necessary and sufficient condition for the offset curve to be regular and to have the same tangent direction with the given quadratic rational Bezier curve, and give a simple algorithm to find it. (C) 1998 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：71 / 83
页数：13
相关论文
共 50 条
  • [1] Improved derivative bounds of the rational quadratic Bezier curves
    Zhang, Ren-Jiang
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 250 : 492 - 496
  • [2] ISOGONAL AND ISOTOMIC CONJUGATES OF QUADRATIC RATIONAL Bezier CURVES
    Yun, Chan Ran
    Ahn, Young Joon
    JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2015, 22 (01): : 25 - 34
  • [3] Necessary and Sufficient Conditions for Expressing Quadratic Rational Bezier Curves
    Yang, Chaoyu
    Yang, Jie
    Liu, Ying
    Geng, Xianya
    FRONTIERS IN PHYSICS, 2020, 8
  • [4] Gaussian and mean curvatures of rational Bezier patches
    Zheng, J
    Sederberg, TW
    COMPUTER AIDED GEOMETRIC DESIGN, 2003, 20 (06) : 297 - 301
  • [5] Rational Bezier form of hodographs of rational Bezier curves and surfaces
    Kim, DS
    Jang, T
    Shin, H
    Park, JY
    COMPUTER-AIDED DESIGN, 2001, 33 (04) : 321 - 330
  • [6] Rational Quadratic Bezier Spirals
    Ahmad, Azhar
    Gobithaasan, R. U.
    SAINS MALAYSIANA, 2018, 47 (09): : 2205 - 2211
  • [7] REPRESENTING THE VORONOI DIAGRAM OF A SIMPLE POLYGON USING RATIONAL QUADRATIC BEZIER CURVES
    KIM, DS
    HWANG, IK
    PARK, BJ
    COMPUTER-AIDED DESIGN, 1995, 27 (08) : 605 - 614
  • [8] ALGORITHMS FOR RATIONAL BEZIER CURVES
    FARIN, G
    COMPUTER-AIDED DESIGN, 1983, 15 (02) : 73 - 77
  • [9] Complex rational Bezier curves
    Sanchez-Reyes, J.
    COMPUTER AIDED GEOMETRIC DESIGN, 2009, 26 (08) : 865 - 876
  • [10] ON THE GEOMETRY OF RATIONAL BEZIER CURVES
    Ceylan, Ayse Yilmaz
    Turhan, Tunahan
    Tukel, Gozde Ozkan
    HONAM MATHEMATICAL JOURNAL, 2021, 43 (01): : 88 - 99
12345