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三次三角域Bézier 曲面的同次扩展

  

  1. 东华理工大学理学院，江西 南昌 330013
  • 出版日期:2018-02-28 发布日期:2018-02-06
  • 基金资助:
    国家自然科学基金项目(11261003，11761008)；江西省自然科学基金项目(20161BAB211028)；江西省教育厅科技项目(GJJ160558)

Extension of the Cubic Triangular Bézier Surface of the Same Degree

  1. College of Science, East China University of Technology, Nanchang Jiangxi 330013, China
  • Online:2018-02-28 Published:2018-02-06

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摘要： 为了在不提升基函数次数的前提下赋予三次三角域Bézier 曲面形状调整的能力，
构造了一组含一个参数的三次双变量基函数，由之定义了由10 个控制顶点确定的三角域曲面
片。新曲面具有角点插值性，在角点处的切平面为由角点和其所在的两条边上与之相邻的两个
顶点确定的平面。改变参数取值，可以调整曲面形状。为了方便应用，给出了曲面片之间的G1
光滑拼接条件及曲面的几何迭代算法，分析了算法的收敛性以及收敛速度与参数取值之间的关
系。图例显示了所给方法的正确性和有效性。

关键词: 三角域Bé, zier 曲面, 形状调整, 几何迭代, 插值, 曲面拼接

Abstract: In order to endow the cubic triangular Bézier surface the ability of shape adjustment, this
paper constructs a set of cubic bivariate basis functions with a parameter and defines a new triangular
surface determined by ten control points. The new surface has corner interpolation property. The tangent
planes at the corner points are determined by the corner points and the two adjacent points which lie on
the same edges. Changing the parameter value can adjust the shape of the surface. For convenient
application, the G1 smooth join condition and the geometric iterative algorithm of the surface are given.
The convergence as well as the relationship of the convergent rate and the parameter selection of the
algorithm is analyzed. The legends show the correctness and validity of the method.

Key words: triangular Bézier patch, shape adjustment, geometric iteration, interpolation, surface joining