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图学学报

• 专论：第十九届全国图象图形学学术会议(NCIG2018) • 上一篇    下一篇

三角域上带形状参数的四次 Bézier 曲面

  

  1. 1. 东华理工大学理学院，江西 南昌  330013；
    2. 湖北省麻城市第一中学，湖北 麻城  438300
  • 出版日期:2018-12-31 发布日期:2019-02-20
  • 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)

Quartic Bézier Surface with Shape Parameters on Triangular Domain

  1. 1. College of Science, East China University of Technology, Nanchang Jiangxi 330013, China; 
    2. The First Secondary School in Macheng City Hubei Province, Macheng Hubei 438300, China
  • Online:2018-12-31 Published:2019-02-20

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摘要： 为了在控制顶点固定的前提下仍然能够调整四次三角域 Bézier 曲面的形状，基于 由可调控制顶点定义可调曲面的思想，从几何直观的角度出发，构造了一组含 2 个参数的四次 双变量基函数，定义了由15个控制顶点确定的三角域曲面片。新曲面不仅具有四次三角域Bézier 曲面的特性，而且拥有 2 个用于调整形状的参数。与现有构造形状可调三角域 Bézier 曲面的方 法相比，从几何而非代数角度出发定义新曲面，引入的参数具有明确的几何作用，并未提升基 函数的次数。为了方便应用，给出了曲面片之间的 G1 光滑拼接条件。图例显示了该方法的正确 性和有效性。

关键词: 曲面设计, Bé, zier 曲面, 三角域, 形状调整

Abstract: This paper aims at adjusting the shape of the quartic triangular Bézier surface without changing the control points. Based on the idea of defining adjustable surfaces by adjustable control points, starting from a geometric perspective, a set of quartic bivariate basis functions with two parameters are constructed and a new triangular patch determined by fifteen control points is defined. The new surface not only inherits the properties of the quartic triangular Bézier surface, but also possesses two parameters which can be used to adjust its shape. Compared with the existing method of constructing triangular Bézier surface whose shape is adjustable, the method provided here defines the new surface from a geometric rather than an algebraic perspective, hence the introduced parameters have definite geometric effect, and the method here does not increase the degree of the basis functions. For convenient application, the G1 smooth join condition of the surface is given. The legends show the correctness and validity of the method.

Key words: surface design, Bézier surface, triangular domain, shape adjustment