计算机工程与应用Issue(17)：7-11,5.DOI:10.3778/j.issn.1002-8331.1403-0209
Bézier曲线到AH-Bézier曲线的升阶算法
Degree elevation algorithm from Bézier curve to AH-Bézier curve
摘要
Abstract
The existing results about curve degree elevation are mainly limited to the same type of curves. In order to push the limit and consider degree elevation between different types of curves, this paper focuses on degree elevation algo-rithm from Bézier curve, defined on algebraic polynomial space, to AH-Bézier curve, defined on algebraic and hyperbolic polynomial space. The study begins with basis functions. Firstly, the transformation matrix from AH-Bézier basis to Bern-stein basis is built by using the block matrix idea and the same property of Bézier and AH-Bézier that the order of basis is reduced for derivative. Secondly, the degree elevation formula of control points is obtained. Lastly, the degree elevation algorithm is given. Results show that any Bézier curve of degree n can be turned into an AH-Bézier curve of order n+3(i.e. degree n+2)by using this algorithm. The algorithm gives an accurate transformation from Bézier to AH-Bézier curve model.关键词
Bézier曲线/AH-Bézier曲线/升阶/基函数/转换矩阵Key words
Bézier curve/AH-Bézier curve/degree elevation/basis function/transformation matrix分类
信息技术与安全科学引用本文复制引用
沈莞蔷,汪国昭..Bézier曲线到AH-Bézier曲线的升阶算法[J].计算机工程与应用,2014,(17):7-11,5.基金项目
国家自然科学基金专项数学天元基金项目（No.11326243）；国家自然科学基金面上项目（No.61272300，No.11371174）；江苏省自然科学基金青年基金项目（No.BK20130117）。 （）
