基于分块矩阵求导的Bézier曲线降阶方法

兰州大学机构库 >数学与统计学院

	基于分块矩阵求导的Bézier曲线降阶方法
Alternative Title	A Method for Degree Reduction of Bézier Curve Based on Partitioned Matrix Derivation
	杨艳
Thesis Advisor	伍渝江
	2013-12-07
Degree Grantor	兰州大学
Place of Conferral	兰州
Degree Name	硕士
Keyword	Bézier曲线降阶分块矩阵求导中点分割
Abstract	Bézier曲线的降阶逼近有着实际应用价值，但是逼近程度受端点约束条件的影响。首先简单介绍了Bézier曲线的定义和性质，以及Bézier曲线降阶逼近的概念与意义。然后对降阶逼近中的三种著名方法做了详细分析和实验对比。接着提出了基于分块矩阵求导的降阶逼近方法，这种方法能够产生降多阶，且满足端点约束条件的显式表达式。最后将中点分割法与分块矩阵求导的降阶方法结合，应用到数值实验中，验证了该算法的优越性。
Other Abstract	The approximation of degree reduction to Bézier curve has its practical application value but limited by constrained condition of endpoints. The essay first introduces Bézier curve with definition and properties, also including the definition and purpose of degree reduction of Bézier curve. After thoroughly analysis and experimental compare of three famous methods in degree reduction approximation, it comes up a new method for degree reduction approximation based on partitioned matrix derivation. This new method can produce explicit formulation with multi-degree reduction and satisfies constrained condition of endpoints. Finally combined mid-point segmentation with partitioned matrix’s derivation and put them into numerical experiment show the advantages of this algorithm.
URL	查看原文
Language	中文
Document Type	学位论文
Identifier	https://ir.lzu.edu.cn/handle/262010/225179
Collection	数学与统计学院
Recommended Citation GB/T 7714	杨艳. 基于分块矩阵求导的Bézier曲线降阶方法[D]. 兰州. 兰州大学,2013.

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