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硕士学位论文
⑧
培养单位
逝鎏盘堂熬鲎亟
学科(专业)盐簋垫熊壁丝笪遮盐盘图受鲎
作者姓名
指导教师
鱼垫室
遵鱼鲢童送
二零零五年五月
浙江大学硕士学位论文
摘要
溺甄样祭趋线奁计算机辅助凡何设计与工韭裁逡孛都有菲常重簧的应麓。在
刀具加工中,刀具路径经常如直线段和圆弧缀成。而圆弧样条的段数以及首末切
向和曲线的保形性,通常情况下是比较重要而且富有实际意义的。本文针对广泛
应爱熬圆弧撵条改进了传统熬G‘圆弧样条撬蕊算法,这穆冀法疼爨涎连接点与
型值点错开,并且尽可能的过鼹个型值点作圆弧,这样在型馕点列满足较弱的条
件下,具有程事先给定首末切向的情况下,厕弧总段数比型假点个数少,且保形
懿特点。
第二章中提出了闭圆弧样条插值算法。该算法以尽量减少圆弧段数为目的,
首先对螫篷点迸幸亍了分类,并且对鞭痔连接激值点静线段送行了分类。接下来给
出了初始圆和公切圆的作法,并且给出了保诞最后得到为保形曲线的定理。绶后
给出了完整的算法以及此算法的一些基本性质,并且讨论了优化的主题以及算法
熬铡子。
第三章中提出了开圆弧样条插值算法。在进一步减少凰弧段数的耍求下,按
照嚣有的算法此闻麓是无群髓,雨诧算法使得茈闻藤在满越一个较弱条件下有
解。麓先根搬开圆弧样条与闭圆弧样条的不同给出了酋末切肉的特殊处理,接下
来给出了算法及性质和优化的例子。
篱霆章孛鼹望了本算法懿遴一步浚送,攒出了将来骚究互{乍懿方蠢。
关键字:圆弧样条,插值,保形,算法
浙江大学硕士学位论文
Abstract
Circular arCS
are
widely applied in CAGD and industrial
machinery,NC tool paths are always made of circular and strmght-line
segment number of arcs,the start
tangent,the
end tangent and the shape—preserving
property are
usually
important
and
this
paper,we
introduce
a
G‘
shape・preserving arC interpolation algorithm under
a
weak improves the
traditional method and tries its best
to
reduce the segment number of circular
the segment number of circular arCS is less than that of data ,the
interpolating
curve
Can
keep the shape of original data well.
In chapter two,we present
a
method for close interpolation by circular
purpose of this method is
to
reduce the number of ,we classify the data
points and the lines
between data
we discuss how
to construct
the initial
circle
and
common circle and list the theorems which
ensure
the
curve
we finally get
is shape- We present the formal algorithm and its basic properties.
In addition,we consider the topic of optimization
and
give some examples.
In chapter three,we present
a