我喜欢你英文一类自动生成光滑插值曲线的方法
摘要
怠速曲线曲面插值有很长的历史，从传统的多项式插值到目前常用的样条插值，以及新近的基函数插值方法等，都有广泛的实际应用或理论意义。本文研究的曲线曲面插值主要是，给定一组有序点列或网格点，构造一条光滑曲线或一张曲面通过该点列或网格点。本文主要分偏重代数与几何两方面研究构造插值曲线与曲面。
在偏重代数方法上，本文研究构造分段的低次Bézier曲线，通过有序拼接组合成一条通过所有给定点的光滑插值曲线。插入的控制顶点由本文提供的一类固定格式的线性公式得到，使用不同的插入公式可得到具有不同连续阶的插值曲线。本文方法的突出优点是曲线形状局部可调，具有仿射不变性和线性正确性，其算法简单，对海量数据插值更有优势。从该插值方法容易导出一系列插值基函数，由基函数可快速构造光滑插值曲面或重建曲面。
在偏重几何方法上，本文介绍了利用保广义凸点列的概念，提出了利用有序
G保凸连续条件插入三个新控制点列连成的折线内在性质在每相邻两点间基于2
G保凸连续条件创新性地转化为直观的几何条件，从而点的新方法，该方法将2
G保凸连可一次性地获得分段四次Bézier曲线的五个控制点，从而构造了整体2
G连续的曲线，且是逐段保广义凸续的曲线。本方法对非广义凸点列也可产生2
的。这些方法都具有算法简单，有统一的计算格式，计算便捷。最后通过实例说明文中方法的有效性。
G连续；曲线拼接
关键词：广义凸点列；保凸插值；Bézier曲线曲面；2
A kind of Methods to Produce an Interpolation Smooth
Curves Automatically
ABSTRACT
The interpolation of curves and surfaces has a long history.From traditional polynomial interpolation to the commonly ud spline interpolation,and the recent basic function interpolation methods,there are a wide range of practical applications or theoretical significance.The curve surface interpolation s
tudied in this paper is mainly to give a t of ordered point columns or grid points,construct a smooth curve or a surface through the point column or grid point.In this paper,we mainly study the construction of interpolation curves and surfaces by focusing on algebra and geometry.
In the method of partial algebra,this paper studies the construct ion of gmented low-order Bézier curves,which are combined into a smooth interpolation curve through all given points by orderly s plicing.The inrted control vertices are obtained from a fixed-form linear formula provided in this paper.Interpolation curves with diff erent successive orders can be obtained using different interpolation formulas.The outstanding advantage of this method is that the sha pe of the curve is locally adjustable,with affine invariance and line ar correctness.The algorithm is simple and has more advantages fo r the interpolation of massive data.From the interpolation method, a ries of interpolation basis functions are easily derived,and the basis function can quickly construct a smooth interpolation surface
or reconstruct a surface.
In the geometric method,this paper introduces the concept of using the generalized bump column,and propos a new method of inrting three new control points bad on the conrved co
ntinuous condition between each adjacent two points by using the intrinsic property of the polyline connected by ordered points.The method innovatively transforms the G-2conrved convex continuous condition into an intuitive geometric condition,so that the five control points of the gmented four-time Bézier curve can be obtained at one time,thereby constructing the overall G-2conrving convex continuous curve.This method can also produce G-2continuous curves for non-generalized bump columns,and is generalized convex one by one.The methods have simple algorithms,a unified calculation format,and convenient calculation.Finally,an example is given to illustrate the effectiveness of the method.
KEYWORDS:generalized convex column;convex interpolation;Bézier curves and surfaces;2G continuous;curve stitching
目录
摘要............................................................................................................................III 第1章绪论 (1)
1.1研究背景和意义 (1)
1.2研究现状分析 (1)
1.3研究内容 (3)
deepavali>defenders1.4论文结构安排 (3)
第2章预备知识 (4)
2.1Bézier曲线的定义和性质 (4)
北京翻译公司2.1.1Bézier曲线的定义 (4)
2.1.2Bernstein基函数的定义及性质 (4)
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2.1.3Bézier曲线的性质 (6)
2.1.4小结 (6)
2.2细分造型方法 (7)
2.3曲线的拼接 (8)
2.3.1曲线的连续性 (8)
2.3.22
G连续定义介绍 (8)
2.4保广义凸点列 (8)
第3章一类新的自动插值公式 (10)
3.1曲线构造思想 (10)
3.2曲线构造原理 (11)
3.3几个插值公式及应用 (13)
3.4小结 (20)2019专四答案
第4章四次Bézier曲线
2
G连续插值 (21)
4.1G连续条件 (21)
cpa是什么
4.21
G连续保凸插值 (23)
4.32
G连续保凸插值 (28)
ted演讲稿
4.4原点列存在共线的特殊情况 (30)
4.5原点列存在共点的特殊情况 (33)
4.6实例 (33)
第5章总结与展望 (38)
beetles5.1总结 (38)
5.2展望 (38)
参考文献 (39)
致谢 (42)
独创性声明和论文使用授权说明..................................................错误！未定义书签。
