直接上代码,多的不再说了. %------------------非均匀B样条拟合MATLAB程序----------------- clear k=; x=load('data.txt'); [n,m]=size(x); %-----------弦长参数化-------------------------------------- u(k+n)=; :n- u(k+i+)=u(k+i)+sqrt((x(i+,)-x(i,))^+(x(i+,)-x(i,))^); end; L=u(n+k);

计算机图形学(Conputer Graphics):非均匀有理B样条 非均匀有理B样条(Non-Uniform Rational B-Spline)英文缩写,NURBS. 它是贝塞尔曲线的一个推广,而贝塞尔曲线可以视为均匀有理B样条.NURBS是计算机辅助设计(CAD).制造(CAM)和工程(CAE)中重要的组成部分,同时也是很多业界广泛采用的标准的一部分,例如IGES, STEP和PHIGS. 连续性 一个结构的曲面,例如,一艘机动游艇的船体,通常由几个NURBS曲面构成,称之为包(patch

定义:令U={u0,u1,…,um}是一个单调不减的实数序列,即ui≤ui+1,i=0,1,…,m-1.其中,ui称为节点,U称为节点矢量,用Ni,p(u)表示第i个p次(p+1阶)B样条基函数,其定义为 由此可知: (1)Ni,0(u)是一个阶梯函数,它在半开区间u∈[ui,ui+1)外都为零: (2)当p>0时,Ni,p(u)是两个p-1次基函数的线性组合: (3)计算一组基函数时需要事先制定节点矢量U和次数p: (4)定义式中可能出现0/0,我们规定0/0=0: (5)Ni,p(u)是定义

Bezier曲线.B样条和NURBS,NURBS是Non-Uniform Rational B-Splines的缩写,都是根据控制点来生成曲线的,那么他们有什么区别了?简单来说,就是: Bezier曲线中的每个控制点都会影响整个曲线的形状,而B样条中的控制点只会影响整个曲线的一部分,显然B样条提供了更多的灵活性: Bezier和B样条都是多项式参数曲线,不能表示一些基本的曲线,比如圆,所以引入了NURBS,即非均匀有理B样条来解决这个问题: Bezier曲线只是B样条的一个特例而已,而B样条又是

在数学的子学科数值分析里,B-样条是样条曲线一种特殊的表示形式.它是B-样条基曲线的线性组合.B-样条是贝兹(贝塞尔)曲线的一种一般化,可以进一步推广为非均匀有理B样条(NURBS),使得我们能给更多一般的几何体建造精确的模型. 常数B样条 常数B样条是最简单的样条.只定义在一个节点距离上,而且不是节点的函数.它只是不同节点段(knot span)的标志函数(indicator function). 线性B样条 线性B样条定义在两个相邻的节点段上,在节点连续但不可微. 三次B样条 一个片断上的B

功能:根据参数u值和k(大小为阶数值)与节点矢量,计算第i个k次B样条基数 输入参数: u—参数值:k—大小值为阶数:i—第i个k次B样条的支撑区间左端节点的下标:aNode为节点向量. 输出参数:返回函数值. double GetBaseFunVal(double u, int i, int k, vector <double> m_aNode) { double Val = 0.0; double Val1 = 0.0; double Val2 = 0.0; if (k==0) { if

Function Set in OPEN CASCADE eryar@163.com Abstract. The common math algorithms library provides a C++ implementation of the most frequently used mathematical algorithms. These include: algorithms to solve a set of linear algebraic equations, algorit

Apply Newton Method to Find Extrema in OPEN CASCADE eryar@163.com Abstract. In calculus, Newton’s method is used for finding the roots of a function. In optimization, Newton’s method is applied to find the roots of the derivative. OPEN CASCADE implem

OPEN CASCADE Gauss Least Square eryar@163.com Abstract. The least square can be used to solve a set of n linear equations of m unknowns(n >= m). The OPEN CASCADE class math_GaussLeastSquare implements the least square solution of the linear equations

OPEN CASCADE BSpline Curve Interpolation eryar@163.com Abstract. Global curve interpolation to point data is a way to construct curves. The paper focus on the interpolate algorithm in OPEN CASCADE, and give a simple example to demonstrate the usage o

OpenCASCADE Linear Extrusion Surface eryar@163.com Abstract. OpenCASCADE linear extrusion surface is a generalized cylinder. Such a surface is obtained by sweeping a curve (called the “extruded curve” or “basis”) in a given direction (referred to as

OpenNURBS to OpenCASCADE eryar@163.com Abstract. The OpenNURBS initiative provides CAD/CAM/CAE and computer graphics software developers the tools to accurately transfer 3D geometry between applications. The OpenNURBS C++ source code is clean and fai

OpenCASCADE Root-Finding Algorithm eryar@163.com Abstract. A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f(x)=0, for a given function f. Such an x is called a root of the function f. In OpenCASCADE math

OpenCASCADE Conic to BSpline Curves-Circle eryar@163.com Abstract. The conic sections and circles play a fundamental role in CAD/CAM applications. Undoubtedly one of the greatest advantages of NURBS is their capability of precisely representing conic

OpenCASCADE Conic to BSpline Curves-Hyperbola eryar@163.com Abstract. Rational Bezier Curve can represent conic curves such as circle, ellipse, hyperbola, .etc. But how to convert a conic curve to BSpline curve is still question, i.e. Represent a con

OpenCASCADE Conic to BSpline Curves-Parabola eryar@163.com Abstract. Rational Bezier Curve can represent conic curves such as circle, ellipse, hyperbola, .etc. But how to convert a conic curve to BSpline curve is still question, i.e. Represent a coni

OpenCASCADE Rational Bezier Curves eryar@163.com Abstract. Although polynomials offer many advantages, there exist a number of important curve and surface types which cannot be represented precisely using polynomials, e.g., circles, ellipses, hyperbo

Visualize Surface by Delaunay Triangulator eryar@163.com Abstract. Delaunay Triangulation is the core algorithm for mesh generation. By Delaunay Triangulator you can make a general method to visualize geometry surfaces, so does OpenCascade. The paper

Polynomial Library in OpenCascade eryar@163.com 摘要Abstract:分析幂基曲线即多项式曲线在OpenCascade中的计算方法,以及利用OpenSceneGraph来显示OpenCascade的计算结果,加深对多项式曲线的理解. 关键字Key Words:OpenCascade.PLib.OpenSceneGraph.Polynomial Library 一. 概述 Overview CAGD(Computer Aided Geometry D

1 B样条曲线 1.1 B样条曲线方程 B样条方法具有表示与设计自由型曲线曲面的强大功能,是形状数学描述的主流方法之一,另外B样条方法是目前工业产品几何定义国际标准——有理B样条方法 (NURBS)的基础.B样条方法兼备了Bezier方法的一切优点,包括几何不变性,仿射不变性等等,同时克服了Bezier方法中由于整体表示带来不具有局部性质的缺点(移动一个控制顶点将会影响整个曲线).B样条曲线方程可表示为 其中,di(i=0,1...n)为控制顶点(坐标),Ni,k(i=0,1...n)为k次规范

本文信息资源来源于网络,欢迎转载!转载时请保留本文链接(http://www.shopliyang.com.cn/)! OpenGL中的gl库是核心库,glu是实用库,glut是实用工具库. gl是核心,glu是对gl的部分封装,glut是OpenGL的跨平台工具库. gl中包含了最基本的3D函数,而glu似乎对gl的辅助,如果数学功底好,在不用glu的情况下,也是可以做出同样的效果.glut是基本的窗口界面, 是独立于gl和glu的,如果不喜欢用glut可以用MFC和Win32窗口等代替:但是