Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterizations

Introduction Curves and surfaces can be represented using coefficients and a set of basis functions[1]. In the following, only curves are considered, but all statements apply equally to surfaces. Different representations use different sets of basis functions. These basis functions can be, for example, polynomials for polynomial curves, Bernstein-polynomials for Bézier curves, or B-spline basis functions for B-spline curves. As long as the general representation is of the form: 0( ) ( )ni i…     

圆弧曲线的二次NURBS表示方法研究

由于用NURBS曲线表示圆弧时,因圆弧圆心角不同,圆弧方向不同,难于找到圆弧NURBS通用算法,以满足控制顶点少、紧凑凸包、良好参数化等特点,因此从二次NURBS曲线插入节点算法入手,提出一种基于等分圆心角的二次NURBS曲线表示方法。     

关于在NURBS 双向蒙皮造型中保持凸包性及提高精度方法的讨论

通过对ＮＵＲＢＳ双向蒙皮造型插值计算的讨论,要保证曲面具有强的凸包性的前提下,提出了两种插值算法,并对不同插值算法的计算复杂度及计算精确度进行了比较。     

NURBS曲面和隐式曲面求交的局部加密算法

基于等值线法求取NURBS曲面与隐式曲面交线的原理,提出了一种局部加密的改进算法。通过局部加密算法减少正则网格单元顶点处h值计算数目。采用拟牛顿迭代法求交点、B样条曲线拟合参数域上的交线等改进算法,提高了NURBS曲面与隐式曲面求交算法的效率和精度,并通过MATLAB编程进行了验证。     

Combined back analysis method of ground stress based on refined geological modeling

A new back-analysis method of ground stress is proposed with comprehensive consideration of influence of topography, geology and nonlinear physical mechanical properties of rock on ground stress. This method based on non-uniform rational B-spline (NURBS) technology provides the means to build a refined three-dimensional finite element model with more accurate meshing under complex terrain and geological conditions. Meanwhile, this method is a back-analysis of ground stress with combination of multivariable linear regression model and neural network (ANN) model. Firstly, the regression model is used to fit approximately boundary loads. Regarding the regressed loads as mean value, some sets of boundary loads with the same interval are constructed according to the principle of orthogonal design, to calculate the corresponding ground stress at the observation positions using finite element method. The results (boundary loads and the corresponding ground stress) are added to the samples for ANN training. And on this basis, an ANN model is established to implement higher precise back-analysis of initial ground stress. A practical application case shows that the relative error between the inversed ground stress and observed value is mostly less than 10 %, which can meet the need of engineering design and construction requirements.     

基于图切分的交互式图像分割算法

提出一种基于图切分(Graph Cut)的交互式图像分割新算法。首先,使用图切分技术获取初始轮廓并采取非均匀有理B样条(NURBS)拟合边界曲线。由于NURBS具有局部可控性,其控制点可视为隐式马尔可夫模型(HMM)的隐状态,边界特征和区域同一性被视为HMM观察状态,然后采用轮廓平滑性作为约束来定义一个状态转移模型。最后,通过维特比算法递归求取最优轮廓。实验证明该法鲁棒性好,允许用户简易、高效地分割图像。     

转子齿面的NURBS表示及啮合线的数值解法

提出了离散参数曲线并用插值NURBS曲面的形式表示转子齿面的方法 ,在用NURBS表示齿面的基础上首次提出了在转子啮合过程中利用其相对速度在法线方向的投影值求啮合线的数值解法 .     

曲面的NURBS插值问题

对于给定的曲面型值点及边界条件 ,本文利用二次NURBS曲面的矩阵表达式 ,给出一个反求二次NURBS曲面控制顶点的算法。     

椭圆的三次NURBS表示及生成算法

首先介绍了用三次NURBS表示圆弧和整圆的方法。然后提出了用三次NURBS表示椭圆的方法及其生成算法，并用解析法解出了用三次NURBS表示椭圆的条件。讨论了用三次NURBS表示椭圆和用三次NURBS表示圆之间的区别和联系。指出圆的三次NURBS表示实质上是椭圆的三次NURBS表示的一种特殊情况：当椭圆的长半轴、短半轴相等(a0=b0)时。椭圆的三次NURBS表示转化为圆的三次NURBS表示。这与圆和椭圆的代数方程的关系是一致的。     

用OpenGL和MFC实现NURBS曲面的绘制及裁剪

NURBS方法因其表示法的同一性、形状控制灵活性，在曲面造型和重构中具有重要作用．该文通过分析，完成了在MFC中用OpenGL实现NURBS曲面的绘制及裁剪，为在逆向工程中实现基于型值点的曲面拟合和裁剪奠定了基础．