有理四次插值样条曲线的区域控制

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题.构造了一种分母为线性的C1连续有理四次插值样条.该有理四次插值样条中含有参数和调节参数,因而可以在插值条件不变的情况下通过对参数的选择进行曲线的局部修改,给约束控制带来了方便,同时可以通过对参数的控制实现C2连续的插值.对该种插值曲线的区域控制问题进行了研究,给出了将其约束于给定的折线、二次曲线之上、之下或之间的充分条件.最后给出了数值例子.     

一类加权有理四次插值样条曲线的形状控制

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题。利用带导数的和不带导数的分母为线性的有理四次插值样条构造了一类新的加权有理四次插值样条函数,插值函数具有简单的显示表示,这类新的插值样条中含有权系数,因而增加了处理问题的灵活性,给约束控制带来了方便。给出了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的充分条件。证明了满足约束条件的加权有理样条的存在性。     

一类加权有理插值样条曲面及局部约束控制

目的 构造一类新的基于函数值与偏导数值的加权有理插值样条曲面,讨论该样条曲面的相关性质并分析曲面的局部约束控制。方法 一方面,先从x方向构造有理三次插值样条,再从y方向构造二元有理插值样条曲面;另一方面,按相反次序构造另一个二元有理插值样条曲面;最后将两种插值曲面加权得到一类新的有理插值样条曲面。结果 讨论插值曲面的性质,包括基函数、边界性质、积分加权系数的性质以及误差估计。通过选择合适的参数和加权系数,在不改变插值数据的前提下实现对插值区域内的局部约束控制。结论 实验结果表明,新的加权有理插值样条曲面具有良好的约束控制性质。     

A New Local Control Spline with Shape Parameters for CAD/CAM

Anew local control spline based on shape parameterw with G^3 continuity,called BLC-spline,is pro* posed.Not only is BLC-spline very smoot,but also the spline curve‘s characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of Iocal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β0，β1and β2 of BLC-spline,which are independent of the control vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construcet a space are spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.     

Cubic spline curve fitting with controlled end conditions

Several approximate methods for cubic spline curve fitting have been developed and successfully used. This paper presents a more flexible version of a proven technique by using a set of end conditions suggested by Nutbourne. The advantages and disadvantages of several techniques are clarified and sample graphical output is given. The results should be of greatest interest to users of inexpensive, computer graphics equipment who are interested in improving passive graphical output.     

Moment computation for objects with spline curve boundary

A new approach is proposed for computation of area and geometric moments for a plane object with a spline curve boundary. The explicit formulae are obtained for area and low order moment calculation. The complexity of calculation depends on the moment order, spline degree, and the number of control points used in spline representation. The formulae proposed use the advantage that the sequence of spline control points is cyclic. It allowed us to reduce substantially the number of summands in them. The formulae might be useful in different applications where it is necessary to perform measurements for shapes with a smooth boundary.     

基于函数值的有理四次样条曲线的区域控制

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题。构造了一种分母为线性的基于函数值的C¹连续有理四次插值样条。这种有理四次插值样条中含有参数,因而可以在插值条件不变的情况下通过对参数的选择进行曲线的局部修改,给约束控制带来了方便。对该种插值曲线的区域控制问题进行了研究,给出了将其约束于给定的折线,二次曲线之上、之下或之间的充分条件.最后给出了数值例子。     

带形状参数的C~2连续类三次三角样条曲线

传统的三次均匀B样条曲线在给定控制顶点时其形状不能调整,以及不能精确表示圆锥曲线。针对三次均匀B样条曲线的不足,提出了一种带形状参数的C2连续的类三次三角样条曲线。该曲线不仅与三次均匀B样条曲线具有相似的性质,而且在控制顶点保持不变时其形状可通过形状参数的取值进行调整。在适当条件下,类三次三角样条曲线比三次均匀B样条曲线更能逼近于控制多边形,且能精确表示圆、椭圆、抛物线等圆锥曲线。     

A locally controllable spline with tension for interactive curve design

We describe a new type of parametrically defined space curve. The parameters which define these curves allow for the convenient control over local shape attributes while maintaining global second order geometric continuity. The coordinate functions are defined by piecewise segments of rational functions, each segment being the ratio of cubic polynomials and a common quadratic polynomial. Each curve segment is a planar curve and where two segments meet the curvature is zero. This simple mathematical representation permits these curves to be efficiently manipulated and displayed.     

A constrained guided G continuous spline curve

A method for drawing a guided G¹ continuous planar spline curve that falls within a closed boundary is presented. The curve is composed of segments of quadratic polynomials (parabolas) and rational quadratics (conics) that join with continuous unit tangent vectors. The boundary is composed of straight line segments and circular arcs.     

二次B样条曲线曲面的扩展

构造了一组由三个含参数m的函数构成的函数组, 该函数组线性无关, 称之为mB基。mB基具有非负性、规范性、对称性等良好的性质, 而且具有非常特殊的端点性质。基于mB基定义了一种新的样条曲线, 称之为mB曲线。mB曲线段可以转化为Bézier曲线的形式, 借助Bézier曲线的de Casteljau算法, 给出了mB曲线段的递推求值算法。mB曲线具有与二次均匀B样条曲线相同的端点行为, 即插值于控制多边形首末边的中点, 与控制多边形的首末边相切。另外, mB曲线的形状和连续性均可以通过参数m进行自由调节, 而且调节方式既可以是整体的, 又可以是局部的。利用张量积方法, 将mB曲线推广到了曲面, 称之为mB曲面。mB曲面具有与mB曲线类似的性质。     

三次插值样条曲线拟合多核并行算法

充分利用多核技术提升多核处理器的资源利用率,缩短执行时间,发挥多核系统的优异性能。在多核计算机上设计了解三对角方程组的奇偶约化多线程并行程序,实现了三次样条曲线拟合的快速计算。通过实验结果的加速比对比,可以看出并行后缩短了求解方程组的时间,多核资源得到充分利用。结果表明,奇偶约化多核并行算法在三次样条曲线拟合中的应用是有效及可行的。     

带形状控制的自由曲线曲面参数样条

目的 样条曲线曲面的构造是工程制图中的一个重要部分。针对双曲抛物面上参数样条曲线的构造,在已有的研究基础上提出了一种样条方法使曲线曲面可以任意地逼近一个多边形或者一个网格。方法 在标准四面体内构造一个双曲抛物面,在该曲面上以基函数参数化的方法定义一种带形状参数的参数样条曲线曲面,样条基函数通过将双曲抛物面的有理参数化进行限定,生成单参数有理样条基函数。详细研究了样条的保形性及其端点性质。结果 样条曲线具有一个可变的形状控制因子,可以对曲线进行调整,能以任意精度逼近这个控制四边形或网格。对空间节点列,利用该样条可以生成G²-连续空间曲线,同样对于空间网格可以构造G²-连续的拟合曲面,它所对应的基函数可以是有理形式。结论 实验结果表明,本文在笔者已有的研究基础上提出的参数样条曲线可以通过重心坐标系变换适应为任意的四边形,除了空间四面体内的样条曲线,四面体退化成四边形同样可实现。     

Orthogonal local spline discriminant projection with application to face recognition

In this paper, an efficient feature extraction algorithm called orthogonal local spline discriminant projection (O-LSDP) is proposed for face recognition. Derived from local spline embedding (LSE), O-LSDP not only inherits the advantages of LSE which uses local tangent space as a representation of the local geometry so as to preserve the local structure, but also makes full use of class information and orthogonal subspace to improve discriminant power. Extensive experiments on several standard face databases demonstrate the effectiveness of the proposed method.     

Spline and Bézier polygons associated with a polynomial spline curve

Parametrized polynomial spline curves are defined by an S-polygon, but locally they are Bézier curves defined by a B-polygon. Two algorithms are given which construct one polygon from the other and vice versa. The generalization to surfaces is straightforward. This may be of some interest in CAD because of the good local properties of the B-polygon     

二次均匀B样条曲线的双圆弧逼近方法*

提出了一种用双圆弧对二次均匀B样条曲线的分段逼近方法。首先,对一条具有n 1个控制顶点的二次均匀B样条曲线按照相邻两节点界定的区间分成n-1段只有三个控制顶点的二次均匀B样条曲线段;然后对每一曲线段构造一条双圆弧进行逼近。所构造的双圆弧满足端点及端点切向量条件,即双圆弧的两个端点分别是所逼近的曲线段的端点,而且双圆弧在两个端点处的切向量是所逼近的曲线段在端点处的单位切向量。同时,双圆弧的连接点是双圆弧连接点轨迹圆与其所逼近的曲线段的交点。这些新构造出来的双圆弧连接在一起构成了一条圆弧样条曲线,即二次均匀B样条曲线的逼近曲线。另外给出了逼近误差分析和实例说明。     

一种B样条曲线描述图像边界的算法

型值点的个数与分布对B样条曲线的形状有直接影响,为了让B样条曲线能很好地描述图像区域边缘,研究了一种自适应3次非均匀B样条曲线插值算法。利用B样条曲线在型值点处曲率较大的性质,调整型值点的位置和个数,通过B样条曲线与图像边缘的误差,对型值点进一步优化,使B样条曲线贴合边缘。实验结果表明,该方法得到的B样条曲线能很好地描述区域边缘。     

基于样条曲线拟合的肺区轮廓修补算法*

当肿瘤处于肺的边缘时,依据CT图像分割出的肺区有缺陷,肿瘤可能被排除在分割出的肺区外.为了解决这一问题,根据肺区外侧轮廓的形状特征,抽取多个控制点,使用Cardinal样条曲线拟合肺区轮廓.拟合后的边界成功地把肿瘤包含在肺区内.     

基于Cardinal样条曲线的虚拟漫游路径优化

漫游路径不平滑和漫游相机视角方向固定是导致虚拟漫游沉浸感差的主要问题.基于此,提出一种基于Cardinal样条曲线拟合的漫游路径平滑过渡算法,解决漫游中由于漫游路径不平滑造成的视点跳跃问题;提出一种虚拟漫游相机视角方向动态更新算法,实现漫游相机视角方向沿路径方向动态更新,更加符合人们的观察习惯;最后,基于开源场景图形引擎(OpenSceneGraph,OSG)对上述算法进行了实现和实验验证.结果表明,基于所提方法生成的漫游路径平滑、漫游相机视角方向过渡自然,有效提高了漫游的虚拟沉浸感.     

Supervised local spline embedding for medical diagnosis

A common difficulty of intelligent medical diagnosis is the high dimensionality of medical data. Manifold learning provides an elegant way to solve this problem by mapping the high-dimensional data into the low-dimensional embedding. However, traditional manifold learning algorithms fail to fully utilize the supervised information in medical diagnosis. To overcome this problem, in this paper we propose a novel Supervised Local Spline Embedding (SLSE) algorithm, which incorporates the supervised information into the local spline manifold embedding. SLSE not only preserves the local neighborhood structure, but also utilizes the global manifold shape through spline interpolation. Moreover, SLSE leverages the supervised information by maximizing the inter-class scatterness and minimizing the intra-class scatterness in the low-dimensional embedding. The promising experimental results on real-world medical datasets illustrate the superiority of our proposed approach in comparison with the existing popular manifold learning algorithms.