自动绘制等值线图形

本文叙述微机自动绘制等值线图形软件的原理和方法。该程序是用三角网法结合Ｂ样条函数绘制成光滑曲线图形，由于三角网的形成和Ｂ样条曲线的建立均可由计算机自动实现，这大大提高了自动绘制等值线图的速度和质量。     

基于不规则三角网(TIN)的追踪等值线算法及对等值线光滑算法的研究

介绍了基于不规则三角网(TIN)的存贮结构和追踪等值线算法,并针对奇点处理提出了新的改进算法;其次根据生成的等值线,分别对以下几种光滑算法:线形迭代法、Bezier函数法、三次B样条函数法等,通过对其算法数学原理的研究分析,比较了各种曲线在曲线光滑应用中的特点,根据在应用中结果的比较,提出了用张力样条曲线作为拟合等值线的光滑曲线具有重要的参考价值。     

基于Delaunay三角网的等值线绘制算法*

提出了一种快速构建Delaunay三角网算法（QGDTN）。在每次迭代中,该算法从点集P最左边的两点中,选取离凸边中点距离最近的一点与凸边构成Delaunay三角形,并加入三角网中,算法实现简单,且时间复杂度为O(n)。基于Delaunay三角网,根据三角形的各边上是否有等值点,用内插值法求出等值点坐标,跟踪、连接等值点生成等值线;最后,采用三次方Bezier曲线平滑等值线。实验证明,基于Delaunay三角网的等值线绘制算法是高效的,并且具有一定的实用价值。     

等值线的绘制

等值线的绘制是CAD的一个重要方面,这项工作在科学预测和研究中得到广泛应用,常常用于地质、勘测、勘探、气象、绘制地图及考古等等。本文介绍在平面上绘制等值线的方法。     

基于三角网的等值线填充算法研究

通过对现有等值线填充算法的深入研究,提出了一种覆盖填充等值线的算法。该算法把等值线分类为凸包边封闭等值线(CHCL)和自封闭等值线(SCL),充分利用等值线的特点,使对等值线拓扑关系及填充颜色的判定达到最简化。对于CHCL采用对凸包边等值点及凸包点追踪来确定填充区域,对于SCL则根据拓扑关系以最外层的SCL为根节点构建一棵多叉树以确定填充顺序.通过对等值区域依次反复覆盖填充,最终完成所有等值线的填充。采用了一种穿过原始离散点平滑等值线的算法,减小了等值线平滑造成的精度损失。并运用客户端语言AS3.0(ActionScript3.0)实现了算法模型。实验结果表明,该算法简单易于实现,而且运算速度能满足业务需要。     

地质数据的等值线绘制方法研究

等值线图是地质研究工作中的一种重要表示方法,它通过处理一些离散的点来生成连续平滑的地质结构图。但是对于不规则离散数据且有断层存在的情况,等值线的绘制是比较困难的,很难满足实际的需求。在基于断层恢复法的基础上对其进行了一些优化,既考虑到了断层的落差距离,又考虑到了断层的水平断距,使绘制出的等值线图误差更小,更加符合断层的真实情况。方法基于三角网格确定等值点,通过计算出的等值点对进行等值线跟踪,并给出了有断层存在时的等值线处理方法,实验分别给出了有无断层存在时的等值线图,证明了算法的可操作性和可行性。     

等值线绘制中的一些后期处理——裁剪与填充

本文首先简要介绍了等值线的性质及绘制方法，然后对等值线图绘制中经常会用到的一些后期处理方法－－图形的裁剪与填充进行了讨论，并对相应的通用图形学算法进行了一些改进，以适应这种特殊图形的应用需要。     

使用多段Bezier曲线模型的地质等值线光滑算法

在等值线自动生成过程中,如果仅仅将追踪到的等值点依次用线连接起来,那么将会生成一幅折线式的等值线图。文章提出使用多段三次Bezier曲线拟合模型对得到的等值线进行拟合,首先利用三次Bezier曲线的拟合公式和最小二乘法得到首段Bezier曲线的四个控制点,然后依据Bezier曲线拼接的光滑条件和首段Bezier曲线的控制点,再次使用最小二乘法得到次段Bezier曲线的四个控制点,依此类推,从而得到由多段Bezier曲线组成的光滑的等值线图。除此之外,本文给出构建网格较小情况下的多段Bezier曲线拟合模型特例。实验结果证实,本文提出的方法易理解,可行性好,光滑效果显著。     

生物电场分析可视化方法及实现

在生物电场分析过程中,每次运算都将产生大量的数据(如电导率、电阻率分布),这些数据反映的规律不直观,不便于理解.如何将这些计算结果很好的以图形方式显示出来,直观地看出电导率、电阻率等参数分布,这对计算结果的分析、理解都有着重要的作用.本文主要从等值线及色彩地形图的绘制两个方面讲述了电阻抗成像中有限元后处理的实现,并用Visual C + + .NET结合OpenGL编写了有限元后处理软件,解决了等值线及色彩地形图的绘制问题.     

降雨分析系统的设计与算法

等值线是反映空间地理信息数据关系的最重要的表现方式之一,但编程实现等值线的绘制并用其进行GIS软件的二次开发却并不容易。在实际开发降雨分析系统的基础上介绍了在数据可视化和地理信息系统中非常重要的等值线绘制和轮廓图填充算法,并且给出了基于动态链接库和XML技术的模块化系统整体架构。实际的绘制效果与计算速度可与美国GoldenSoft公司的著名软件Surfer相媲美。降雨数据来源包括以数据库和文件存储的一切实测、遥感数据。该系统已在杭州、温州、上虞、金华、台州等多个地市的防汛抗旱部门投入使用,改变了原先等值线主要由手工绘制的情况。本系统可以同样用于等高线的绘制。     

Controlled-topology filtering

Many applications require the extraction of isolines and isosurfaces from scalar functions defined on regular grids. These scalar functions may have many different origins: from MRI and CT scan data to terrain data or results of a simulation. As a result of noise and other artifacts, curves and surfaces obtained by standard extraction algorithms often suffer from topological irregularities and geometric noise.While it is possible to remove topological and geometric noise as a post-processing step, in the case when a large number of isolines are of interest there is a considerable advantage in filtering the scalar function directly. While most smoothing filters result in gradual simplification of the topological structure of contours, new topological features typically emerge and disappear during the smoothing process.In this paper, we describe an algorithm for filtering functions defined on regular 2D grids with controlled topology changes, which ensures that the topological structure of the set of contour lines of the function is progressively simplified.     

有理多结点样条插值曲线及曲面

鉴于多结点样条曲线（MSIC）是一种点点通过的插值样条曲线,因此在多结点样条插值曲线研究的基础上,给出了有理多结点条插值曲线和有理多结点样条插值曲面的定义,并讨论了有理多结点样条的性质,对有理多结 样条曲线和有理多结点样条曲面的光滑拼接问题进行了讨论,此外,还对有理多结点样条在计算机辅助几何设计中的若干应用问题进行了说明。     

An efficient method for smoothing indicator-dilution and other unimodal curves

A mathematical function has been developed for approximating unimodal functions, particularly those which are non-Gaussian, skewed, and incomplete. It is useful as an alternative to cubic splines in smoothing noisy experimental data. Particular applications are to indicator-dilution curves and probability density functions of varied form. In its Fortran implementation, SMOEX, it is computationally inexpensive compared to standard cubic spline smoothing routines and requires less storage to preserve the smoothed function for retrieval or interpolation.     

三种形状可调三角样条曲线

构造了3种带参数的三角样条基,基于这3组基定义了3种三角样条曲线。与二次B样条曲线类似,这3种曲线的每一段都由相继的3个控制顶点生成,且这3种曲线具有许多与二次B样条曲线类似的性质。但这3种曲线的连续性都比二次B样条曲线要好。对于等距节点,在一般情况下,这3种曲线都是整体C²连续的,在特殊条件下它们都可以达到C³连续。另外,这3种曲线都具有比二次B样条曲线更好的对控制多边形的逼近性。     

Spline smoothing for experimental data under zero median of the noise

We propose an algorithm for computing parameter estimates for a smoothing cubic spline that minimize the estimated expectation of losses. Instead of the usual assumption that the noise is centered we use an assumption which is more realistic for many practical smoothing problems, namely that it is zero median. The problem setting is augmented by prior deterministic information in the form of constraints on linear combinations of parameters of spline functions. We obtain explicit representations of such estimates and give their qualitative interpretation. Based on the results of a numerical experiment, we establish a high degree of robustness of the solutions to the presence of outliers in the measurements, including same sign outliers, and the possibility to fairly reliably determine the actual accuracy of the resulting estimates of spline parameters by the attained minimum risk value.     

基于样条的矢量数据多尺度表达与压缩算法

传统矢量曲线压缩算法不能解决曲线压缩后的平滑问题,并可能产生拓扑异化。为此,提出基于样条的矢量数据多尺度表达与压缩算法。选择样条的光滑因子作为阈值对曲线进行多尺度表达与压缩,保持压缩前后曲线的光滑特性,利用少量的控制点描述整条曲线,从而提高矢量曲线处理的速度和质量。实验结果表明,该算法仅需9个控制点就能逼近给定的一条原始曲线,验证了其高效性。     

Periodic smoothing splines

Periodic smoothing splines appear for example as generators of closed, planar curves, and in this paper they are constructed using a controlled two point boundary value problem in order to generate the desired spline function. The procedure is based on minimum norm problems in Hilbert spaces and a suitable Hilbert space is defined together with a corresponding linear affine variety that captures the constraints. The optimization is then reduced to the computationally stable problem of finding the point in the constraint variety closest to the data points.     

A note on bimodality in the log-likelihood function for penalized spline mixed models

For a smoothing spline or general penalized spline model, the smoothing parameter can be estimated using residual maximum likelihood (REML) methods by expressing the spline in the form of a mixed model. The possibility of bimodality in the profile log-likelihood function for the smoothing parameter of these penalized spline mixed models is demonstrated. A canonical transformation into independent observations is used to provide efficient evaluation of the log-likelihood function and gives insight into the incompatibilities between the model and data that cause bimodality. This transformation can also be used to assess the influence of different frequency components in the data on the estimated smoothing parameter. It is demonstrated that, where bimodality occurs in the log-likelihood, Bayesian penalized spline models may show poor mixing in MCMC chains and be sensitive to the choice of prior distributions for variance components.     

Flexible smoothing with periodic cubic splines and fitting with closed curves

An algorithm is presented for constructing a smoothing cubic spline with periodic end conditions. The Lagrangian multipliers for pointwise individual closeness of fit conditions serve as control parameters. Using this algorithm parametrically the fitting of given points in the plane or in the three-dimensional space by smooth closed curves can easily be established.