面向对象的三次参数样条曲线技术

本文利用Ｃ＋＋面向对象的特征，对三次参数样条曲线的定义和生成过程进行封装，从而极大地简化了三次参数样条曲线的定义和绘制过程     

Data fitting with a spline using a real-coded genetic algorithm

To obtain a good approximation for data fitting with a spline, frequently we have to deal with knots as variables. The problem to be solved then becomes a continuous nonlinear and multivariate optimization problem with many local optima. Therefore, it is difficult to obtain the global optimum. In this paper, we propose a method for solving this problem by using a real-coded genetic algorithm. Our method can treat not only data with a smooth underlying function, but also data with an underlying function having discontinuous points and/or cusps. We search for the best model among candidate models by using the Bayes Information Criterion (BIC). With this, we can appropriately determine the number and locations of knots automatically and simultaneously. Five examples of data fitting are given to show the performance of our method.     

Analysis and design of Hermite subdivision schemes

Published online: 14 May 2002     

基于偏微分的图像放大算法研究

在研究图片放大算法中,分析了现有的运用偏微分算法在图像法大中的不足,利用图像放大过程中的边缘信息可预知性,本文提出一种新的基于偏微分方程的图像放大算法,这种算法通过将图像边缘检测、平滑处理,然后采用三次样条插值算法对边缘进行相应倍数的放大,并通过对可能出现的锯齿边缘进行细化处理;将处理过的边缘作为放大图像的边缘,从而可以将源图像的边缘很好的保持下来,避免了偏微分方程放大过程中出现的边缘模糊现象。实验结果显示,该方法是一种能够很好的保存图像的边缘信息的图像放大算法。     

精确实验数据曲线方程的求解

针对精确实验数据的曲线拟合方程化处理方法已不再适应高精度测试技术的问题,提出了用三次样条插值函数进行曲线方程化处理的新方法,并创建了用MATLAB语言编写遗传算法程序进行曲线斜率求解的方法,通过实例表明,采用遗传算法求解出的三次样条插值函数非常适合精确实验数据的曲线方程化处理。     

Spline multiresolution and wavelet-like decompositions

Splines are useful tools to represent, modify and analyze curves and they play an important role in various practical applications. We present a multiresolution approach to spline curves with arbitrary knots that provides good feature detection and localization properties for non-equally distributed geometric data. In addition, we show how equidistributed data and knot sequences can be efficiently handled using signal processing techniques.     

A data porting tool for coupling models with different discretization needs

The presented work is part of a larger research program dealing with developing tools for coupling biogeochemical models in contaminated landscapes. The specific objective of this article is to provide researchers with a data porting tool to build hexagonal raster using information from a rectangular raster data (e.g. GIS format). This tool involves a computational algorithm and an open source software (written in C). The method of extending the reticulated functions defined on 2D networks is an essential key of this algorithm and can also be used for other purposes than data porting. The algorithm allows one to build the hexagonal raster with a cell size independent from the geometry of the rectangular raster. The extended function is a bi-cubic spline which can exactly reconstruct polynomials up to degree three in each variable. We validate the method by analyzing errors in some theoretical case studies followed by other studies with real terrain elevation data. We also introduce and briefly present an iterative water routing method and use it for validation on a case with concrete terrain data.     

Computing a compact spline representation of the medial axis transform of a 2D shape

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.     

Feedrate Optimization for Spline Interpolation In High Speed Machine Tools

A feedrate optimization technique has been developed for minimizing the cycle time in machining spline toolpaths. Axis velocity, torque and jerk limits are considered throughout the motion in order to ensure smooth and linear operation of the servo drives with minimal tracking error. Feed modulation is achieved by manipulating segment durations which define the overall minimum jerk feed profile. Long toolpaths are handled by applying a windowing technique. The optimized feed profile allows nonzero acceleration and jerk values at segment connections, resulting in continuous and smooth motion within the velocity, torque, and jerk limits of the drives. The cycle time reduction obtained with the proposed technique is demonstrated in high speed contouring experiments.     

Modeling on triangulations with geodesic curves

This paper discusses the problem of modeling on triangulated surfaces with geodesic curves. In the first part of the paper we define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. In the second part we discuss the construction of C ⁰ and C ¹ piecewise Bézier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks. The third part is devoted to the definition and study of convex sets on triangulated surfaces. We derive the convex hull property of geodesic Bézier curves.