Iso-planar interpolation for the machining of implicit surfaces

The paper presents an approach for on-line path generation and interpolation for the machining of implicit surfaces. For a given implicit surface, once the cutting plane direction and cut-in points have been selected, iso-planar tool paths and interpolated points can be calculated on-line according to the feedrate and scallop height requirements. The approach enables the tool position and orientation to be correctly calculated at each interpolated point. Validation examples are provided for the interpolation of cyclide surfaces with planar and curved boundaries.     

多坐标曲面加工中进给速度的优化控制

介绍了基于曲面CNC(Computer Numerical Control)直接插补方式的多坐标曲面加工中进给速度的控制原理.综合考虑刀具相对零件表面切削进给速度的恒定,曲面形状引起的各运动轴速度及其变化率不超过伺服驱动能力,以及饥床在启动、停止和速度变化时的平滑加减速运动控制等因素,实现了进给速度的合理确定与控制,可有效提高曲面加工质量和加工效率.     

Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system

In this paper, the time-optimal feedrate planning problem under confined feedrate, axis velocity, axis acceleration, axis jerk, and axis tracking error for a high-order CNC servo system is studied. The problem is useful in that the full ability of the CNC machine is used to enhance the machining productivity while keeping the machining precision under a given level. However, the problem is computationally challenging. The main contribution of this paper is to approximate the problem nicely by a finite-state convex optimization problem which can be solved efficiently. The method consists of two key ingredients. First, a relationship between the tracking error and the input signal in a high-order CNC servo system is established. As a consequence, the tracking error constraint is reduced to a constraint on the kinematic quantities. Second, a novel method is introduced to relax the nonlinear constraints on kinematic quantities to linear ones. Experimental results are used to validate the proposed method.     

Quart-parametric interpolations for intersecting paths

The intersecting path is an important tool path generation method. This paper proposes an approach for the quart-parametric interpolation of intersecting paths. The objective of our approach is that the intersecting paths for surface machining can be directly interpolated within the computer numerical control (CNC) system. This enables the CNC interpolator to process the intersecting paths without geometric approximation as in existing approaches and take into consideration any specific feedrate profiles and further machining dynamical issues along the path.The interpolation of the intersection of two general parametric surfaces is transferred into interpolation of its projection curves and the time trajectories of four parameters along the intersecting curves are obtained. Our strategy is to carry out the quart-parametric interpolation based on the projection interpolation. The feedrate control method is developed, and then the interpolation algorithms for two projection curves are proposed. An error reduction scheme is presented to alleviate point deviation from the drive parametric surface. Simulations of quart-parametric interpolation have been carried out to verify the effectiveness of the proposed algorithm.     

Isophote interpolation

The isophote is an important class of characteristic curves on a parametric surface. Accordingly, as a kind of feature based path generation method, isophote based tool paths has been proposed as an important path pattern for parametric surface machining. In this paper, an approach has been proposed for the isophote interpolation on a parametric surface. The paper has related the arc-length derivatives to time derivatives of parameters along the isophote. The results are then used to derive the parametric interpolation. The isophote curve interpolation is developed based on parametric interpolation. The proposed interpolation guarantees that interpolated points always stay on the parametric surface. An improvement interpolation has been presented to alleviate inclination errors and point deviation from the isophote. Simulations of isophote interpolation have been carried out to verify the effectiveness of the proposed algorithm. The proposed algorithm has applications in real time tool path interpolation for the machining of parametric surfaces.     

Angular interpolation of bi-parameter curves

This paper presents an approach to the interpolation of angular feedrate for bi-parameter curve paths in multi-axis machining. A bi-parameter curve is the intersection of a parametric surface and an implicit surface. A tool path is identified by a position curve and an orientation curve, both of which are generated based on the bi-parameter curve. The angular feedrate interpolator calculates the tool position and orientation at each sampling cycle according to the specified angular feedrates and the given tool path. The paper analytically relates the angular arc-length derivatives to the time derivatives of the parameters along the path making use of both angular feedrates and angular feed acceleration. The results are then used to interpolate the parameters of the bi-parameter curve leading to an accurate calculation of the position and orientation of the cutting tool. A general parametric surface has been used to verify the effectiveness of the algorithm. The bi-parameter curves of the surface have been computed for arbitrarily selected intersecting cylinders.     

High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine.For the consecutive micro-line segments interpolation,the velocities at the junction of two segments are the bottlenecks for the machining efficiency.This paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode,whi...     

A class of general quartic spline curves with shape parameters

With a support on four consecutive subintervals, a class of general quartic splines are presented for a non-uniform knot vector. The splines have C² continuity at simple knots and include the cubic non-uniform B-spline as a special case. Based on the given splines, piecewise quartic spline curves with three local shape parameters are given. The given spline curves can be C²∩G³ continuous by fixing some values of the curve?s parameters. Without solving a linear system, the spline curves can also be used to interpolate sets of points with C² continuity. The effects of varying the three shape parameters on the shape of the quartic spline curves are determined and illustrated.     

MATLAB在数控系统速度曲线分析中的应用

数控系统软件研发中往往需要对插补后的速度曲线进行分析,通过速度曲线的分析判断加减速是否正确.结合MAT-LAB优良的绘图功能,提出了一种利用MATLAB快速进行速度曲线分析的方法,供数控系统软件开发人员参考.     

基于隐曲线的速度插值算法研究与实现

本文主要研究了隐曲线在行为动画中的应用,提出并进一步研究了隐曲线在行为动画中的任务指定作用.提出了基于隐曲线的速度插值算法.隐曲线用于指定行为动画的运动路径,速度曲线用于描述运动的时间分布.基于角色的运动路径和运动速度,速度插值技术生成与速度映射的插值位置点,进而通过逆向运动学技术,可以求解得到动画角色的骨架序列.同时对本文提出的隐曲线速度插值算法进行了实现和分析.通过设置不同的运动路径和速度曲线,速度插值技术可直观、快速地满足用户的具体要求创建不同的运动序列,且运动复用性强.     

保形五次几何Hermite插值的构造算法

讨论了计算机辅助几何设计中的GHI问题,GHI曲线需要型值点处的切线和曲率信息,所以GHI曲线比一般的插值曲线更困难.首先将保概念引入到GHI曲线,再用分段五次Bezier曲线构造了GC2保形GHI算法.该曲线的所有Bezier点由型值点及相应的曲率信息直接计算产生,无需求解矢量方程组,因此该曲线计算简单,局部修改方便.最后,两个数值例子被给出。     

变曲率对称圆弧曲线及其在圆弧样条拟合中的应用

针对数控加工的需要,对圆弧样条拟合曲线的形状进行局部修改和优化,提出了一种新的圆弧样条曲线的基本形式－变曲率对称圆弧曲线,并给出了其计算方法和具体应用,该方法可满足不同运算字长数控系统对拟合后圆弧样条曲线最大曲率半径的要求,同时还可满足随动控制加工对拟合曲率变动量的要求。     

Pixel-level singular point detection from multi-scale Gaussian filtered orientation field

Singular point, as a global feature, plays an important role in fingerprint recognition. Inconsistent detection of singular points apparently gives an affect to fingerprint alignment, classification, and verification accuracy. This paper proposes a novel approach to pixel-level singular point detection from the orientation field obtained by multi-scale Gaussian filters. Initially, a robust pixel-level orientation field is estimated by a multi-scale averaging framework. Then, candidate singular points in pixel-level are extracted from the complex angular gradient plane derived directly from the pixel-level orientation field. The candidate singular points are finally validated via a cascade framework comprised of nested Poincare indices and local feature-based classification. Experimental results over the FVC 2000 DB2 confirm that the proposed method achieves robust and accurate orientation field estimation and consistent pixel-level singular point detection. The experimental results exhibit a low computational cost with better performance. Thus, the proposed method can be employed in real-time fingerprint recognition.     

GP-Stability of two-step implicit runge-kutta methods for delay differential equations

The GP-stability of two-step implicit Runge-Kutta (TIRK) methods for the numerical solution of systems of delay differential equations (DDEs) is considered. We focus on the stability behaviour of TIRK methods in the solution of the linear constant-coefficient systems of DDE with a single delay. We present a sufficient condition of GP-stability of TIRK methods.     

An optimization approach for biarc curve-fitting of B-spline curves

We present an approach to the optimal fitting of a biarc-spline to a given B-spline curve. The objective is to minimize the area between the original B-spline curve and the fitted curve. Such an objective has obvious practical implications. This approach differs from conventional biarc curve-fitting techniques in two main aspects and has some desirable features. Firstly, it exploits the inherent freedom in the choice of the biarc that can be fitted to a given pair of end-points and their tangents. The conventional approach to biarc curve-fitting introduces additional constraints, such as the minimal difference in curvature or others to uniquely determine successive biarcs. In this approach, such constraints are not imposed. Instead, the freedom is exploited in the problem formulation to achieve a better fit. Secondly, the end-points do not lie on the curve so that appropriate tolerance control can be imposed through the use of additional constraints. Almost all previous biarc-fitting methods consider end-points that are on the original curve. As a result of these two aspects, the resulting biarc curve fits closely to the original curve with relatively fewer segments. This has a desirable effect on the surface finish, verification of CNC codes and memory requirement. Numerical results of the application of this approach to several examples are presented.     

插值算法的研究

主要研究应用于图像放大技术领域的处理算法,常用的图像放大技术即为插值算法,主要插值处理方法有最邻近插值算法、双线性插值法、双三次插值。实验仿真结果表明最邻近算法处理后的图像效果较差,双线性算法处理后图像质量较高。而双三次插值算法处理后的图像质量最高,但运行时间较长。     

三次B样条插值曲面及其实现

目前在ＣＡＭ／ＣＡＭ的自由曲面构造方法中，较流行的有Ｂ样条曲面，Ｂｅｚｉｅｒ曲面、Ｂａｌｌ曲面等方法，但由这几种方法和成都是拟合曲面，而百插值曲面，常常不能满足一些工程实际中严格插值的要求，本文构造了一种自由插值曲面生成方法－Ｂ样条母线法，所生成曲面达到Ｃ＾２级光滑，适用机械，模具、汽车、造船等制造加工行业的复杂曲面设计。     

Geometric Hermite interpolation for space curves

This paper considers the geometric Hermite interpolation for spacial curves by parametric quartic Bézier curve. In additon to position and tangent direction, the curvature vector is prescribed at each knot. We prove that under appropriate assumptions the interpolant exists locally with one degree of freedom. Moreover, we prove the interpolant is 6th order accurate.