正弦B样条类曲线及其在曲线参数化中的应用

从B样条基函数出发,导出了正弦B样条类SBSC（Sine Basic Spline Class）函数,定义了SBSC曲线,讨论了SBSC曲线和B样条曲线的关系,提供了B样条曲线重新参数化的一种有效方法。     

Optimal parametrization of curves for robot trajectory design

A numerical method is presented for the offline determination of the minimum-time parameterization of a fixed path in robot joint space, assuming start and end at rest conditions and subject to constraints on manipulator joint torques. A numerical method for solving the problem is discussed in which the derivative of the change of variables is approximated by a cubic spline. Numerical results for a three-axis manipulator are presented     

On the performance of the approximate parametrization algorithm for curves

In Pérez-Díaz et al. (2009) [5], the authors present an algorithm to parametrize approximately ?-rational curves, and they show that the Hausdorff distance, w.r.t. the Euclidean distance, between the input and output curves is finite. In this paper, we analyze this distance for a family of curves randomly generated and we empirically find a reasonable upper bound of the Hausdorff distance between each input and output curve of the family.     

Automatic parametrization of rational curves and surfaces II: cubics and cubicoids

Algorithms that can obtain rational and special parametric equations for degree three algebraic curves (cubics) and degree three algebraic surfaces (cubicoids), given their implicit equations are described. These algorithms have been implemented on a VAX8600 using VAXIMA.     

As-rigid-as-possible spherical parametrization

In this paper, we present an efficient approach for parameterizing a genus-zero triangular mesh onto the sphere with an optimal radius in an as-rigid-as-possible (ARAP) manner, which is an extension of planar ARAP parametrization approach to spherical domain. We analyze the smooth and discrete ARAP energy and formulate our spherical parametrization energy from the discrete ARAP energy. The solution is non-trivial as the energy involves a large system of non-linear equations with additional spherical constraints. To this end, we propose a two-step iterative algorithm. In the first step, we adopt a local/global iterative scheme to calculate the parametrization coordinates. In the second step, we optimize a best approximate sphere on which parametrization triangles can be embedded in a rigidity-preserving manner. Our algorithm is simple, robust, and efficient. Experimental results show that our approach provides almost isometric spherical parametrizations with lowest rigidity distortion over state-of-the-art approaches.     

Accurate parametrization of conics by NURBS

One argument often given to explain the popularity of NURBS (nonuniform rational B-spline) is that it permits the definition of free-form curves and surfaces (as do most spline models). It also provides an exact representation of conic sections and thus of a large set of curves and surfaces used intensively in CAD: circular arcs, circles, cylinders, cones, spheres, surfaces of revolution and so forth. Nevertheless, few published works discuss the mathematical properties behind the representation of conics by NURBS except for two monographs by Piegl and Tiller (1995) and Farin (1995). The article does not pretend to fill this theoretical lack but rather deals with the following problems: all known NURBS representations of curves and surfaces based on conics have only a C^l continuity. Moreover, no technique exists that would eventually allow us to find a parametrization with a higher level of continuity. The parametrization resulting from the NURBS representation of conics can deviate significantly from the ideal are length (that is, uniform) parametrization. The only known solution to reduce this deviation is to increase the number of control points of the spline by using refinement algorithms, for instance, but such a process converges only slowly to the uniform parametrization. The solution proposed uses an original reparametrization process called zigzag reparametrization, based on a specific family of rational polynomials     

Curves with rational chord-length parametrization

It has been recently proved that rational quadratic circles in standard Bézier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue in bipolar coordinates of nonparametric curves. This interpretation furnishes a compact explicit expression for all planar curves with rational chord-length parametrization. In addition to straight lines and circles in standard form, they include remarkable curves, such as the equilateral hyperbola, Lemniscate of Bernoulli and Limaçon of Pascal. The extension to 3D rational curves is also tackled.     

A parametrization for dissipative behaviors

The behavioral equivalent of single input single output (SISO) systems are behaviors with two manifest variables. Passive SISO systems can, therefore, be viewed as J-dissipative behaviors with two manifest variables. Here the special matrix J defines a QDF that captures the passivity property of SISO systems. In this paper, we investigate more general QDFs Q_Φs induced by some operator Φ. These QDFs define some relation between the input, the output and their derivatives of a SISO system. We characterize all behaviors that are dissipative with respect to the prescribed QDF Q_Φ. In fact, we parametrize all the behaviors dissipative with respect to Q_Φ in terms of those dissipative with respect to the special QDF Q_J induced by the matrix J. Similar results can also be given for lossless systems.     

An improved Hoschek intrinsic parametrization

Smoothing a set of points p_i with a B-spline curve is an usual CAGD application, which remains an open problem due to the choice of the parameter values. J. Hoschek proposed one of the first iterative solution called intrinsic parametrization. This idea has been improved several times by introducing different parameter corrections. This paper deals with a new improvement of Hoschek's method providing better results with a higher speed of convergence. Examples are proposed and compared with the different approaches.     

Symbolic Testing and the DISSECT Symbolic Evaluation System

Symbolic testing and a symbolic evaluation system called DISSECT are described. The principle features of DISSECT are outlined. The results of two classes of experiments in the use of symbolic evaluadon are summarized. Several classes of program errors are defined and the reliability of symbolic testing in finding bugs is related to the classes of errors. The relationship of symbolic evaluation systems like DISSECT to classes of program errors and to other kinds of program testing and program analysis tools is also discussed. Desirable improvements in DISSECT, whose importance was revealed by the experiments, are mentioned.     

符号模拟

符号模拟将模拟验证从布尔值扩展到符号领域,是集成电路验证行业中的重要分支。符号方法将符号值加到待验证电路的基本输入端,依次计算每个结点的布尔函数,直到在电路的输出端得到由这些初始符号变量组成的布尔表达式,并判断其是否具有所期望的特征。该文介绍了符号模拟的发展过程、基本技术及其所面临的BDD爆炸问题,并对消除该问题的两种技术：近似值法和参数方法,进行了讨论。介绍了具有一定自动机处理能力的符号轨迹评价方法。     

A convex parametrization of risk-adjusted stabilizing controllers

The focal point of this paper is the synthesis of controllers under risk-specifications. In recent years there has been a growing interest in the development of techniques for controller design where, instead of requiring that the performance specifications are met for every possible value of admissible uncertainty, it is required that the risk of performance violation is below a small well-defined risk level. In contrast to previous work, where the search for the controller gains is done using randomized algorithms, the results in this paper show that for a class of uncertain linear time invariant systems, the search for the “risk-adjusted” controller can be done efficiently using deterministic algorithms. More precisely, for the case when the characteristic polynomial of the closed loop system depends affinely on the uncertainty, we provide a convex parametrization of “risk-adjusted” stabilizing controllers.     

Almost rotation-minimizing rational parametrization of canal surfaces

Almost rotation minimizing parametrization of the canal surface is given. The basic building block of our approach is the curve approximation scheme that enables us to construct a curve, called the parameter curve, on the canal surface that produces, when projected and rescaled, an almost parallel normal vector field on the spine curve. Its construction relies on our earlier methods and results on relating the geometry of the canal surface to the Lorentzian geometry of the Minkowski geometry via the Clifford algebra formalism. We then iteratively construct patches out of the parameter curves via suitable interpolation procedure. Furthermore, its rotational deviation, i.e., the angle deviation from the parallel (no rotation) frame along the spine curve, can be controlled with the use of the rotation deviation estimate of the parameter curves. Our numerical experiment shows that the rotation deviation is minuscule. When compared with other earlier results including our earlier one, our result fares extremely favorably. To facilitate the implement, a practitioners' summary is given in the appendix.     

Controller parametrization for time-varying multirate plants

The authors obtain a parametrization of all stabilizing controllers for a given discrete-time time-varying linear finite-dimensional multirate system. The parametrization is a natural extension of the Youla parametrization of all stabilizing controllers to the setting of multirate systems. The set of all stabilizing controllers is shown to be the set of all closed-loop systems obtained by terminating a fixed two-port multirate system in a stable multirate system. State-space formulas for the parametrization are also given     

Structure and parametrization of periodic linear systems

In this paper, the beginnings of a structure theory for discrete-time periodic linear systems are developed. Canonical forms for state space realizations are described, structural invariants and their combinatorics are studied and geometric aspects of the parametrization of periodic systems are treated.     

Localization and parametrization of linear multidimensional control systems

We study the link existing between the parametrization of differential operators by potential-like arbitrary functions and the localization of differential modules, while applying these results to the parametrization of linear multidimensional control systems. We show that the localization of differential modules is a natural way to generalize some well-known results on transfer matrix, classically obtained by using Laplace transform, to time-varying ordinary differential control systems and to partial differential control systems with variable coefficients. In particular, we show that the parametrizations obtained by localization are simpler than those obtained by formal duality but are worse in the sense of Palamodov–Kashiwara's classification of differential modules.     

Partial parametrization eliminates multiple traversals of data structures

Summary The use of higher order functions in functional programming opens up the possibility of defining functions by partial parametrization, and lazy evaluation brings out a new approach in programming methodology. This paper describes a new transformation technique based on partial parametrization and fully lazy evaluation for eliminating multiple traversais of data structures. It uses no particular mechanisms in functional programming, whereas it transforms a wider class of programs into efficient ones than that proposed so far.