参数曲线近似弧长参数化方法

１．引 言 曲线参数化是对一条曲线建立参数方程的过程,而弧长参数化是指以曲线本身的弧长为参数建立参数方程．但是,我们知道曲线的弧长是由曲线的参数方程来计算的．设曲线的参数方程为它的弧长可表示为 显然,弧长函数Ｓ（ｔ）一般没有解析表达式,即使有,它的反函数ｔ＝ｔ（ｓ）也未必能求出．因此,精确地实现一般参数曲线的弧长参数化是不可能的．然而,在实际应用中弧长参数化是十分重要的．例如,在 ＣＡＤ系统中,沿一条参数曲线等距离（弧长）分布铆钉;数控加工中要求快速实现刀具运动轨迹的弧长空间位置“时空”转换,这里要…     

新型细胞自动机规则空间的参数化

细胞自动机在复杂性科学研究中占有重要地位,规则空间的规律性是细胞自动机理论研究的核心问题。本文首次引入沃尔什正交变换,结合计算机实验,提出了刻画细胞自动机规则空间规律性的δ参数。通过对所有初等细胞自动机的分析,并与朗顿λ参数的对比研究,结果表明该参数能更好地刻画细胞自动机规则空间中从有序到混沌的相变,不存在关于相变临界值的争论。     

连续体结构的参数化水平集统一优化

针对传统分步式结构优化设计的不足,提出一种同时进行结构拓扑、形状和尺寸统一优化的设计方法.首先采用水平集函数描述统一的结构优化模型和几何尺寸边界,通过引入紧支径向插值基函数将结构拓扑优化变量、形状优化变量和尺寸优化变量变换为基函数的扩展系数;然后取该扩展系数为设计变量,借助一种参数的变化表达3种优化要素对结构性能的影响,将复杂的多变量优化问题变换为相对简单的参数优化问题,有利于与相对成熟的优化算法相结合提高求解效率;进一步用R函数将其融合为一个整体,构造出统一优化模型,并用最优化准则法进行求解.最后通过数值案例证明了该方法的有效性和精确性.     

A Fast Sweeping Method for Computing Geodesics on Triangular Manifolds

A wide range of applications in computer intelligence and computer graphics require computing geodesics accurately and efficiently. The fast marching method (FMM) is widely used to solve this problem, of which the complexity is O(Nlog N), where N is the total number of nodes on the manifold. A fast sweeping method (FSM) is proposed and applied on arbitrary triangular manifolds of which the complexity is reduced to O(N). By traversing the undigraph, four orderings are built to produce two groups of interfering waves, which cover all directions of characteristics. The correctness of this method is proved by analyzing the coverage of characteristics. The convergence and error estimation are also presented.     

A Parameterization Method from Conic Spline Interpolation

Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital step before constructing interpolation functions. The most widely used parameterization method is accumulative chord length parameterization. In this paper, we give out a better method based on the interpolation of conics. Based on this method, a sequence of fairer Hermite curves can be constructed.     

基于网格简化的参数化方法

提出一种基于网格简化的三角网格参数化方法,该方法通过构建并参数化边界三角网格来自动完成复杂三角网格边界的参数化,然后通过一系列局部计算完成网格内部点的参数化．采用该方法得到的参数值可较好地反映三角网格的特性,而且计算具有较高的效率．     

点集表面的共形参数化

基于点的图形系统成为图形学研究中的一个热点。该文介绍了一种无组织点集表面的共形参数化方法,在该参数化方法中,传统算法中经常使用的欧氏距离被测地线距离所代替。相对于欧氏距离,测地线距离能够更好地描述点集所隐含的表面,减少由点集表面无拓扑性质带来的误差,保持点集曲面的形状不变,提高参数化的质量。     

Dynamic Parameterization for Path Following Control

Path following is a basic skill for robots in industrial use. Since the objective of path following is to make a robot follow the reference path, the velocity of the robot or the timing of the motion does not need to be strictly controlled. In this paper, the reference path is defined as a function of the parameter that has dynamics. Using this parameter, we can define the contour error, which is the error that enables us to measure the distance from the reference path to the configuration of the robot. Although the contour error is suitable for use in path following, the dynamics of the parameter contain singular points at which the dynamics cannot be defined. In order to overcome this difficulty, globally defined dynamics are introduced, and two dynamics are integrated with a switching scheme. In this paper, the asymptotic stability of the whole system is proved theoretically. Computer simulation results also show the effectiveness of the method.     

三角网格曲面的球面参数化

提出了一种球面参数化三角网格曲面的方法。结合平面凸参数化和球面参数化,计算出封闭网格的切割线边界,网格边界映射到球面的凸区域边界上。然后分别参数化各子网格,最后将三角网格内部点映射到球面上。并用实例验证了此方法的可行性和有效性。     

DeepBRDF: A Deep Representation for Manipulating Measured BRDF

Effective compression of densely sampled BRDF measurements is critical for many graphical or vision applications. In this paper, we present DeepBRDF, a deep-learning-based representation that can significantly reduce the dimensionality of measured BRDFs while enjoying high quality of recovery. We consider each measured BRDF as a sequence of image slices and design a deep autoencoder with a masked L₂ loss to discover a nonlinear low-dimensional latent space of the high-dimensional input data. Thorough experiments verify that the proposed method clearly outperforms PCA-based strategies in BRDF data compression and is more robust. We demonstrate the effectiveness of DeepBRDF with two applications. For BRDF editing, we can easily create a new BRDF by navigating on the low-dimensional manifold of DeepBRDF, guaranteeing smooth transitions and high physical plausibility. For BRDF recovery, we design another deep neural network to automatically generate the full BRDF data from a single input image. Aided by our DeepBRDF learned from real-world materials, a wide range of reflectance behaviors can be recovered with high accuracy.     

A Control Parameterization Approach with Variable Time Nodes for Optimal Control Problems

This paper presents a novel computational approach to deal with optimal multivariable control problems using a control vector parameterization approach with multiple time grids, where each of the control variables has its own time grid of parametrization. Both the control parameters and time nodes in the grid partition are treated directly as variables to be optimized. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient formulae for parameters are presented. Compared with the existing approaches, for which all the control variables are parameterized on the same time grid, the proposed method is more general and flexible. To illustrate, two numerical cases are tested, and the results demonstrate that fewer parameters are needed to achieve the same level of optimization.     

一个基于模式匹配的参数化尺寸标注系统

文章讨论了一个新的参数化尺寸标注系统的实现原理、关键技术和设计方法。该系统在以下几个方面取得明显进展,其一,基于AutoCAD的尺寸标注功能及存储格式,设计了新的通用、完整、可靠的尺寸标注系统,为AutoCAD增添了新的标注功能,使其能够准确地标注国家机械制图标准所规定的尺寸标注模式。其二,归纳了AutoCAD和国家标准的各种尺寸标注模式,借助于模式匹配及其推理,自动标注不同类型的尺寸标注,实现了智能化尺寸标注功能。其三,尺寸标注变量及其约束表达式功能,在参数化模型图的参数编辑、尺寸驱动和尺寸标注图素自动生成方面显示出极大的效率。     

A Local/Global Approach to Mesh Parameterization

We present a novel approach to parameterize a mesh with disk topology to the plane in a shape‐preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global “stitch” operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as‐similar‐as‐possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as‐rigid‐as‐possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre‐factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape‐preserving results than other state‐of‐the‐art approaches. We present also a more general “hybrid” parameterization model which provides a continuous spectrum of possibilities, controlled by a single parameter. The two cases described above lie at the two ends of the spectrum. We generalize our local/global algorithm to compute these parameterizations. The local phase may also be accelerated by parallelizing the independent computations per triangle.     

点模型曲面的调和映射参数化

利用调和映射的平面和球面中值性质,提出了确定点模型曲面参数化映射中有关权因子的两种新方法,设计了能够达到内在变形较小的相应参数化方法,并将参数化方法应用于点模型曲面上的纹理映射．实验和统计结果表明,文中方法是比较有效的点模型曲面的参数化方法．     

基于USB的通用机器人控制器

本文介绍了一种通用教学机器人控制器。该控制器采用PC DSP的主从式 2级CPU控制结构 ,CPU之间通过USB进行通讯。控制器的硬件采用模块化结构设计 ,控制器的软件使用通用化的机器人数学模型来描述机器人对象 ,因而能够适用于多种不同类型的开链结构的机器人的控制。     

A Comprehensive and Versatile Camera Model for Cameras with Tilt Lenses

We propose camera models for cameras that are equipped with lenses that can be tilted in an arbitrary direction (often called Scheimpflug optics). The proposed models are comprehensive: they can handle all tilt lens types that are in common use for machine vision and consumer cameras and correctly describe the imaging geometry of lenses for which the ray angles in object and image space differ, which is true for many lenses. Furthermore, they are versatile since they can also be used to describe the rectification geometry of a stereo image pair in which one camera is perspective and the other camera is telecentric. We also examine the degeneracies of the models and propose methods to handle the degeneracies. Furthermore, we examine the relation of the proposed camera models to different classes of projective camera matrices and show that all classes of projective cameras can be interpreted as cameras with tilt lenses in a natural manner. In addition, we propose an algorithm that can calibrate an arbitrary combination of perspective and telecentric cameras (no matter whether they are tilted or untilted). The calibration algorithm uses a planar calibration object with circular control points. It is well known that circular control points may lead to biased calibration results. We propose two efficient algorithms to remove the bias and thus obtain accurate calibration results. Finally, we perform an extensive evaluation of the proposed camera models and calibration algorithms that establishes the validity and accuracy of the proposed models.     

Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces

Efficient parameterization of point-sampled surfaces is a fundamental problem in the field of digital geometry processing. In order to parameterize a given point-sampled surface for minimal distance distortion, a differentialslbased segmentation and parameterization approach is proposed in this paper. Our approach partitions the point-sampled geometry based on two criteria： variation of Euclidean distance between sample points, and angular difference between surface differential directions. According to the analysis of normal curvatures for some specified directions, a new projection approach is adopted to estimate the local surface differentials. Then a k-means clustering （k-MC） algorithm is used for partitioning the model into a set of charts based on the estimated local surface attributes. Finally, each chart is parameterized with a statistical method -- multidimensional scaling （MDS） approach, and the parameterization results of all charts form an atlas for compact storage.     

Intrinsic Polynomials for Regression on Riemannian Manifolds

We develop a framework for polynomial regression on Riemannian manifolds. Unlike recently developed spline models on Riemannian manifolds, Riemannian polynomials offer the ability to model parametric polynomials of all integer orders, odd and even. An intrinsic adjoint method is employed to compute variations of the matching functional, and polynomial regression is accomplished using a gradient-based optimization scheme. We apply our polynomial regression framework in the context of shape analysis in Kendall shape space as well as in diffeomorphic landmark space. Our algorithm is shown to be particularly convenient in Riemannian manifolds with additional symmetry, such as Lie groups and homogeneous spaces with right or left invariant metrics. As a particularly important example, we also apply polynomial regression to time-series imaging data using a right invariant Sobolev metric on the diffeomorphism group. The results show that Riemannian polynomials provide a practical model for parametric curve regression, while offering increased flexibility over geodesics.     

Discrete Calabi Flow: A Unified Conformal Parameterization Method

Conformal parameterization for surfaces into various parameter domains is a fundamental task in computer graphics. Prior research on discrete Ricci flow provided us with promising inspirations from methods derived via Riemannian geometry, which is rigorous in theory and effective inpractice. In this paper, we propose a unified conformal parameterization approachfor turning triangle meshes into planar and spherical domains using discrete Calabi flow onpiecewise linear metric. We incorporate edge‐flipping surgery to guarantee convergence as well as other significant improvements including approximate Newton's method, optimal step‐lengths, priority embedding and boundary customizing, which achieve better performance and functionality with robustness and accuracy.