A unified, integral construction for coordinates over closed curves

We propose a simple generalization of Shephard's interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A third instance of this family yields a previously unknown generalization of discrete harmonic coordinates to smooth curves. For closed, piecewise linear curves, we prove that our interpolant reproduces a general family of barycentric coordinates considered by Floater, Hormann and Kós that includes Wachspress coordinates, mean value coordinates and discrete harmonic coordinates.     

A framework based on barycentric coordinates for localization in wireless sensor networks

Localization is a fundamental and vital problem in wireless sensor networks. This paper presents an optimizing framework for localization based on barycentric coordinates. The framework consists of two components. The first component retains the structure revealed by the distances between pairs of nodes; the second component constrains the boundary nodes to maintain the distance with their neighbor nodes. A hybrid localization algorithm is derived on top of the optimizing framework. A part of the computation is performed collaboratively by nodes, whereas the rest is executed on the sink node. Experimental results show that the proposed localization algorithm obtains lower location errors without higher communication costs.     

基于衍生多边形的混合坐标

将多边形三角化,利用三角网格将三角形衍生为点多边形、边多边形和面多边形,再根据已有的重心坐标提出基于衍生多边形的混合坐标.首先在三角网格内根据初始多边形内部一点所在的三角形得到衍生多边形,然后使用调和坐标、局部重心坐标、迭代坐标中任意一种计算衍生多边形的顶点关于初始多边形顶点的重心坐标,再使用迭代坐标计算初始多边形内部...     

基于极坐标的树木叶片特征提取方法

提出了一种在极坐标下进行特征提取的方法,并将其应用于树木叶片图像识别中。该方法首先将目标图像二值化并映射到极坐标下,提取具有旋转、缩放、平移不变性的曲线面积比率、跨度比、饱和度和高度变化率等特征。然后通过最小欧式距离对叶片进行计算、识别。该方法克服了直角坐标系下特征提取方法计算量大,花费的时间长的缺陷。基于该方法的叶片特征提取算法的时间复杂度为[O(n)]。对于叶型有区分,且需要快速进行树叶识别的树叶数据集有很好的效果。该方法在常见的13种树木叶片中进行测试,平均正确识别率达到90%以上。     

凸六面体上的双有理映射

借助三维重心坐标的特性,将二维双有理映射的结果推广到三维凸六面体的情形下,即给凸六面体上的每个顶点赋予适当的权值,从而得到凸六面体上的一个三线性双有理映射;此外,通过一个实例说明了该方法的有效性。     

Perimeter discovery in wireless sensor networks

In this paper, we focus on the perimeter detection problem using wireless sensor networks, as perimeter detection has a wide range of uses in several areas. We present a decentralized localized algorithm where sensor nodes determine if they are located along the perimeter of a wireless sensor network. Our proposed algorithm uses the location neighborhood information in conjunction with the Barycentric technique to determine if the sensor node enclosed by neighboring nodes, and consequently, if it is located within the interior of the wireless sensor network. We define performance metrics to analyze the performance of our approach and the simulation shows that the algorithm gives fairly accurate results.     

Homogeneous coordinates for computer graphics

Some mathematical aspects of homogeneous coordinates are presented. It is shown that the usual methods applied by workers in computer graphics are theoretically sound provided care is exercised in defining the range of the coordinate chart. The mechanics of the linear representation of transformations are explained in terms of commutative diagrams. Finally some familiar examples are discussed.     

Interacting with parallel coordinates

Parallel coordinate visualizations have a reputation of being difficult to understand, expert-only representations. We argue that this reputation may be partially unfounded, because many of the parallel coordinate browser implementations lack essential features. This paper presents a survey of current interaction techniques for parallel coordinate browsers and compares them to the visualization design guidelines in the literature. In addition, we report our experiences with parallel coordinate browser prototypes, and describe an experiment where we studied the immediate usability of parallel coordinate visualizations. In the experiment, 16 database professionals performed a set of tasks both with the SQL query language and a parallel coordinate browser. The results show that although the subjects had doubts about the general usefulness of the parallel coordinate technique, they could perform the tasks more efficiently with a parallel coordinate browser than with their familiar query language interface.     

The plane with parallel coordinates

By means ofParallel Coordinates planar graphs of multivariate relations are obtained. Certain properties of the relationship correspond tothe geometrical properties of its graph. On the plane a point line duality with several interesting properties is induced. A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results inComputational Geometry. There is also a suprising cusp inflection point duality. The narrative ends with a preview of the corresponding results inR ^N .     

Homogeneous coordinates

This paper presents an overview of homogeneous coordinates in their relation to computer graphics. A brief historical review is given, followed by the introduction of the homogeneous coordinate system. We elucidate its application in two-dimensional Euclidean space. Particular attention is given to the subjects of affine transformations effected with matrix multiplication and the intersection of two-dimensional lines. Homogeneous coordinates in three dimensions and, in detail, perspective transformations are also discussed. A method for clipping lines with respect to the viewing frustum is provided.     

Modeling smooth shape using subdivision on differential coordinates

Traditional subdivision schemes are applied on Euclidean coordinates (the spatial geometry of the control mesh). Although the subdivision limit surfaces are almost everywhere C² continuous, their mean-curvature normals are only C⁰. In order to generate higher quality surfaces with better-distributed mean-curvature normals, we propose a novel framework to apply subdivision for shape modeling, which combines subdivision with differential shape processing. Our framework contains two parts: subdivision on differential coordinates (a kind of differential geometry of the control mesh), and mutual conversions between Euclidean coordinates and differential coordinates. Further discussions about various strategies in both parts include a special subdivision method for mean-curvature normals, additional surface editing options, and a version of our framework for curve design. Finally, we demonstrate the improvement on surface quality by comparing the results between our framework and traditional subdivision methods.     

Twenty-five years of natural coordinates

In the early eighties, the author and co-workers created and further developed the natural coordinates to describe the motion of 2-D and 3-D multibody systems. Natural coordinates do not need angles or angular parameters to define orientation, leading to constant inertia matrices and to the simplest form of the constraint equations. Natural coordinates are composed by the Cartesian coordinates of some points and the Cartesian components of some unit vectors distributed on the different bodies of the system. The points and vectors can be located in the joints, being shared by contiguous bodies, decreasing or even eliminating the need to set joint constraints and reducing the total number of variables. However, other authors prefer not to share variables in order to get even simpler equations and to keep a bigger decoupling of equations, which is preferable in some cases. In this paper the history of natural coordinates is reviewed, as well as the main contributions coming from other research groups. In the second part of the paper some application areas in which natural coordinates can be particularly advantageous are examined. Commemorative Contribution.     

基于平行坐标的贝叶斯可视化分类方法

结合信息可视化与机器学习技术,提出一种基于多元数据平行坐标图表示的贝叶斯可视化分类方法。该方法基于类条件概率密度估计对平行坐标图表示进行优化,最后对变换后的各变量值加权求和,用贝叶斯法则分类。这种方法通过平行坐标来使不可见的数据和算法变得可见,从而易于利用专家领域知识,分类结果容易理解,特别适合应用到疾病诊断等医学领域的模式识别问题。     

基于平行坐标的多个体绘制参数的优化调节*

提出基于平行坐标概念的参数控制平台来对体绘制中多个参数进行优化调节的方法。参数控制平台提供了一种调节和控制绘制参数的简单而有效的界面,它能把所有相关参数组织在一个空间,并且给用户同时显示所有参数配置的一个视图。用户可以在参数控制平台记录不同的历史绘制参数,并在一个空间对不同的参数进行比较,用户还可以重组不同的优化参数以生成新的绘制。参数控制平台有效地提高了用户对多个绘制参数进行优化调节的效率。     

Cooperative tracking of vessel trajectories based on curved dynamic coordinates

A novel cooperative motion problem for multiple surface vessels is investigated based on multiple referential points and a terminal sliding mode control method. To overcome the difficulties of modeling some special tracking trajectories like rivers and coastlines in a traditional Cartesian coordinate system, a novel local curved‐dynamic coordinate system is constructed, and multiple referential points with given intervals on the curved coordinates are used as the consensus reference for the group. Then cooperative cruise of surface vessels is analyzed, based on which a local‐to‐global terminal sliding mode controller is designed to keep the relative pose of the dynamic unmanned vessels. At last, the formation trajectory constraint conditions are further discussed and some simulation results show the validity of the presented methods.     

基于极坐标的改进灰度积分投影法的人眼检测

为了克服传统灰度积分投影方法无法有效定位旋转人脸图像中人眼的缺点,提出了一种基于极坐标系的灰度积分投影方法。利用肤色特征对给定图像进行人脸区域的确定,在人脸区域内按极角方向进行灰度积分投影,确定出人眼所在角度,将人眼角度方向的像素灰度值做水平方向积分投影,从而确定出人眼的位置。该方法能够实现同一幅图像中多个不同姿态人脸的人眼定位。大量的仿真实验表明,该方法的识别性能对人脸的旋转变化具有良好的鲁棒性,能够提高灰度积分投影方法对人眼定位的适用范围。     

点阵测头成像视觉坐标测量系统的研究

柔性三维坐标测量在工业现场测量有较多应用.分析多目标点透视成像原理的基础上,提出了点阵测头成像视觉坐标测量的概念,给出系统完整的三种数学模型及求解方法.设计了一种实用测头,基于单台面阵CCD摄像机实现由三种类型测头组成的视觉测量样机.在距离摄像机1 000 mm,样机进行实际测量,并与三坐标测量机的检测结果进行比对.测试结果表明在摄像机成像面平行的两个方向的测量精度高于摄像机轴向测量精度.     

基于拉普拉斯网格变形的三维植物叶片建模

论文提出一种基于拉普拉斯网格变形的三维植物叶片交互式设计方法。该 方法以叶片轮廓及叶片主脉中轴点数据输入并生成网格曲面,通过拉普拉斯网格变形技术对 叶片的曲面网格进行交互式编辑。轮廓中轴数据点既可以通过三维数字化获得,也可以根据 叶脉形态计算得到。实验证明,该方法具有较好的普适性,变形计算快速,能够达到实时交 互设计的需要,所生成的叶片不仅能够很好地保持叶片的面积特征,同时在形态上具有较强 的真实感。