Estimation of the Bezout number for piecewise algebraic curve

A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper.a coniecture on trianguation is confirmed The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented.By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method,an upper     

Smooth surface reconstruction via natural neighbour interpolation of distance functions

We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and accommodates non-uniform samples. The reconstructed surface interpolates the data points and is implicitly represented as the zero set of some pseudo-distance function. It can be meshed so as to satisfy a user-defined error bound, which makes the method especially relevant for small point sets. Experimental results are presented for surfaces in .     

Hamilton cycles in plane triangulations

We extend Whitney's Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely, we define a decomposition of a plane triangulation G into 4‐connected ‘pieces,’ and show that if each piece shares a triangle with at most three other pieces then G is hamiltonian. We provide an example to show that our hypothesis that each piece shares a triangle with at most three other pieces' cannot be weakened to ‘four other pieces.’ As part of our proof, we also obtain new results on Tutte cycles through specified vertices in planar graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 138–150, 2002     

On a proper acute triangulation of a polyhedral surface

Let Σ be a polyhedral surface in R³ with n edges. Let L be the length of the longest edge in Σ, δ be the minimum value of the geodesic distance from a vertex to an edge that is not incident to the vertex, and θ be the measure of the smallest face angle in Σ. We prove that Σ can be triangulated into at most CLn/(δθ) planar and rectilinear acute triangles, where C is an absolute constant.     

On the stretch factor of Delaunay triangulations of points in convex position

Let S be a finite set of points in the Euclidean plane. Let G be a geometric graph in the plane whose point set is S. The stretch factor of G is the maximum ratio, among all points p and q in S, of the length of the shortest path from p to q in G over the Euclidean distance |pq|. Keil and Gutwin in 1989 [11] proved that the stretch factor of the Delaunay triangulation of a set of points S in the plane is at most 2π/(3cos(π/6))≈2.42. Improving on this upper bound remains an intriguing open problem in computational geometry.In this paper we consider the special case when the points in S are in convex position. We prove that in this case the stretch factor of the Delaunay triangulation of S is at most ρ=2.33.     

On plane geometric spanners: A survey and open problems

Given a weighted graph $G=(V,E)$ and a real number $t?1$, a t-spanner of G is a spanning subgraph $G^{\prime }$ with the property that for every edge xy in G, there exists a path between x and y in $G^{\prime }$ whose weight is no more than t times the weight of the edge xy. We review results and present open problems on different variants of the problem of constructing plane geometric t-spanners.     

Estimating a Nonstationary Spatial Structure Using Simulated Annealing

During the past decade, a useful model for nonstationary random fields has been developed. This consists of reducing the random field of interest to isotropy via a bijective bi-continuous deformation of the index space. Then the problem consists of estimating this space deformation together with the isotropic correlation in the deformed index space. We propose to estimate both this space deformation and this isotropic correlation using a constrained continuous version of the simulated annealing for a Metropolis-Hastings dynamic. This method provides a nonparametric estimation of the deformation which has the required property to be bijective; so far, the previous nonparametric methods do not guarantee this property. We illustrate our work with two examples, one concerning a precipitation dataset. We also give one idea of how spatial prediction should proceed in the new coordinate space.     

结构现场可调的点激光精密测量系统

为了实现激光传感器测头可以根据现场条件来实时改变入射角度,建立了结构可调的点激光测量系统。建立了相机的针孔模型,利用张正友标定算法得到该相机模型的内部参数,定义点激光测量系统中的光心角,推导出利用像点坐标和相机内部参数实时求取光心角公式。建立了点激光测量系统的数学模型,引入点激光测量系统的结构参数:基线距和基准角,利用零平面和两个基准面标定系统结构参数。利用标定得到的系统结构参数进行实时的逆向工程在线测量。实验结果表明:测量系统量程为75mm时,该标定算法最大标定误差≤0.02mm,点激光测量系统的测量误差≤0.06mm,达到精密测量的要求。     

一种基于光学三角法的形貌测量系统

提出了一种基于光学三角原理的物体形貌测量方法。从理论上推导出了被测点的相对高度与像点距离的线性公式,通过这个公式可以由像点距离计算出被测点的高度。在实际的测量系统中,通过工作台的精确位移和像点的移动距离可标定出线性公式中的未知系数。把被测物体放在工作台上,先测出被测点的像的相对位移,然后再通过公式计算出被测点相对屏幕的距离。试验中测量了一个圆柱体上的一些点的三维坐标,通过这些数据绘出了圆柱体的三维形貌。