Least cost distance analysis for spatial interpolation

Spatial interpolation allows creation of continuous raster surfaces from a subsample of point-based measurements. Most interpolation approaches use Euclidean distance measurements between data points to generate predictions of values at unknown locations. However, there are many spatially distributed data sets that are not properly represented by Euclidean distances and require distance measures which represent their complex geographic connectivity. The problem of defining non-Euclidean distances between data points has been solved using the network-based solutions, but such techniques have historically relied on a network of connected line segments to determine point-to-point distances. While these vector-based solutions are computationally efficient, they cannot model more complex 2- and 3-dimensional systems of connectivity. Here, we use least-cost-path analyses to define distances between sampled points; a solution that allows for arbitrarily complex systems of connectivity to be interpolated. We used least-cost path distances in conjunction with the inverse distance weighting interpolation for a proof-of-concept interpolation of water temperature data in a complex deltaic river system. We compare our technique to Euclidean distance interpolation, and demonstrate that our technique, which follows connectivity rules, yields are more realistic interpolation of water temperature.     

基于误差控制的自适应3次B样条曲线插值

针对现有曲线插值算法不能有效压缩型值点的缺陷,研究了一种自适应三次B样条曲线插值算法。从型值点序列中选用最少的点插值一条初始曲线,基于提出的点到曲线的最小距离计算方法,分别计算各非插值点对应的插值误差,并从中提取最大插值误差。若最大误差大于给定的误差阈值,则将其对应的型值点加入插值型值点序列,重新插值曲线,直到最大插值误差满足误差要求。与现有曲线插值算法相比,该算法可以在保证插值精度的前提下有效压缩数据量。     

Adaptive-feedrate interpolation for parametric curves with a confined chord error

Recently, modern manufacturing systems have been designed which can machine arbitrary parametric curves while greatly reducing data communication between CAD/CAM and CNC systems. However, a constant feedrate and chord accuracy between two interpolated points along parametric curves are generally difficult to achieve due to the non-uniform map between curves and parameters. A speed-controlled interpolation algorithm with an adaptive feedrate is proposed in this paper. Since the chord error in interpolation depends on the curve speed and the radius of curvature, the feedrate in the proposed algorithm is automatically adjusted so that a specified limit on the chord error is met. Both simulation and experimental results for non-uniform rational B-spline (NURBS) examples are provided to verify the feasibility and precision of the proposed interpolation algorithm.     

Residual-based specification of a hidden random field included in a hierarchical spatial model

A method for specifying a hidden random field (HRF) included in a hierarchical spatial model is proposed. In hierarchical models of interest the first stage describes, conditional on a realization of the HRF, a response variable which is observable on a continuous spatial domain; the second stage models the HRF which reflects unobserved spatial heterogeneity. The question which is investigated is how can the HRF be modeled, i.e. specified. The method developed to address this question is based on residuals obtained when the base model, i.e. the hierarchical model in which the HRF is assumed constant, is fitted to data. It is shown that the residuals are linked with the HRF, and the link is used to specify the HRF. The method is applied to simulated data in order to assess its performance, and then to real data on radionuclide concentrations on Rongelap Island.     

Error analysis of the derivative of rational interpolation with a linear denominator

This paper deals with the approximation properties of the derivatives of rational cubic interpolation with a linear denominator. Error expressions of the derivatives of interpolating functions are derived, convergence is established and the optimal error coefficient c _i is proved to be symmetric about the parameters of the rational interpolation. The unified integral form of the error of the second derivative in all subintervals is obtained. A simple expression of the jump of the second derivative at the knots and the conditions for the interpolating function to be C ² in the interpolating interval are given.     

大规模数字高程模型的可视化研究

根据细节层次模型（LOD）的设计思想,提出了大规模数字高程模型的数据组织和可视化方法。该方法在数据分页算法和细节层次模型相结合的基础上,采用视区计算和边界融合算法,实现了地形的快速绘制。实验证明该方法实现了高性能绘制大规模数字高程模型。     

Hermite interpolation with a pair of spirals

The Hermite interpolation problem in the plane considered here is to join two points and to match given unit tangent vectors and signed curvatures at the two points with various G² curves consisting of a pair of spirals. The rotation of the tangent vector of the interpolating curve from one point to the other is restricted to being less than π. The necessary and sufficient conditions for the existence of each of the various curves are given.     

Statistical analysis of positioning error of a CNC milling machine

The characteristics of the positioning error of a NC milling machine were studied through statistical analysis. It was found that (1) the mean of the error is significantly affected by the table position, (2) the variances of the error at different table positions are from the same population, and (3) the effect of the feedrate on positioning error is not significant. Also, a software correction technique was applied and workpiece error was decreased by 40%.     

An adaptive mesh refinement of quadrilateral finite element meshes based upon an a posteriori error estimation of quantities of interest: modal response

Modal analysis is commonly performed in a vehicle development process to assess dynamic responses of structure designs. This paper presents an adaptive quadrilateral refinement process for modal analysis of elastic shells based upon a posteriori error estimation in natural frequencies. The process provides engineers with an estimation of their modal analysis quality and an effective adaptive refinement tool for quadrilateral meshes. The effectiveness of the process is demonstrated on the eigenvalue analyses of two numerical examples, a shock tower cap and a roof structure. It shows that the solution error in the frequency of interest is effectively reduced through the adaptive refinement process, and the resulting frequency of interest converges to the solution of a very fine model.     

Consistency and error analysis of Prior-Knowledge-Based Kernel Regression

Incorporating prior knowledge (PK) into learning methods is an effective means to improve learning performance. The consistency and error theories of PK-based methods, which are of great theoretical importance, are still far from well established. Concentrating on the PK-based kernel regression, this paper proposes a methodology of analyzing the consistency and error. This methodology converts the specific methods firstly to a unified optimization problem and then to a unified solution expression, and a general consistency and error analysis tool is proposed and applied. A few examples are given to illustrate the analysis procedure.     

Light mesh: soft shadows as interpolation of visibility

The light meshes (LM) method is a modification of the recursive ray tracing algorithm (RRTA). In this paper we consider an original procedure of shadow calculations, which allows soft shadows to be obtained. The light meshes method can be integrated easily into existing implementations of RRTA as a supplementary technique or plug-ins. In comparison with conventional RRTA the suggested technique allows us to: (a) build soft shadows, (b) speed up a process of shadow calculations, (c) simulate main effects of diffuse interreflections, (d) omit the ambient term. Obviously, visual results of the LM method differ slightly from those calculated with the help of the basic RRTA.

A light mesh is a point set in the 3D space of a scene. In practice, it is approximated by a finite set of points, as a rule, by evenly spaced grids. At each mesh point we compute illuminance, which characterizes some kind of “light field intensity” in the scene space. Then an important part of resulting illumination of a scene object point is obtained by the interpolation of the stored values of nearby mesh points.

Experiments show that the approach proposed reduces computational time with respect to the ray tracing algorithm if a scene contains a lot of light sources and/or an image has a large resolution.     

A distribution-free geometric upper bound for the probability of error of a minimum distance classifier

An upperbound to the probability of error per class in a multivariate pattern classification is derived. The bound, given by

$\text{P(E|class w}{}_{\mathrm{i}}\text{)≤}\text{N}\text{R}{}^2{}_{\mathrm{i}}$

is derived with minimal assumptions; specifically the mean vectors exist and are distinct and the covariance matrices exist and are non-singular. No other assumptions are made about the nature of the distributions of the classes. In equation (i) N is the number of features in the feature (vector) space and R_i is a measure of the “radial neighbourhood” of a class. An expression for R_i is developed. A comparison to the multivariate Gaussian hypothesis is presented.     

INTAMAP: The design and implementation of an interoperable automated interpolation web service

INTAMAP is a Web Processing Service for the automatic spatial interpolation of measured point data. Requirements were (i) using open standards for spatial data such as developed in the context of the Open Geospatial Consortium (OGC), (ii) using a suitable environment for statistical modelling and computation, and (iii) producing an integrated, open source solution. The system couples an open-source Web Processing Service (developed by 52°North), accepting data in the form of standardised XML documents (conforming to the OGC Observations and Measurements standard) with a computing back-end realised in the R statistical environment. The probability distribution of interpolation errors is encoded with UncertML, a markup language designed to encode uncertain data. Automatic interpolation needs to be useful for a wide range of applications and the algorithms have been designed to cope with anisotropy, extreme values, and data with known error distributions. Besides a fully automatic mode, the system can be used with different levels of user control over the interpolation process.     

Constrained surface interpolation by means of a genetic algorithm

We propose an evolutionary technique (a genetic algorithm) to solve heavily constrained optimization problems defined on interpolating tensor product surfaces by adjusting the parameter values associated with the data points to be interpolated. Throughout our study we assume that the functional, which operates on these types of interpolating surfaces, is described by a surface integral and fulfills the following conditions: it is not necessarily a smooth functional (i.e., it may have vanishing gradient vectors), it is bounded (i.e., the optimization algorithm can converge in a finite number of steps), it is invariant under parametrization, rigid body transformation and uniform scaling (i.e., different surface parametrization at different scales should generate the same optimized shape). We have successfully tested the proposed algorithm for functionals that involve: minimal surface area, minimal Willmore, umbilic deviation and total curvature energies, minimal third-order scale invariant weighted Mehlum–Tarrou energies, and isoperimetric like problems. In general, our algorithm can be used in the case of any kind of not necessarily smooth surface fairing functionals. The run-time and memory complexities of the suggested algorithm are reasonable. Moreover, the algorithm is independent of the type of tensor product surface.     

Relations between task and activity: elements for elaborating a framework for error analysis

The notion of error, when applied to an activity or the result of an activity, implies the notion of task: it expresses the deviation between the activity and the task being considered from an angle which is judged to be relevant. The task and the activity are the object of representations for the analyst (or specialist) and for the driver. Four representations are dealt with in this paper: the task and the activity for the specialist and the task and the activity for the driver. An interpretation is proposed for these tasks, and they are illustrated using some of the work already carried out in this field. The signification of deviations between these representations is then discussed, together with the advantage of studying these deviations in order to clarify error-producing mechanisms. Analysis in terms of task and activity raises methodological and practical problems which are touched upon; it does not exclude referring to psychological theoretical frameworks to which it is worthwhile linking it. This perspective raises questions which make it possible to enhance the study of errors: it could be completed at a later date by extending it to include other representation categories.     

Effect of differing DEM creation methods on the results from a hydrological model

It is known that digital elevation models (DEMs) can vary in quality depending on their method of creation. Six DEMs derived from digitised contours from the British Ordnance Survey were compared. The DEMs were used to run TOPMODEL for a small catchment in Devon. There were differences between the DEMs in the prediction of the catchment area and the spatial pattern of topographic index values, although these differences were reduced by smoothing the DEMs. Because runoff in the area is dominated by subsurface flow, many of the model predictions were not sensitive to differences between the DEMs. However, predictions of surface runoff differed by over 200%, and caused variations of up to 25% in the prediction of hourly flow values. The predicted spatial pattern of surface runoff was strongly affected by the presence of interpolation artefacts in the DEM, with completely unrealistic predictions in the case of the worst quality DEMs.     

Fair, G- and C-continuous circle splines for the interpolation of sparse data points

This paper presents a carefully chosen curve blending scheme between circles, which is based on angles, rather than point positions. The result is a class of circle splines that robustly produce fair-looking G²-continuous curves without any cusps or kinks, even through rather challenging, sparse sets of interpolation points. With a simple reparameterization the curves can also be made C²-continuous. The same method is usable in the plane, on the sphere, and in 3D space.     

液氨贮罐液位测量的误差分析及解决方案

本文通过一个具体的实例，详细分析了差压式液位测量系统的误差来源及其消除方法，提出了在DCS中充分利用现有仪表资源构建新型测量系统(软仪表)的基本思想。     

Identifying and comparing changes in the spatial concentrations of urban poverty and affluence: a case study of inner London

There is increasing interest, both academically and politically, in the spatial concentrations of poverty and affluence within cities. Although there has been a long history of research in this area, the majority of work has been concerned with poverty rather than affluence and has relied upon methods and measurement techniques that do not take into account the spatial concentrations of poverty. This research attempts to address this problem by measuring poverty and affluence using GIS and spatial statistical methods. By utilising contemporary census data and data collected by Charles Booth one hundred years ago, the research attempts to reveal the long-term changes in the spatial concentrations of poverty and affluence within inner London.     

Hydraulic head interpolation using anfis—model selection and sensitivity analysis

The aim of this study is to investigate the efficiency of anfis (adaptive neuro fuzzy inference system) for interpolating hydraulic head in a 40-km² agricultural watershed of the Seine basin (France). Inputs of anfis are Cartesian coordinates and the elevation of the ground. Hydraulic head was measured at 73 locations during a snapshot campaign on September 2009, which characterizes low-water-flow regime in the aquifer unit. The dataset was then split into three subsets using a square-based selection method: a calibration one (55%), a training one (27%), and a test one (18%).First, a method is proposed to select the best anfis model, which corresponds to a sensitivity analysis of anfis to the type and number of membership functions (MF). Triangular, Gaussian, general bell, and spline-based MF are used with 2, 3, 4, and 5 MF per input node. Performance criteria on the test subset are used to select the 5 best anfis models among 16. Then each is used to interpolate the hydraulic head distribution on a (50×50)-m grid, which is compared to the soil elevation. The cells where the hydraulic head is higher than the soil elevation are counted as “error cells.” The anfis model that exhibits the less “error cells” is selected as the best anfis model. The best model selection reveals that anfis models are very sensitive to the type and number of MF. Finally, a sensibility analysis of the best anfis model with four triangular MF is performed on the interpolation grid, which shows that anfis remains stable to error propagation with a higher sensitivity to soil elevation.