Let E⊂R2 be a finite set, and let f:E→0,∞). In this paper, we address the algorithmic aspects of nonnegative C2 interpolation in the plane. Specifically, we provide an efficient algorithm to compute ...a nonnegative C2(R2) extension of f with norm within a universal constant factor of the least possible. We also provide an efficient algorithm to approximate the trace norm.
Combined Global Surface Summary of Day and European Climate Assessment and Dataset daily meteorological data sets (around 9000 stations) were used to build spatio‐temporal geostatistical models and ...predict daily air temperature at ground resolution of 1 km for the global land mass. Predictions in space and time were made for the mean, maximum, and minimum temperatures using spatio‐temporal regression‐kriging with a time series of Moderate Resolution Imaging Spectroradiometer (MODIS) 8 day images, topographic layers (digital elevation model and topographic wetness index), and a geometric temperature trend as covariates. The accuracy of predicting daily temperatures was assessed using leave‐one‐out cross validation. To account for geographical point clustering of station data and get a more representative cross‐validation accuracy, predicted values were aggregated to blocks of land of size 500×500 km. Results show that the average accuracy for predicting mean, maximum, and minimum daily temperatures is root‐mean‐square error (RMSE) =±2°C for areas densely covered with stations and between ±2°C and ±4°C for areas with lower station density. The lowest prediction accuracy was observed at high altitudes (>1000 m) and in Antarctica with an RMSE around 6°C. The model and predictions were built for the year 2011 only, but the same methodology could be extended for the whole range of the MODIS land surface temperature images (2001 to today), i.e., to produce global archives of daily temperatures (a next‐generation http://WorldClim.org repository) and to feed various global environmental models.
Key Points
Global spatio‐temporal regression‐kriging daily temperature interpolation
Fitting of global spatio‐temporal models for the mean, maximum, and minimum temperatures
Time series of MODIS 8 day images as explanatory variables in regression part
Radar‐rain gauge merging techniques have been widely used to improve the applicability of radar and rain gauge rainfall estimates by combining their advantages, while partially overcoming their ...individual weaknesses. Despite significant research in this area, guidance on the suitability of and factors affecting merging techniques at the fine spatial‐temporal resolutions required for urban hydrological applications is still insufficient. In this paper, an in‐depth review of radar‐rain gauge merging techniques is conducted, with a focus on their potential for urban hydrological applications. An overview is first given of existing merging techniques and an application‐oriented categorization is proposed: (1) radar bias adjustment methods, (2) rain gauge interpolation methods using radar spatial association as additional information, and (3) radar‐rain gauge integration methods. A detailed review is given of studies focusing on the evaluation and intercomparison of merging methods, based upon which the most widely used and best performing techniques from each category are identified. These are mean field bias adjustment, kriging with external drift, and Bayesian merging. Climatological, operational, and methodological factors affecting merging performance are then reviewed and their relevance for urban applications discussed. Based on this review, conclusions on merging potential for urban applications are drawn and research gaps are identified, which should be addressed to provide further guidance on the use of merging techniques for urban hydrological applications.
Key Points
An in‐depth review of radar‐rain gauge merging methods is presented, which compiles much of the work undertaken in this area to date
It includes a categorization of methods, summary of merging intercomparison studies to date, and factors affecting merging performance
The potential and challenges of applying merging at the fine spatial‐temporal resolutions required for urban hydrology are discussed
Fast data search is an important element of big data in the modern era of internet of things, cloud computing, and social networks. Search using traditional binary-search algorithm can be accelerated ...by employing an interpolation search technique when the data is regularly distributed. In this work, the interpolation search is investigated in which the search results provided unexpected sluggish progress during a search in a large database due to the irregular distribution of data. Irregular distribution of data does not allow the interpolation to make a good prediction about the location of the search item. To overcome this issue, an interpolation–extrapolation search (IES) method is proposed where the interpolation method is integrated with an extrapolation method that balances the lower and upper bounds of the search interval. The proposed method provides faster convergence property than the binary search and the interpolation method. Hence, the proposed IES method provides a faster search for items in a big database.
A recently developed demosaicing methodology, called residual interpolation (RI), has demonstrated superior performance over the conventional color-component difference interpolation. However, it has ...been observed that the existing RI-based methods fail to fully exploit the potential of RI strategy on the reconstruction of the most important G channel, as only the R and B channels are restored through the RI strategy. Since any reconstruction error introduced in the G channel will be carried over into the demosaicing process of the other two channels, this makes the restoration of the G channel highly instrumental to the quality of the final demosaiced image. In this paper, a novel iterative RI (IRI) process is developed for reconstructing a highly accurate G channel first; in essence, it can be viewed as an iterative refinement process for the estimation of those missing pixel values on the G channel. The key novelty of the proposed IRI process is that all the three channels will mutually guide each other until a stopping criterion is met. Based on the restored G channel, the mosaiced R and B channels will be, respectively, reconstructed by exploiting the existing RI method without iteration. Extensive simulations conducted on two commonly-used test datasets for demosaicing algorithms have demonstrated that our algorithm has achieved the best performance in most cases, compared with the existing state-of-the-art demosaicing methods on both objective and subjective performance evaluations.
ABSTRACT
High‐resolution monthly precipitation climatologies for Italy are presented. They are based on 1961–1990 precipitation normals obtained from a quality‐controlled dataset of 6134 stations ...covering the Italian territory and part of the Northern neighbouring regions. The climatologies are computed by means of two interpolation methods modelling the precipitation‐elevation relationship at a local level, more precisely a local weighted linear regression (LWLR) and a local regression kriging (RK) are performed. For both methods, local optimisations are also applied in order to improve model performance. Model results are compared with those provided by two other widely used interpolation methods which do not consider elevation in modelling precipitation distribution: ordinary kriging and inverse distance weighting. Even though all the four models produce quite reasonable results, LWLR and RK show the best agreement with the observed station normals and leave‐one‐out‐estimated mean absolute errors ranging from 5.1 mm (July) to 11 mm (November) for both models. Their better performances are even clearer when specific clusters of stations (e.g. high‐elevation sites) are considered. Even though LWLR and RK provide very similar results both at station and at grid point level, they show some peculiar features. In particular, LWLR is found to have a better extrapolation ability at high‐elevation sites when data density is high enough, while RK is more robust in performing extrapolation over areas with complex orography and scarce data coverage, where LWLR may provide unrealistic precipitation values. However, by means of prediction intervals, LWLR provides a more straightforward approach to quantify the model uncertainty at any point of the study domain, which helps to identify the areas mainly affected by model instability. LWLR and RK high‐resolution climatologies exhibit a very heterogeneous and seasonal‐dependent precipitation distribution throughout the domain and allow to identify the main climatic zones of Italy.
The paper presents high‐resolution monthly precipitation climatologies for Italy. They are computed by means of two interpolation methods modelling the precipitation‐elevation relationship at a local level: local weighted linear regression (LWLR) and regression kriging (RK). The monthly errors turn out to range from 5 mm to 11 mm for both models. LWLR shows a better extrapolation ability at high‐elevated sites, while RK is preferable over areas with complex orography and scarce data coverage, where LWLR may provide unrealistic precipitation values.
G01 codes generated by CAM (Computer Aided Manufacturing) system are the most common form of tool path in CNC (Computer Numerical Control) machining. For the piecewise linear path, tangential and ...curvature discontinuities bring about large fluctuation of feedrate and acceleration, which produces vibration of machine tool. In recent studies, the methods for G2 (curvature-continuous) tool-path smoothing and jerk-limiting feedrate scheduling were developed. However there still exist the deficiencies when these methods are employed in CNC machining. It is difficult to simultaneously ensure that the tool path is chord-error-constrained and G01-point-interpolated in real time. In addition, heavy computational load hinders realtime processing in CNC system. Recently the scholars experimentally found the potential of G3 (curvature-smooth) trajectory and jerk-continuous motion in reducing the vibration of machinery. This work proposes a realtime tool-path smoothing algorithm, generating G3 interpolative tool path composed by mixed linear and quartic Bezier segments. The purpose of the smoothing scheme is the simultaneous considerations of G3 continuity, confined chord error, G01 points interpolated, and realtime performance. And the tool path generated is optimized in curvature variation energy (CVE) and analytical curvature extrema is available. To reduce the vibration, a high-efficient algorithm of jerk-continuous (JC) feedrate scheduling for G3 tool path is provided. Finally, a realtime tool-path processing scheme is developed, including G3 interpolation and motion planning functions. As shown in the simulation, the contour error, curvature of tool path, feedrate fluctuation and machining time are reduced compared with G2 transition scheme. The experiment on a machine tool is conducted to demonstrate the advantages of the proposed algorithm in vibration reduction and surface quality, compared with G2 transition scheme.
•The tool path is G01-point-interpolated and chord-error-constrained.•The tool path is G3, shape-preserving, curvature-extrema-analytical, CVE-optimized.•The realtime algorithm with JC motion planning can reduce feedrate fluctuation.•Method has advantages in reducing contour error and raising tool-path uniformity.•Method performs better in vibration reduction and surface quality than G2 transition.
In this paper, a new class of rational quadratic/linear trigonometric Hermite functions with two shape parameters is proposed. Based on these Hermite functions, new improved first class of Side-Side ...(FCSS), second class of Side-Side (SCSS), first class of Side-Vertex (FCSV) and second class of Side-Vertex (SCSV) interpolation operators are proposed respectively, which can be used to construct C.sup.1 Coons surfaces over triangular domain. By altering the values of two shape parameters, the shape of the Coons surface patch can be adjusted flexibly, but without affecting the function values and partial derivatives of the boundaries. For constructing the triangular surface patches with the center of mass passing through a fixed point, we also give a center of mass function value control method, by which we can solve the corresponding shape parameter values. Moreover, we also apply these four improved interpolation operators to image interpolation. Compared with some widely used image interpolation methods, our methods achieve competitive performance.
In this paper the fundamental concept of repeated linear interpolation and its possible applications in computer-aided geometric design, and start considering basic constructive methods for curves ...and surfaces. We discuss here a repeated linear interpolation method that we commonly find in computer graphics and geometric modelling. Repeated linear Interpolation means to calculate a polynomial by using several points. For a given sequence of points, this means to estimate a curve that passes through every single point. The purpose of this paper is to construct a polynomial of degree less than or equal to n, by using repeated linear Interpolation.
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