Background: Many different methods are applied for radon mapping depending on the purpose of the map and the data that are available. In addition, the definitions of radon priority areas (RPA) in EU Member States, as requested in the new European EURATOM BSS (1), are diverse. Objective: 1) Comparison of methods for mapping geogenic and indoor radon, 2) the possible transferability of a mapping method developed in one region to other regions and 3) the evaluation of the impact of different mapping methods on the delineation of RPAs. Design: Different mapping methods and several RPA definitions were applied to the same data sets from six municipalities in Austria and Cantabria, Spain. Results: Some mapping methods revealed a satisfying degree of agreement, but relevant differences were also observed. The chosen threshold for RPA classification has a major impact, depending on the level of radon concentration in the area. The resulting maps were compared regarding the spatial estimates and the delinea- tion of RPAs. Conclusions: Not every mapping method is suitable for every available data set. Data robustness and harmon- isation are the main requirements, especially if the used data set is not designed for a specific technique. Different mapping methods often deliver similar results in RPA classification. The definition of thresholds for the classification and delineation of RPAs is a guidance factor in the mapping process and is as relevant as harmonising mapping methods depending on the radon levels in the area.

This paper proposes a new methodology for the interpolation of a given set of 3D rotation poses that have to be reached in successive times by preserving continuity in orientation, angular velocity and angular acceleration. The discussed algorithm ensures the generation of smooth angular trajectories without singularities. The distinctive features of the proposed approach are the straightforward formulation, the reduced computational burden and the lack of iterative procedures. The presented methodology has applications in the generation of spatial motion of mechanical systems (e.g. robotics, flying devices) or in 3D computer graphics. After a theoretical introduction, the proposed algorithm is compared with other methods available in literature and some possible applications are presented.

Exposure indices are significant quantities in the assessment of human exposure to electromagnetic fields, especially in the work environment, because they consider both the field spectrum and the frequency dependency of regulatory limits. Some measurement instruments available on the market allow to measure these indices, by expressing them as a percentage or unit value. In many situations, a parameter that allows to characterize the exposure and give synthetic and effective indications on risk assessment and risk reduction is the respect distance, i.e. the distance from the source beyond which the exposure index considered is less than 100% (or unity, depending on adopted standardization ). This definition implicitly assumes that a reference direction has been chosen so that, moving away from the source along it, the intensity of the exposure decreases with the distance itself. This work describes how the respect distance could be determined starting from exposure index measurements, thanks to a flexible interpolation method to be used in combination with different source models and that allows to propagate the uncertainty of each measurement on the result of the interpolation and therefore determine the uncertainty related to the respect distance.

The investigation of form and processes in geomorphology and ecology is highly dependent on topographic data: a reliable digital terrain representation is in fact a key issue across environmental and earth sciences. In many cases, the processing of high-resolution topographic data (e.g., light detection and ranging (LiDAR), structure from motion) has to face issues such as void filling, vegetation/feature removal and interpolation accuracy that are usually related to (i) intrinsic limitations of the adopted technology, (ii) local conditions affecting the survey or (iii) specific design scenario. In this paper, we develop a methodology to test the accuracy of an image inpainting algorithm to fill data voids in complex mountain areas. The devised experiment exploits the availability of a high-resolution, LiDAR-derived digital terrain model and the inpainting approach accuracy is checked against some widely used interpolation techniques (natural neighbor, spline, inverse distance weighting, kriging). In order to better mimic the actual surface texture, a methodology to introduce local topographic variability to the interpolated surface is also presented. The results show a better performance of the inpainting algorithm especially in the case of complex and rugged topography. Two examples showing an effective usage and accuracy of the proposed technique are reported, highlighting the drawbacks that a poor surface representation can introduce. The whole procedure is made freely available within a Matlab (R) script with the addition of sample files. (c) 2019 John Wiley & Sons, Ltd. (c) 2020 John Wiley & Sons, Ltd.

The 1981-2010 monthly precipitation climatologies for Norway at 1 km resolution are presented. They are computed by an interpolation procedure (HCLIM+RK) combining the output from a numerical model with the in situ observations. Specifically, the regional climate model data set HCLIM-AROME, based on the dynamical downscaling of the global ERA-Interim reanalysis onto 2.5 km resolution, is considered together with 2009 rain-gauges located within the model domain. The precipitation climatologies are defined by superimposing the grid of 1981-2010 monthly normals from the numerical model and the kriging interpolation of station residuals. The combined approach aims at improving the quality of gridded climatologies and at providing reliable precipitation gradients also over those remote Norwegian regions not covered by observations, especially over the northernmost mountainous areas. The integration of rain-gauge data greatly reduces the original HCLIM-AROME biases. The HCLIM+RK errors obtained from the leave-one-out station validation turn out to be lower than those provided by two considered interpolation schemes based on observations only: a multi-linear local regression kriging (MLRK) and a local weighted linear regression (LWLR). As average over all months, the mean absolute (percentage) error is 10.0 mm (11%) for HCLIM+RK, and 11.4 (12%) and 11.6 mm (12%) for MLRK and LWLR, respectively. In addition, by comparing the results at both station and grid cell level, the accuracy of MLRK and LWLR is more sensitive to the spatial variability of station distribution over the domain and their interpolated fields are more affected by discontinuities and outliers, especially over those areas not covered by the rain-gauge network. The obtained HCLIM+RK climatologies clearly depict the main west-to-east gradient occurring from the orographic precipitation regime of the coast to the more continental climate of the inland and it allows to point out the features of the climatic subzones of Norway.

The result addresses the control software devoted to piloting Additive manufacturing machine with Multi-material single screw extruder for the realisation of personalised Movement Assistive Devices (MADs) The control software is a PC-based application suite and it consists of several software modules cooperating for the control of the whole manufacturing process: oA Rhino-script processing data from Rhinoceros CAD to deliver dedicated MAD CAM has been realized. oAn GUI with HMI functions for governing the various steps for logical sequencing (file import and machine configuration), processing (printing session configuration) and session launch oA logic control module, in charge of performing the handling of machine logic control (auxiliaries system, safety, thermal management) oA Numeric Control kernel of algorithms in charge of the interpolation of six-axes (linear X-Y-Z axes + A-B-C rotary axes) together with the extruder (interpolated as 7th axis) has been totally developed in C/C++ using open LINUX RTAI OS, IGH EtherCAT master.

This paper presents a software package for the automatic processing of bioclimatic data in the space and time domains whose final goal is to provide land and water management authorities with reliable information about the moisture/dryness level of a region and its water requirements. The current state of development of package is reported, presenting an example of application of the program to a specific case study.

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 5.1mm (July) to 11mm (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.

Wind speed and direction are fundamental data in many fields such as power generation, and hydrological modeling. Within the hydrological domain, among other uses, wind data are used to compute evapotranspiration and correct precipitation measurement. Wind measurements are sparse, hence spatial interpolation of wind data is required. In mountainous area with complex topography, accurate interpolation of wind data should consider topographic effects. The wind field can be generated by several methods, including: 1) applying a physically based, full atmospheric model which satisfy all relevant momentum and continuity equations, 2) applying an atmospheric model in which1only mass continuity is satisfied, 3) interpolation using wind-speed and direction observations in conjunction with empirical wind-topography relationships. Due to computational constraints, methods 1 and 2 can not be applied for long time simulations like the ones required for assessing climate change impacts. The aim of this work is to compare different techniques to interpolate wind speed in a complex topography area. The subject area is the upper Po River basin and covers 38000 km2. This is predominantly an alpine region located in Northern Italy that is bounded on three sides by mountain chains covering 73% of its territory. Impact of wind data interpolation accuracy is assessed by running the FEST-WB model (Flash Flood Event based Spatially distributed rainfall runoff Transformation, including Water Balance), a spatially distributed model that computes the main processes of the hydrological cycle: evapotranspiration, infiltration, surface runoff, flow routing, subsurface flow, and snow melt and accumulation. Results show that the use of empirical methods based on wind-topography relationships provide good accuracy for river basin hydrological analysis at a fraction of the computational cost required by physically based atmospheric models.

We consider here the problem of constructing a general recursive algorithm to interpolate a given set of data with a rational function. While many algorithms of this kind already exists, they are either providing non minimal-degree solutions (like the Schur algorithm), or exhibit jumps in the degree of the interpolants (or of the partial real- ization, as the problem is called when the interpolation is at infinity, see Rissanen [10] and Gragg-Lindquist [5]). By imbedding the solu- tion into a larger set of interpolants, we show that the increase in the degree of this representation always equals the increase in the length of the data. We provide an algorithm to interpolate multivariable tan- gential sets of data with arbitrary nodes, generalising in a fundamental manner the results of Kuijper in [8].

A collection of MATLAB software to simulate: - multirobot systems behaviours (motion coordination and rendering using Robotic Toolbox) - inverse kinematic algorithms - interpolation algorithms - accuracy error propagation

Sparse phase measurements often need to be interpolated on regular grids, to extend the information to unsampled locations. Typical cases involve the removal of atmospheric phase screen information from Interferometric Synthetic Aperture Radar (InSAR) stacks, or the retrieval of displacement information over extended areas in Persistent Scatterers Interferometry (PSI) applications, when sufficient point densities are available. This operation is usually done after a phase unwrapping (PU) of the sparse measurements to remove the sharp phase discontinuities due to the wrap operation. PU is a difficult and error-prone operation, especially for sparse data. In this work, we investigate from the empirical point of view an alternative procedure, which involves an interpolation of the complex field derived from the sparse phase measurements. Unlike traditional approaches, our method allows to bypass the PU step and obtain a regular-grid complex field from which a wrapped phase field can be extracted. Under general conditions, this can be shown to be a good approximation of the original phase without noise. Moreover, the interpolated, wrapped phase field can be fed to state-of-the-art, regular-grid PU algorithms, to obtain an improved absolute phase field, compared to the canonical method consisting of first unwrapping the sparse-grid data. We evaluate the performance of the method in simulation, comparing it to the classical methodology described above, as well as to an alternative procedure, recently proposed, to reduce a sparse PU problem to a regular-grid one, through a nearest-neighbor interpolation step. Results confirm the increased robustness of the proposed method with respect to the effects of noise and undersampling.

The aim of this paper is to provide a fast method, with a good quality of reproduction, to recover functions from very large and irregularly scattered samples of noisy data, which may present outliers. To the given sample of size N, we associate a uniform grid and, around each grid point, we condense the local information given by the noisy data by a suitable estimator. The recovering is then performed by a stable interpolation based on isotropic polyharmonic B-splines. Due to the good approximation rate, we need only M\lt N degrees of freedom to recover the phenomenon faiythully.

We propose an adaptive local procedure, which uses the modified Shepard's method with local polyharmonic interpolants. The aim is to reconstruct, in a faithful way, a function known by a large and highly irregularly distributed sample. Such a problem is generally related to the recovering of geophysical surfaces, where the sample is measured according to the behaviour of the surface. The adaptive local procedure is used to calculate, by an efficient algorithm, an interpolating polyharmonic function, when a very large sample is assigned. When we consider a sample of size $N<10^4$, we propose an approximating polyharmonic function obtained by combining adaptively a global interpolant, relevant to a subset of the data, with local adaptive interpolants. The goodness of the approximating functions in two different cases is shown by real examples.

Interferometric synthetic aperture radar processing requires interpolating a slave image onto a master one. Since the signals requiring interpolation are limited in both time and bandwidth, the Knab sampling window provides an almost optimal and viable interpolation kernel. Its performance in terms of coherence preservation and interferometric phase error as a function of the number of retained samples and oversampling factor are shown.

In this note we shall present some problems about fitting scattered data in 2d from regular functions, and that, in our opinion, have to be studied more in depth.