Combination of regional and global geoid models at continental scale: application to Iranian geoid

High precision geoid determination is a challenging task at the national scale. Many efforts have been conducted to determine precise geoid, locally or globally. Geoid models have different precision depending on the type of information and the strategy employed when calculating the models. This contribution addresses the challenging problem of combining different regional and global geoid models, possibly combined with the geometric geoid derived from GNSS/leveling observations. The ultimate goal of this combination is to improve the precision of the combined model. We employ fitting an appropriate geometric surface to the geoid heights and estimating its (co)variance components. The proposed functional model uses the least squares 2D bi-cubic spline approximation (LS-BICSA) theory, which approximates the geoid model using a 2D spline surface fitted to an arbitrary set of data points in the region. The spline surface consists of third- order polynomial pieces that are smoothly connected together, imposing some continuity conditions at their boundaries. In addition, the least-squares variance component estimation (LS- VCE) is used to estimate precise weights and correlation among different models. We apply this strategy to the combined adjustment of the high-degree global gravitational model EIGEN-6C4, the regional geoid model IRG2016, and the Iranian geometric geoid derived from GNSS/leveling data. The accuracy of the constructed surface is investigated with five randomly selected subsamples of check points. The optimal combination of the two geoid models along with the GNSS/leveling data shows a reduction of 21 mm (~20%) in the RMSE values of discrepancies at the check points.

Key-Point Interpolation: A Sparse Data Interpolation Algorithm based on B-splines

B-splines are widely used in the fields of reverse engineering and computer-aided design, due to their superior properties. Traditional B-spline surface interpolation algorithms usually assume regularity of the data distribution. In this paper, we introduce a novel B-spline surface interpolation algorithm: KPI, which can interpolate sparsely and non-uniformly distributed data points. As a two-stage algorithm, our method generates the dataset out of the sparse data using Kriging, and uses the proposed KPI (Key-Point Interpolation) method to generate the control points. Our algorithm can be extended to higher dimensional data interpolation, such as reconstructing dynamic surfaces. We apply the method to interpolating the temperature of Shanxi Province. The generated dynamic surface accurately interpolates the temperature data provided by the weather stations, and the preserved dynamic characteristics can be useful for meteorology studies.

Analysis of Temporal Characteristics of Burglary Crime

Social security order had generally stabilized, and various major criminal crimes had been effectively controlled, but the problem of burglary crime was very serious. Burglary crime had gradually shown the different characteristics from the past, making it increasingly difficult to control. Data of Burglary crime from 2015 to 2019 in Danyang City, Jiangsu Province, was collected. The main contents of the study included temporal trend analysis based on time series, temporal hotspot analysis based on Biharmonic Spline Surface Interpolation, and temporal correction analysis based on Time Period Probability. Characteristics of burglary cases in yearly scale, monthly scale, and daily scale were extracted in this paper. This study found that the burglary cases in Danyang showed different temporal distributions on different time scales. This study further enriched the spatio-temporal analysis methods of burglary crime, and put forward targeted and reliable suggestions for police departments.

A Review of T-Splines Surfaces

Background: Curved modeling technology is originated from the geometric lofting and designing of aircraft, automobiles, and ships. The control points of the traditional B-spline mesh should be placed regularly in rows and columns. A T-spline surface is a type of B-spline surface that allows T-junctions. It can overcome the limitations of traditional B-mesh topology and has its own advantages in surface splicing, surface fining, surface simplification, and so on. T-spline has wide application prospects in product modeling, art design, animation production, numerical control machining, volume data expression, and other aspects. Objective: The objective of this paper is to summarize the properties, algorithms, and applications of T-splines. It helps scholars in determining the research status of T-splines and further exploring the theories and applications of T-splines. Methods: This paper reviews the theories of T-splines and their applications from four aspects. First, we discuss the development of the concept, properties, algorithms, and reconstruction of the T-spline. Then, we conduct an isogeometric analysis using T-splines. Next, we demonstrate the applications of T-splines in actual scenarios. Finally, we present a brief summary of the paper and future expectations. Results: The paper provides a brief introduction of the relevant papers on T-splines. Currently, many studies have been carried out on theories and applications of T-spline. Among these, the spline theory on T-mesh has aroused widespread interest in engineering, especially in computer-aided geometric design (CAGD) and computer graphics. Conclusion: The T-spline surface is the most important new spline surface in the CADG field since the creation of the B-spline surface and non-uniform rational B-spline surface. Although the surface modeling technology based on the T-spline surface is developing rapidly, there are still some problems that need to be further studied.

Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

Development of Support System for Ship-Hull Plate Forming Using Laser Scanner

In this study, we developed a new system that outputs the additional press work procedures necessary to obtain the desired ship-hull surface. This study is unique in terms of determining the additional press work procedures required according to the current plate shape at any work stage by measuring the plate shape using a laser scanner. In the proposed method, a B-spline surface is constructed from a point cloud measured using a laser scanner, and the current plate shape is analyzed based on differential geometry. Additional press lines are estimated based on the difference in the normal curvature along the lines of curvature between the designed target surface and the current surface. We demonstrated the effectiveness of our proposed method through experiments at a shipyard. The proposed system may be used to enhance the efficiency of press work and is expected to be an effective tool for training beginners in the future.