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.

An Adaptive Surface Interpolation Filter Using Cloth Simulation and Relief Amplitude for Airborne Laser Scanning Data

Separating point clouds into ground and nonground points is an essential step in the processing of airborne laser scanning (ALS) data for various applications. Interpolation-based filtering algorithms have been commonly used for filtering ALS point cloud data. However, most conventional interpolation-based algorithms have exhibited a drawback in terms of retaining abrupt terrain characteristics, resulting in poor algorithmic precision in these regions. To overcome this drawback, this paper proposes an improved adaptive surface interpolation filter with a multilevel hierarchy by using a cloth simulation and relief amplitude. This method uses three hierarchy levels of provisional digital elevation model (DEM) raster surfaces with thin plate spline (TPS) interpolation to separate ground points from unclassified points based on adaptive residual thresholds. A cloth simulation algorithm is adopted to generate sufficient effective initial ground seeds for constructing topographic surfaces with high quality. Residual thresholds are adaptively constructed by the relief amplitude of the examined area to capture complex landscape characteristics during the classification process. Fifteen samples from the International Society for Photogrammetry and Remote Sensing (ISPRS) commission are used to assess the performance of the proposed algorithm. The experimental results indicate that the proposed method can produce satisfying results in both flat areas and steep areas. In a comparison with other approaches, this method demonstrates its superior performance in terms of filtering results with the lowest omission error rate; in particular, the proposed approach retains discontinuous terrain features with steep slopes and terraces.

Near-to-Far Field Transformation in FDTD: A Comparative Study of Different Interpolation Approaches

Equivalence theorems in electromagnetic field theory stipulate that farfield radiation pattern/scattering profile of a source/scatterer can be evaluated from fictitious electric and magnetic surface currents on an equivalent imaginary surface enclosing the source/scatterer. These surface currents are in turn calculated from tangential (to the equivalent surface) magnetic and electric fields, respectively. However, due to the staggered-in-space placement of electric and magnetic fields in FDTD Yee cell, selection of a single equivalent surface harboring both tangential electric and magnetic fields is not feasible. The work-around is to select a closed surface with tangential electric (or magnetic) fields and interpolate the neighboring magnetic (or electric) fields to bring approximate magnetic (or electric) fields onto the same surface. Interpolation schemes available in the literature include averaging, geometric mean and the mixed-surface approach. In this work, we compare FDTD farfield scattering profiles of a dielectric cube calculated from surface currents that are obtained using various interpolation techniques. The results are benchmarked with those obtained from integral equation solvers available in the commercial packages FEKO and HFSS.

FRACTAL SURFACE INTERPOLATION BASED ON CLASSICAL SUBDIVISION SCHEMES

A method to create a differentiable complex shapes from simple polygonal models is proposed. It is shown that classical schemes of “smooth” subdivision can be obtained from local self-similarity ratios if “deflection arrows” are scaled as s2, where s is the linear compression coefficient calculated for a flat regular grid of the same structure. The surfaces obtained by a smooth subdivision do not contain sharp features other than the vertices and edges of the original model, so in order to create a surface of more exotic shape one must use more complex model. The article describes an alternative approach, in which a fractal forecast of the position of embedded vertices, calculated using the local geometric self-similarity ratio, is used to obtain a pronounced surface shape. Fractal forecast transfers the properties of the original polygonal model to a smaller scale, thereby generating secondary sharp surface features that compose a large-scale texture. To ensure the differentiability of the surface, the fractal forecast is combined with the “smooth” one, and the proportion of the latter increases with decreasing scale.