Search Results (4)

The complex analytic continuation can be developed to enable the Gauss-Krüger projection to be non-zonal and non-singular in polar regions. The series expansion of the traditional Gauss-Krüger projection in terms of third flattening has been derived by using a computer algebra system, leading to a substantial simplification of the final formulas without compromising accuracy compared with the series expansion in terms of eccentricity. Therefore, the non-zonal formulas of the Gauss-Krüger projection in term of third flattening have been expressed, and the non-zonal and the non-singular formulas of the Gauss-Krüger projection has been derived by the conformal colatitude. With respect to the mapping of 4 high-latitude regions (Finland, Sweden, Norway and Alaska) and its isopleth map, it was verified that the non-zonal and the non-singular algorithm of the Gauss-Krüger projection had high precision and minimal distortion in polar regions. The method presented a meaningful supplement to the existing Gauss–Krüger projection family. Full article

Electronic navigational charts (ENCs) are geospatial databases compiled in strict accordance with the technical specifications of the International Hydrographic Organization (IHO). Electronic Chart Display and Information System (ECDIS) is a Geographic Information System (GIS) operated by ENCs for real-time navigation at sea, which is one of the key technologies for intelligent ships to realize autonomous navigation, intelligent decision-making, and other functions. Facing the urgent demand for high-precision and real-time nautical chart products for polar navigation under the new situation, the projection of ENCs for polar navigation is systematically analyzed in this paper. Based on the theory of complex functions, we derive direct transformations of Mercator projection, polar Gauss-Krüger projection, and polar stereographic projection. A rational set of dynamic projection options oriented towards polar navigation is proposed with reference to existing specifications for the compilation of the ENCs. From the perspective of nautical users, rather than the GIS expert or professional cartographer, an ENCs visualization idea based on multithread-double buffering is integrated into Polar Region Electronic Navigational Charts software, which effectively solves the problem of large projection distortion in polar navigation applications. Taking the CGCS2000 reference ellipsoid as an example, the numerical analysis shows that the length distortion of the Mercator projection is less than 10% in the region up to 74°, but it is more than 80% at very high latitudes. The maximum distortion of the polar Gauss-Krüger projection does not exceed 10%. The degree of distortion of the polar stereographic projection is less than 1% above 79°. In addition, the computational errors of the direct conversion formulas do not exceed $10^{-9}$ m throughout the Arctic range. From the point of view of the computational efficiency of the direct conversion model, it takes no more than 0.1 s to compute nearly 8 million points at $1^{\prime }\times 1^{\prime }$ resolution, which fully meets the demand for real-time nautical chart products under information technology conditions. Full article

Compared with complex and lengthy Gauss-Krüger projection series expansions and real number expressions, we improve the complex function representation of Gauss-Krüger projections and rewrite them into the “multiple Angle form”, “exponential form”, and “double Angle form”. The coefficients were expanded in the power series based on the first eccentricity $e$ and the third flattening $n$, respectively, and the truncation difference was analyzed when expanded to different orders to obtain the simplified practical formulas for each form on the premise of meeting the accuracy requirements of geodesy. Through numerical analysis, the computational efficiency of the forward and inverse solutions of the Gauss-Krüger projection is analyzed, which shows the superiority of the “double Angle form”. Through the above measures, the expressions for forward and inverse solutions of the Gauss-Krüger projection are obtained, meeting the accuracy requirements with a higher computational efficiency and a more concise form. Full article

Obtaining the geographic coordinates of single fruit trees enables the variable rate application of agricultural production materials according to the growth differences of trees, which is of great significance to the precision management of citrus orchards. The traditional method of detecting and positioning fruit trees manually is time-consuming, labor-intensive, and inefficient. In order to obtain high-precision geographic coordinates of trees in a citrus orchard, this study proposes a method for citrus tree identification and coordinate extraction based on UAV remote sensing imagery and coordinate transformation. A high-precision orthophoto map of a citrus orchard was drawn from UAV remote sensing images. The YOLOv5 model was subsequently used to train the remote sensing dataset to efficiently identify the fruit trees and extract tree pixel coordinates from the orchard orthophoto map. According to the geographic information contained in the orthophoto map, the pixel coordinates were converted to UTM coordinates and the WGS84 coordinates of citrus trees were obtained using Gauss–Krüger inverse calculation. To simplify the coordinate conversion process and to improve the coordinate conversion efficiency, a coordinate conversion app was also developed to automatically implement the batch conversion of pixel coordinates to UTM coordinates and WGS84 coordinates. Results show that the Precision, Recall, and F1 Score for Scene 1 (after weeding) reach 0.89, 0.97, and 0.92, respectively; the Precision, Recall, and F1 Score for Scene 2 (before weeding) reach 0.91, 0.90 and 0.91, respectively. The accuracy of the orthophoto map generated using UAV remote sensing images is 0.15 m. The accuracy of converting pixel coordinates to UTM coordinates by the coordinate conversion app is reliable, and the accuracy of converting UTM coordinates to WGS84 coordinates is 0.01 m. The proposed method is capable of automatically obtaining the WGS84 coordinates of citrus trees with high precision. Full article