Demand High Precision Research Articles

Comparative Analysis of ANN and RSM for Optimizing Contact Area to Enhance Dimensional Accuracy in Material Processing

The study focuses on improving the production processes' dimensional accuracy for thick materials through the optimization of the area of contact during machining, forming, and additive manufacturing. The performance and dependability of components depend heavily on dimensional accuracy, especially in sectors like heavy machinery, automotive, and aerospace, which demand high precision. The research employs predictive modeling using machine learning algorithms and optimization techniques to determine the optimal contact area that minimizes deviations in final dimensions. The process parameters were modeled, predicted, and enhanced by the use of Response Surface Methodology (RSM) and Artificial Neural Networks (ANN). To design experiments, the central composite design is applied with machining trials conducted on a CNC machine. The results show that optimizing the contact area significantly improves stress distribution, reduces deformation risks, and enhances overall dimensional accuracy. Key findings include the validation of a quadratic model for predicting the area of contact, which demonstrated high statistical significance and predictive accuracy. The ANN model further corroborated these results, showing strong correlation and minimal error in predictions. The study offers a strong framework that producers can use to process thick materials more precisely and effectively by leveraging advanced modeling and optimization techniques.

Research on Stability of Removal Function in Figuring Process of Mandrel of X-Ray-Focusing Mirror with Variable Curvature

Over the past 30 years, researchers have developed X-ray-focusing telescopes by employing the principle of total reflection in thin metal films. The Wolter-I focusing mirror with variable-curvature surfaces demands high precision. However, there has been limited investigation into the removal mechanisms for variable-curvature X-ray mandrels, which are crucial for achieving the desired surface roughness and form accuracy, especially in reducing mid-spatial frequency (MSF) errors. It is essential to incorporate flexible control in deterministic small-tool polishing to improve the tool’s adaptability to curvature variations and achieve stable, Gaussian-like tool influence functions (TIFs). In this paper, we introduce a curvature-adaptive prediction model for compliance figuring, based on the Preston hypothesis, using a compliant shaping tool with high slurry absorption and retention capabilities. This model predicts the compliance figuring process of variable-curvature symmetrical mandrels for X-ray grazing incidence mirrors by utilizing planar tool influence functions. Initially, a variable-curvature pressure model was developed to account for the parabolic and hyperbolic optical surfaces’ curvature characteristics. By introducing time-varying removal functions for material removal, the model establishes a variable-curvature factor function, which correlates actual downward pressure with parameters such as contact radius and contact angle, thus linking the variable-curvature surface with a planar reference. Subsequently, through analysis of the residence time distribution across different TIF models, hierarchical filtering, and PSD distribution, real-time correction of the TIFs was achieved to enable customized variable-curvature polishing. Furthermore, by applying a time-varying deconvolution algorithm, multiple rounds of flexible polishing iterations were conducted on the mandrels of a rotationally symmetric variable-curvature optical component, and the experimental results demonstrate a significant improvement in form accuracy, surface quality, and the optical performance of the mirror.

Optimization strategy of computer numerical control machining process parameters in biomanufacturing mold

With the rapid development of biomanufacturing technology in the medical and pharmaceutical fields, the demand for high-precision and high-quality molds has surged. When Computer numerical control (CNC) machining biomanufacturing molds, the optimization of process parameters becomes the key to improve efficiency and quality. The purpose of this study is to explore the optimization strategy of CNC machining process parameters to achieve the best surface quality, dimensional accuracy and machining efficiency. Through literature review, the spindle speed, feed speed and cutting depth are selected as the key parameters, and the multi-objective optimization model is constructed by response surface method, which is solved by genetic algorithm. The experiment shows that the process parameters of CNC system in mold manufacturing are cutting speed 100 (m/min), feed rate 0.2 (mm/rev) and cutting depth 0.5 (mm), which will effectively reduce the manufacturing cost, and effectively control the alarm times within 35 times in different processing equipment, greatly reduce the risk. The optimization strategy can significantly improve the surface quality and productivity of the mold and reduce the cost. The comparative analysis verifies the effectiveness of the method, which provides new theoretical and technical support for CNC machining in the field of biomanufacturing.

Comparison of ArcFace and Dlib Performance in Face Recognition with Detection Using YOLOv8

This study compares the performance of ArcFace and Dlib models in face recognition with YOLOv8 used for face detection on a limited dataset. The evaluation used metrics such as accuracy, F1-score, recall, and precision. ArcFace, which employs the Additive Angular Margin Loss method, demonstrated superior performance with the highest accuracy of 0.90, precision of 0.90, recall of 1.00, and an F1-score of 0.95. Meanwhile, Dlib achieved an accuracy of 0.57, precision of 0.57, recall of 1.00, and an F1-score of 0.73. The aim of the study was to find the best model in terms of accuracy. ArcFace proved to be more accurate and suitable for applications requiring high reliability, such as advanced security systems, identity verification, and research that demands high precision in face recognition. Dlib, although less accurate, offers speed and simplicity, making it suitable for rapid prototyping and lightweight applications with limited resources. The results indicate that ArcFace outperforms in face recognition on limited datasets, while Dlib is more appropriate for simple applications requiring lightweight computation. This study provides guidance for developers in selecting the appropriate face recognition model to meet specific needs in both industry and research.

Overview of Artificial Neural Network-Based Solution for Ordinary and Partial Differential Equations by Feed Forward Method Using Python

In the modern era, models such as Neural Networks are increasingly used to deal with ordinary and partial differential equations (ODEs-PDEs) because of their related complexity. The main aim of the paper is to focus on Artificial Neural Networks as a method to solve these equations since it is possible to approximate complex nonlinear relationships with great accuracy and adaptively reduce computational costs, thus enhancing the accuracy of solutions within highly dimensional and nonlinear problems. The traditional methods are not applicable to partial differential equations due to the problem of nonlinearity and high dimensionality. However, the Feed Forward method implemented in Python is quite a powerful alternative that can easily approximate complicated functions and very well have a hold on nonlinear equations. This research paper contains differential equations as nonlinear and linear equations and Feed Forward neural network models for both solutions of ODEs and PDEs. Python enables the integration of AI-based algorithms for the enhancement of more accurate and efficient results. This work compares the existing solutions based on ANNs and further highlights the possible advantages of using ANNs in ordinary as well as complex differential equations problems. The results indicate that ANNs have immense potential for further developing computational algorithms applicable to solving ODEs and PDEs, particularly in real-time applications that demand high precision and adaptability.

Digital twin technology facilitates precision improvement in complex product assembly: A progressive deduction method of data-driven tolerance allocation

Advancements in aerospace technology have significantly increased the demands on assembly precision, particularly for large aircraft models. These developments require sub-millimeter precision to be achieved in assembly, posing new challenges for conventional tolerance allocation methods, which rely heavily on theoretical models and static simulations. To address these limitations, this paper proposes a digital twin system for online deduction of assembly tolerances (DTS-ODTA) using point cloud registration and free-form deformation (FFD). The proposed method includes three key innovations. First, a digital twin (DT)-based assembly process control framework supports the simulation of assembly deviations by integrating virtual and actual data. Second, a data-driven method models the actual surface shapes, ensuring synchronization between physical and digital states. Third, a progressive deduction strategy for tolerance allocation combines virtual and actual information, providing effective inputs for real-time assembly process control. This approach was validated through an industrial case study, achieving a prediction accuracy of 91.64 % for assembly precision and effectively preventing out-of-tolerance issues during product assembly. By promptly identifying and addressing potential assembly discrepancies, this method enhances the overall assembly quality and provides critical support for design decisions. In summary, this paper introduces a novel DT-based tolerance allocation method that shifts from traditional open-loop design to closed-loop control, thereby meeting the high precision demands of modern aerospace manufacturing.

A Review of Machine Tool Motorized Spindle Variable Pressure Preload Technology Research

High-precision spindles are a vital study topic because of the growing demand for highspeed, high-precision, reliable, and long-lasting machine tools. Bearing preload is the primary means of improving the accuracy of the spindle rotor system. This study aims to summarize the research results, systematically analyze and evaluate the machine tool motorized spindle variable pressure preload technology, and provide a scientific basis for the practical application of the motor spindle variable pressure preload technology. This study is an in-depth analysis of the basic principles of the electric spindle preloading technology, the study of its influence mechanism on the thermal deformation, stiffness, slewing error, and life of the spindle system, and a discussion of the current shortcomings in the field of spindle preloading to provide a reference for the subsequent optimization. In the spindle system, the performance of rolling bearings and the design of bearing preload have an important impact on the spindle's accuracy and stability. The traditional preload method has yet to meet the requirements of modern high-speed machine tools. Real-time controllable preload has become the new direction of development, but the current preload technology still has certain limitations and needs to be further improved. In the future, the spindle bearing variable pressure preload technology will be more efficient and intelligent.

Development and validation of 3D printed anthropomorphic head phantom with eccentric holes for medical LINAC quality assurance testing in stereotactic radiosurgery

Stereotactic Radiosurgery (SRS) for brain tumors using Medical Linear Accelerator (LINAC) demands high precision and accuracy. A specific Quality Assurance (QA) is essential for every patient undergoing SRS to protect nearby non-cancerous cells by ensuring that the X-ray beams are targeted according to tumor position. In this work, a water-filled generic anthropomorphic head phantom consisting of two removable parts with eccentric holes was developed using Additive Manufacturing (AM) process for performing QA in SRS. In the patient specific QA, the planned radiation dose using Treatment Planning System (TPS) was compared with the dose measured in the phantom. Also, the energy consistency of radiation beams was tested at 200 MU for different energy beams at the central and eccentric holes of the phantom using an ionization chamber. Experimentally examined results show that planned doses in TPS are reaching the target within a 5% deviation. The ratio of the dose delivered in the eccentric hole to the dose delivered to the central hole shows variations of less than 2% for the energy consistency test. The designed, low-cost water-filled anthropomorphic phantom is observed to improve positioning verification and accurate dosimetry of patient-specific QA in SRS treatment.

On-demand jetting of high-viscosity liquid by jet tube impact

The on-demand jetting of high-viscosity liquid has significant applications in fields such as electronic packaging and bioprinting. Conventional methods for high-viscosity liquid jetting often employ a needle propelling the liquid rapidly, which demands high precision in the manufacturing and assembly of the needle and nozzle, and can potentially damage biomaterials. In this study, a novel method utilizing jet tube impact for on-demand high-viscosity liquid jetting is proposed, leveraging the inherent inertia of the liquid to generate the pressure pulse necessary for on-demand jetting. This method reduces the precision requirements for the device, enables device simplification, and avoids harm to biomaterials. The feasibility of this approach for on-demand high-viscosity liquid jetting is validated through experiments, and by combining numerical simulations, the jetting mechanism is revealed and primary factors influencing jetting performance are investigated. It is found that the water hammer pressure wave induced by the liquid inertia during the sudden velocity change of the jet tube is the predominant driving force for jetting, and the peak pressure can exceed 1 MPa and the peak jet velocity can exceed 15 m/s. An increase in the jet tube impact velocity and an extension of the acceleration duration at the same impact velocity both lead to an increase in the pressure wave amplitude. In addition, a decrease in the liquid level height shortens the period of the pressure wave. These factors all have an influence on the jetting performance. This study provides a new insight and theoretical foundation for the on-demand high-viscosity liquid jetting.

Trajectory tracking PID passivity-based control of spacecraft formation flying around Sun-Earth L2 point in the port-Hamiltonian framework

Spacecraft formation flying for interferometric observations around the 2nd Lagrange point in the Sun-Earth system (SEL2) is currently focal point in deep space exploration research, which demands high precision in relative position control of spacecraft. This paper proposes the relative motion dynamics of satellite formations around the L2 point in the port-Hamiltonian framework, and establishes a high-precision nonlinear dynamics model. PID passivity-based control (PID-PBC) is widely used in engineering. However, existing methods of PID-PBC cannot address the trajectory tracking issues in port-Hamiltonian systems. Utilizing the contraction properties of the port-Hamiltonian system, this paper proposes the trajectory tracking PID-PBC (tPID-PBC) approach, effectively resolving trajectory tracking issues for formation dynamics around L2 point in port-Hamiltonian framework. The paper details explicit solutions of the Partial Differential Equations (PDE) for the tPID-PBC method and its controller structure, and references the trajectories of interferometric observation formations, to verify the method’s effectiveness through numerical simulation. The presented control approach is applicable across generic port-Hamiltonian systems, offering substantial theoretical value.

On the calculation of irregular solutions of the Schrödinger equation for non-spherical potentials with applications to metallic alloys

The irregular solutions of the stationary Schrödinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can greatly speed up calculations. Nevertheless, they are seldom considered in numerical treatments because of their divergent behavior at origin. This divergence demands high numerical precision that is difficult to achieve, particularly for non-spherical potentials which lead to different divergence rates in the coupled angular momentum channels. Based on an unconventional treatment of boundary conditions, an integral-equation method is here developed which is capable of dealing with this problem. The available precision is illustrated by electron-density calculations for NiTi in its monoclinic B19’ structure.

Analysis and comparison of the orbit determination accuracy of TianQin based on multiple ground-based measurements

TianQin project, a Chinese initiative in space gravitational wave detection, demands high precision in satellite orbit during both entry and scientific operations. As means of developmental maturation, ground-based measurements play a vital role in ensuring the smooth execution of TianQin satellite’s detection mission. This paper conducts a simulation analysis by utilizing various ground-based measurement data, including the China Deep Space Network (CDSN), S/Ka-band ranging system, and Satellite Laser Ranging (SLR). The main focus is to explore the distinctions in Precise Orbit Determination (POD) capabilities among different methods and to enhance POD accuracy through the integration of multiple techniques for TianQin satellites. The results indicate: (1) Leveraging a strategically positioned station distribution, CDSN stations offer extended observation time, averaging 17.3 h per satellite daily, compared to S/Ka’s 10.5 h. (2) In single-measurement POD scenarios, S/Ka proves superior, achieving accuracy better than 10 m and 0.4 mm s−1 for TianQin satellites with a 7-day orbit arc length. This superiority is attributed to its exceptional observational accuracy, outperforming CDSN’s 40 m and 2.2 mm s−1 for POD accuracy. (3) By integrating high-precision SLR data on the foundation of CDSN or S/Ka observations, the POD accuracy of TianQin satellites is further enhanced, despite the limited SLR data quantity.

High-Precision Drilling by Anchor-Drilling Robot Based on Hybrid Visual Servo Control in Coal Mine

Rock bolting is a commonly used method for stabilizing the surrounding rock in coal-mine roadways. It involves installing rock bolts after drilling, which penetrate unstable rock layers, binding loose rocks together, enhancing the stability of the surrounding rock, and controlling its deformation. Although recent progress in drilling and anchoring equipment has significantly enhanced the efficiency of roof support in coal mines and improved safety measures, how to deal with drilling rigs’ misalignment with the through-hole center remains a big issue, which may potentially compromise the quality of drilling and consequently affect the effectiveness of bolt support or even result in failure. To address this challenge, this article presents a robotic teleoperation system alongside a hybrid visual servo control strategy. Addressing the demand for high precision and efficiency in aligning the drilling rigs with the center of the drilling hole, a hybrid control strategy is introduced combining position-based and image-based visual servo control. The former facilitates an effective approach to the target area, while the latter ensures high-precision alignment with the center of the drilling hole. The robot teleoperation system employs the binocular vision measurement system to accurately determine the position and orientation of the drilling-hole center, which serves as the designated target position for the drilling rig. Leveraging the displacement and angle sensor information installed on each joint of the manipulator, the system utilizes the kinematic model of the manipulator to compute the spatial position of the end-effector. It dynamically adjusts the spatial pose of the end-effector in real time, aligning it with the target position relative to its current location. Additionally, it utilizes monocular vision information to fine-tune the movement speed and direction of the end-effector, ensuring rapid and precise alignment with the target drilling-hole center. Experimental results demonstrate that this method can control the maximum alignment error within 7 mm, significantly enhancing the alignment accuracy compared to manual control. Compared with the manual control method, the average error of this method is reduced by 41.2%, and the average duration is reduced by 4.3 s. This study paves a new path for high-precision drilling and anchoring of tunnel roofs, thereby improving the quality and efficiency of roof support while mitigating the challenges associated with significant errors and compromised safety during manual control processes.

Study on Dynamic Scanning Trajectory of Large Aerospace Parts Based on 3D Scanning

The aim of manufacturing large aerospace parts for the three-dimensional scanning field demands high precision and efficiency. However, it may be more challenging to meet the full coverage of the measurement problems for large aerospace parts with the scanning range of traditional three-dimensional scanning methods. This paper establishes a dynamic posturing scanning measurement system for large aerospace parts with a six-degree-of-freedom posturing platform and a six-degree-of-freedom industrial robot linkage. It establishes a mathematical model of dynamic three-dimensional scanning posturing. It proposes a platform attitude adjustment strategy based on the field of view angle of a 3D scanner during the adjustment of a six-degree-of-freedom platform. The dynamic scanning path planning is carried out using the three-dimensional spatial decomposition method, and the vector coordinates of the critical points at the edges of the missing areas of the scan are used to re-scan the missing areas to establish the dynamic scanning paths of large aerospace parts. It is experimentally verified that the system can realize the dynamic scanning of complex curved large aerospace parts. The experimental results show that the measurement efficiency is improved by more than 75%, and the point cloud coverage of the scanning reconstruction is improved by 18% for large aerospace components with complex surfaces.

Wideband PRM: Highly Accurate and Sensitive Method for High-Throughput Targeted Proteomics.

Targeted mass spectrometry (MS) approaches, which are powerful methods for uniquely and confidently quantifying a specific panel of proteins in complex biological samples, play a crucial role in validating and clinically translating protein biomarkers discovered through global proteomic profiling. Common targeted MS methods, such as multiple reaction monitoring (MRM) and parallel-reaction monitoring (PRM), employ specific mass spectrometric technologies to quantify protein levels by comparing the transitions of surrogate endogenous (ENDO) peptides with those of stable isotope-labeled (SIL) peptide counterparts. These methods utilizing amino acid analyzed (AAA) SIL peptides warrant sensitive and precise measurements required for targeted MS assays. Compared with MRM, PRM provides higher experimental throughput by simultaneously acquiring all transitions of the target peptides and thereby compensates for different ion suppressions among transitions of a target peptide. However, PRM still suffers different ion suppressions between ENDO and SIL peptides due to spray instability, as the ENDO and SIL peptides were monitored at different liquid chromatography (LC) retention times. Here we introduce a new targeted MS method, termed wideband PRM (WBPRM), that is designed for high-throughput targeted MS analysis. WBPRM employs a wide isolation window for simultaneous fragmentation of both ENDO and SIL peptides along with multiplexed single ion monitoring (SIM) scans for enhanced MS sensitivity of the target peptides. Compared with PRM, WBPRM was demonstrated to provide increased sensitivity, precision, and reproducibility of quantitative measurements of target peptides with increased throughput, allowing more target peptide measurements in a shortened experiment time. WBPRM is a straightforward adaptation to a manufacturer-provided MS method, making it an easily implementable technique, particularly in complex biological samples where the demand for higher precision, sensitivity, and efficiency is paramount.

CMOS Based Voltage Reference Designs for Sub - 1V

This review paper presents an analysis of the most recent advancements in sub-1V voltage references, addressing the growing demand for ultra-low power consumption and high precision in modern integrated circuits (ICs). Voltage references are critical components in numerous applications, including IoT devices, wearable electronics, and energy-harvesting systems, where power efficiency and accuracy are paramount. It briefly discusses the challenges associated with designing voltage references at such low voltages, such as limited headroom, reduced noise margin, and process variations. Topics include high-order curvature compensation, modified differential pair configurations, and energy-efficient solutions for integrated energy harvesting. These advancements enhance precision and reliability in low-voltage circuits, paving the way for sustainable, low-power electronics and compact devices in the modern digital landscape. It emphasizes the importance of benchmarking different designs against criteria such as power consumption, line regulation, temperature stability, and supply voltage rejection ratio (PSRR). The paper include insights into the state-of-the-art sub-1V voltage reference designs, identification of design trade-offs, and recommendations for future research directions. It underscores the importance of continuous innovation in voltage reference design to address the evolving requirements of ultra-low power electronics. The study here is setting the stage for a detailed analysis of the latest developments in sub-1V voltage references.

MHC-Fine: Fine-tuned AlphaFold for precise MHC-peptide complex prediction

The precise prediction of major histocompatibility complex (MHC)-peptide complex structures is pivotal for understanding cellular immune responses and advancing vaccine design. In this study, we enhanced AlphaFold’s capabilities by fine-tuning it with a specialized dataset consisting of exclusively high-resolution class I MHC-peptide crystal structures. This tailored approach aimed to address the generalist nature of AlphaFold’s original training, which, while broad-ranging, lacked the granularity necessary for the high-precision demands of class I MHC-peptide interaction prediction. A comparative analysis was conducted against the homology-modeling-based method Pandora as well as the AlphaFold multimer model. Our results demonstrate that our fine-tuned model outperforms others in terms of root-mean-square deviation (median value for Cα atoms for peptides is 0.66 Å) and also provides enhanced predicted local distance difference test scores, offering a more reliable assessment of the predicted structures. These advances have substantial implications for computational immunology, potentially accelerating the development of novel therapeutics and vaccines by providing a more precise computational lens through which to view MHC-peptide interactions.

Optimizing Precision: A Trajectory Tract Reference Approach to Minimize Complications in CT-Guided Transthoracic Core Biopsy.

The advent of computed tomography (CT)-guided transthoracic needle biopsy has significantly advanced the diagnosis of lung lesions, offering a minimally invasive approach to obtaining tissue samples. However, the technique is not without risks, including pneumothorax and hemorrhage, and it demands high precision to ensure diagnostic accuracy while minimizing complications. This study introduces the Laser Angle Guide Assembly (LAGA), a novel device designed to enhance the accuracy and safety of CT-guided lung biopsies. We retrospectively analyzed 322 CT-guided lung biopsy cases performed with LAGA at a single center over seven years, aiming to evaluate its effectiveness in improving diagnostic yield and reducing procedural risks. The study achieved a diagnostic success rate of 94.3%, with a significant reduction in the need for multiple needle passes, demonstrating a majority of biopsies successfully completed with a single pass. The incidence of pneumothorax stood at 11.1%, which is markedly lower than the reported averages, and only 0.3% of cases necessitated chest tube placement, underscoring the safety benefits of the LAGA system. These findings underscore the potential of LAGA to revolutionize CT-guided lung biopsies by enhancing procedural precision and safety, making it a valuable addition to the diagnostic arsenal against pulmonary lesions.

Enhanced accuracy through machine learning-based simultaneous evaluation: a case study of RBS analysis of multinary materials

We address the high accuracy and precision demands for analyzing large in situ or in operando spectral data sets. A dual-input artificial neural network (ANN) algorithm enables the compositional and depth-sensitive analysis of multinary materials by simultaneously evaluating spectra collected under multiple experimental conditions. To validate the developed algorithm, a case study was conducted analyzing complex Rutherford backscattering spectrometry (RBS) spectra collected in two scattering geometries. The dual-input ANN analysis excelled in providing a systematic analysis and precise results, showcasing its robustness in handling complex data and minimizing user bias. A comprehensive comparison with human supervision analysis and conventional single-input ANN analysis revealed a reduced susceptibility of the dual-input ANN analysis to inaccurately known setup parameters, a common challenge in material characterization. The developed multi-input approach can be extended to a wide range of analytical techniques, in which the combined analysis of measurements performed under different experimental conditions is beneficial for disentangling details of the material properties.

Dynamic Projection Method of Electronic Navigational Charts for Polar Navigation

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′×1′ resolution, which fully meets the demand for real-time nautical chart products under information technology conditions.