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An online template attack (OTA) is a powerful technique previously used to attack elliptic curve scalar multiplication algorithms. This attack has only been analyzed in the realm of power consumption and EM side channels, where the signals leak related to the value being processed. However, microarchitecture signals have no such feature, invalidating some assumptions from previous OTA works. In this paper, we revisit previous OTA descriptions, proposing a generic framework and evaluation metrics for any side-channel signal. Our analysis reveals OTA features not previously considered, increasing its application scenarios and requiring a fresh countermeasure analysis to prevent it. In this regard, we demonstrate that OTAs can work in the backward direction, allowing to mount an augmented projective coordinates attack with respect to the proposal by Naccache, Smart and Stern (Eurocrypt 2004). This demonstrates that randomizing the initial targeted algorithm state does not prevent the attack as believed in previous works. We analyze three libraries libgcrypt, mbedTLS, and wolfSSL using two microarchitecture side channels. For the libgcrypt case, we target its EdDSA implementation using Curve25519 twist curve. We obtain similar results for mbedTLS and wolfSSL with curve secp256r1. For each library, we execute extensive attack instances that are able to recover the complete scalar in all cases using a single trace. This work demonstrates that microarchitecture online template attacks are also very powerful in this scenario, recovering secret information without knowing a leakage model. This highlights the importance of developing secure-by-default implementations, instead of fix-on-demand ones. publishedVersion

Machine Learning techniques have proven effective in Side Channel Analysis (SCA), enabling multiple improvements over the already-established profiling process of Template Attacks. Focusing on the need to mitigate their impact on embedded devices, a design model and strategy is proposed that can effectively be used as a backbone for introducing SCA countermeasures on Elliptic Curve Cryptography (ECC) scalar multipliers. The proposed design strategy is based on the decomposition of the round calculations of the Montgomery Power Ladder (MPL) algorithm and the Scalar Multiplication (SM) algorithm into the underlined finite field operations, and their restructuring into parallel-processed operation sets. Having as a basis the proposed design strategy, we showcase how advanced SCA countermeasures can be easily introduced, focusing on randomizing the projective coordinates of the MPL round’s ECC point results. To evaluate the design approach and its SCA countermeasures, several simple ML-based SCAs are performed, and an attack roadmap is provided. The proposed roadmap assumes attackers that do not have access to a huge number of leakage traces, and that have limited resources with which to mount Deep Learning attacks. The trained models’ performance reveals a high level of resistance against ML-based SCAs when including SCA countermeasures in the proposed design strategy.

The public key cryptographic algorithms considered unsuitable for Internet of Things due to use of longer keys, stressful calculations and consumption of battery resources for 16bit processers. This paper presents a novel algorithm based on elliptical curve for securing communication between internet of things by use of single coordinate system of Elliptical curve cryptography. Though lengdre symbol or single coordinate system exist in mathematics literature, it’s use for securing IoT devices is fairly new. In the proposed system IoT device transfer one coordinate of public key with extra bit allowing to save 50 % of bandwidth and storage for IoT devices.

In the traditional cultural relic image digital repair system, there are obvious color aberrations and structural deviations between the restored part and the surrounding part, which weakens the visual connectivity of the restored result. In view of this, this research designs a digital repair system of damaged cultural relics image in professional training of restoration. In the hardware of the system, an integrated fast spherical camera is designed, and the transformation between image and pixel coordinate system is expressed by homogeneous coordinate system according to its parameters. In the system software, the damaged areas of cultural relics images are segmented and marked first, and the optimization algorithm of texture synthesis and restoration based on samples is designed. The experimental test results show that the system in this paper can ensure the use of the known information of the original image to the greatest extent, and make the repair result more reasonable on the basis of the minimum modification of the original image, so as to achieve the effect of professional practical training of repair.

An analysis is presented to the study, the proficient implementation of ancient mathematics formulae for multiplications and squares in the cryptographic system. In this approach, we have used ancient mathematics techniques and algorithms in the different projective coordinates system (Jacobian, Chudnovsky-Jacobian, Modified Jacobian coordinates system) to get minimum steps in the calculation of addition algorithm, doubling algorithm and for improving the speed of processing time in the operations of ECC (points addition, points doubling). The coding and synthesis are done in MATLAB for 16-bit digit multiplications and squares. The results proved that the Vedic mathematics-based scheme shows better performance compared to the conventional method and total delay in computation is reduced by Vedic mathematics Sutras (Urdhva-tiryagbhyam, Dvandva-yoga). The results of some AVIM techniques over ECC were obtained and discussed in the form of tables and graphs.

As the payload of the reconnaissance aircraft, the positioning accuracy of the airborne photoelectric platform is the key to whether the weapon can achieve accurate strike and whether the battlefield information can be obtained accurately. This paper introduces the structure of the photoelectric measurement pod, establishes the auxiliary coordinate system of the positioning model. According to the homogeneous coordinate transformation method, rotates and transforms the parallax vector of two machines into the unified coordinate system, and completes the solution of the target according to the principle of space intersection. Combined with the disadvantages of traditional rendezvous positioning algorithm, an improved algorithm is proposed. Based on the model, the error factors affecting the positioning accuracy are determined, which provides theoretical guidance for engineering application. The simulation results show that the improved algorithm is better than the traditional algorithm.

Based on Montgomery modular multiplication structure, this paper proposed and realized SM2 algorithm core module for IC cards, that is, scalar multiplication hardware structure of elliptic curves in prime field. Modular addition operation was improved so as to gain faster operation and anti-SPA capacity. Point addition and multiple point algorithm of Jacobi projective coordinates and Montgomery modular inversion algorithm were adopted in the structure. Experimental results indicated that, the structure had better performance and met the specific design indicators of the IC cards. Contact IC card communication protocol module (ISO7816 Protocol) was designed, and serving as the interface, it was tested by the contact IC card reader. In previous scalar multiplication designs, designers tended to focus on certain performance improvement of scalar multiplication, rather than a fixed product. This paper designed scalar multiplication encryption module, which was specific to the design of the interface of the contact IC cards widely used in life, so as to make the IC cards work more effectively.

The work presents an elliptic curve crypto accelerator to implement scalar multiplication on standardized NIST curve over Galois binary fields by using polynomial basis. The proposed design provides efficient hardware utilization and low power consumption. For this purpose, hybrid finite field multiplier is proposed using standard Karatsuba multiplier and shlft-and-add multiplication algorithms. The proposed hybrid finite field multiplier can perform one finite field multiplication in $\frac{m}{2}$ clock cycles, with m being the key-length. Montgomery algorithm with projective coordinates (LopezDahab) is used for the computation of scalar multiplication. An FSM based control unit is developed, governing the overall operations of proposed accelerator. The proposed architecture has been modeled in Verilog-HDL and implemented up to place and route level using the Xilinx Vivado and ISE design software for various FPGA devices. The achieved results demonstrate the convenience of proposed ECC accelerator for resource constrained embedded systems applications requiring low area and low power hardware.

This work presents a new solution for coordinated search with a team of heterogeneous robots executing a time-critical mission. It is challenging to specify and represent search locations (targets) in known but dynamic environments as well as to find robotic paths to visit the locations. We propose a technique to construct an information map that includes locations of uncertain targets, and generate optimal paths. We especially focus on combining a satellite map that has global coordinates with local images gathered from an aerial robot. Specific targets are represented on a homogeneous coordinate system, so that different types of robots, capable to gather necessary information, may cooperatively conduct a mission. Once a homogeneous map is constructed, a centralized pathfinding algorithm can be applied. Our path-finding algorithm is to choose a set of paths, suggesting a proper number of robots along with their initial locations. In our work, robots can independently travel search locations, which may have dynamics or changes, but collaboratively cover all target locations. Through the experiments with real robotic platforms, we validate the generation of a map including targets and a choice of paths, and compare with existing algorithms.

Introduction : the main feature of operation of cranes-pipe layers is work in difficult ground conditions, which significantly affects the operating mode of the machine. This factor is one of the main reason leading to the rocking of the load on the crane-pipe laying machine gibbet and as a consequence it leads to emergency and contingency situations. In the research the forced vibration of the load on the crane-pipe layer gibbet and the causes of their occurrence and the problems to which they lead are observed. Engineering solutions of predecessors are considered. A new approach to the solution of these problems is proved. Materials and methods : the design scheme of the crane-pipe laying machine is justified, assumptions are accepted, coordinate systems are introduced, and a mathematical model of the crane-pipe-laying machine is compiled. Results : the following time dependences are constructed: the deflection of the cargo in the transverse plane of the crane-pipe layer (horizontalvibrations), the deflection of the cargo in the longitudinal plane of the pipe laying crane, the roll of the base machine, the change in the load moment are also constructed. The influence of the horizontal vibrations of the load on the change in the load moment and the occurrence of vertical vibrations is determined. Discussion and conclusion : the effect of horizontal vibrations on the change of the load moment is evaluated and as a consequence of the negative effect on the stability of the crane-pipe laying machine is presented.

This paper presents an imaginary planar rack cutter having two parameters of motion to create a spherical gear pair with two degrees of freedom. The working region of the imaginary planar rack cutter is that of symmetrical straight lines. The relationship between the coordinate system of the imaginary planar rack cutter and that of the spherical gear pair having two parameters of motion is illustrated. The two-parameter family of imaginary planar rack cutter surfaces is obtained by using the homogeneous coordinate transformation matrix to transfer the coordinate system of the planar rack cutter to that of the spherical pinion or the spherical gear. Based on the two-parameter enveloping theory, the mathematical models of the spherical gear pair with two degrees of freedom were proposed. The developed mathematical model of the gear pair with two degrees of freedom can be used to analyze undercutting analysis of the imaginary planar rack cutter. Based on the undercutting equation, a minimum number of teeth of the spherical pinion are determined. A line of singular points on the spherical pinion’s teeth are displayed. Results show that a minimum number of teeth of the spherical pinion can be determined in order to avoid undercutting.

Mismatch removal is a key step in many computer vision problems. In this paper, we handle the mismatch removal problem by adopting shape interaction matrix (SIM). Given the homogeneous coordinates of the two corresponding point sets, we first compute the SIMs of the two point sets. Then, we detect the mismatches by picking out the most different entries between the two SIMs. Even under strong affine transformations, outliers, noises, and burstiness, our method can still work well. Actually, this paper is the first non-iterative mismatch removal method that achieves affine invariance. Extensive results on synthetic 2D points matching data sets and real image matching data sets verify the effectiveness, efficiency, and robustness of our method in removing mismatches. Moreover, when applied to partial-duplicate image search, our method reaches higher retrieval precisions with shorter time cost compared with the state-of-the-art geometric verification methods.

This paper presents an EM analysis for extracting a signature generation key from ECDSA hardware. In particular, we presents a horizontal side-channel attack using EM waves radiated from compact ECDSA hardware based on Jacobian projective coordinates. The validity of the attack is demonstrated through an experiment using a prototype LSI. We also mention an efficient algorithm-level countermeasure against the attack.

The requirements of video communication make people to use the Internet daily in their life. The security also plays a vital role to achieve smooth communication in multimedia. Multimedia encryption provides elegant solution to fulfill all these requirements. Among all public key encryption algorithms, elliptic curve cryptography (ECC) is attracted toward encryption of multimedia for better security with less bandwidth. We proposed a method named as perceptual encryption, which performs encryption on selective bitplanes of a grayscale image. The proposed method uses ECC on Koblitz curves with Lopez–Dahab projective coordinates to improve the efficiency of multimedia encryption and decryption. Moreover, scalar multiplication dominates the performance of ECC over Koblitz curves. The performance of Koblitz curves can be further improved by reducing number of field operations required at the time of point addition using Lopez–Dahab projective coordinates, anyway doubling needs less cost due to Frobenius endomorphism. Two parameters such as peak signal-to-noise ratio (PSNR) and structural similarity measure (SSIM) are considered to measure the quality of an image. The requirements of multimedia are analyzed based on the results obtained.

This paper presents design imaginary skew rack cutters having teeth of two parabolic coefficients to generate spur and helical gears. First, a mathematical model of the imaginary rack cutter having teeth of two parabolic coefficients is derived using geometric relations and coordinate transformation. After the relationship between the coordinate system of the imaginary rack cutter and that of the helical gear pair is set up, a family of imaginary rack cutter surfaces is obtained using the homogeneous coordinate transformation matrix to transfer the coordinate system of the rack cutters to that of the helical gear. Based on the gear theory, the equations of meshing between the rack cutter and the helical gear are determined. Substituting the equations of meshing into the family of imaginary rack cutter surfaces, a pinion and a gear are generated and their geometries are plotted using an in-house software package. Based on the assembly errors, tooth contact analysis is performed to determine the influences of kinematic assembly errors and the parabolic coefficients. Results show that maximum parabolic coefficient value of the imaginary skew rack cutter exists in order to avoid undercutting and it can be determined.

Most Escher-like impossible figures admit a realization as 3D objects, when seen from a specific viewpoint. To avoid the restrictions of polyhedral models, we explore how to build these 3D objects with curved surfaces, through the prism of CAGD. Such impossible objects can be regarded as optical anamorphisms, a visual illusion based on depth misperception, which can be achieved by using standard CAGD techniques, in particular homogeneous coordinates and NURBS. The main tool is an anamorphic deformation, i.e., along radial lines through the viewpoint. Deforming NURBS boils down to the straightforward exercise of displacing the control points along such radial directions and simultaneously changing their weights. Thus, we change the distance to the observer of different parts of an object, which leads to depth misperception and apparent contradiction. The deformation alters shading, but the introduction of textures in parameter space, unaffected by the deformation, deceives the eye and helps conceal this artifact, as 3D printouts corroborate. Examples confirm the superiority of our textured NURBS over simpler polyhedral models.

This paper presents an EM analysis for extracting a signature generation key from ECDSA hardware. In particular, we show a possibility of a horizontal side-channel attack using EM waves radiated from compact ECDSA hardware based on Jacobian projective coordinates. We also mention a possible countermeasure against the attack.

This paper presents a fast scalar point multiplier for an elliptic curve crypto-processor in the field \( {\text{GF}}\left( {2^{163} } \right) \). Elliptic curve-based cryptographic algorithms have been in wide use since the early 2000s after being introduced in 1986. With the ever-increasing need for information security, it is essential for systems to perform the required operations in a fast and efficient manner. In this work, a hybrid type Karatsuba multiplier has been used for fast field multiplications and a dedicated inverter module based on the extended Euclidean algorithm is used for fast field inversions. The point multiplication is performed using the standard double-and-add algorithm for which the point doubling and point addition are done using standard projective coordinates. The use of the fast multipliers and field inverters makes the implementation a fast one as compared to other high-performance implementations that have been reported over the years, at the cost of increased resource usage. The results obtained, however, justify this increased resource usage as the point multiplication is the most time-intensive operation in the encryption and decryption process of elliptic curve cryptography.

Risley systems and tilting orthogonal double-prism systems are optical systems consisting of two prisms in series. The analysis of such systems typically involves both direct and inverse problems. Problems of the former type can be easily solved using ray-tracing equations. However, inverse problems are comparatively more difficult if the search direction is not properly given prior to iteration. In the present study, the two optical systems are modeled using the homogeneous coordinate notation. A method is then proposed for solving the direct and inverse problems of both optical systems using a ray-tracing approach and the first- and second-order derivative matrices of the skew rays. In addition, four optimization methods based on the two derivative matrices are proposed for determining the search direction in the inverse problem. Eight illustrative examples are given. It is shown that the proposed method can not only determine the scan patterns and sensitivity coefficients in the direct problem, but also determine the search direction in the inverse problem.

Due to the unfixed state of the workpiece and the dissimilarity between sections in through-feed centerless grinding, the positions and orientations of the workpiece keep changing in the grinding process, which are coupled with the workpiece roundness generation. In this paper the positions and orientations of the workpiece are described by the dynamic equations obtained from Lagrange equation. And the homogeneous coordinate transformation is applied to present the profiles of the workpiece, grinding wheel and control wheel in the reference frame. Finally the time varying profile of the workpiece is obtained for the investigation of the material removal process in 3D space. The material properties of the workpiece, the wheels and the workrest combined with the geometric relationship of their profiles are utilized to calculate the interaction between them, including the three forces along the axes and the three moments about the axes.

The precision of Multiaxial EDM is improved by a geometric and motion error model of EDM. A lower numbered body array is introduced to describe the EDM with a homogeneous coordinate transformation used to model the geometric and motion errors of a typical body in the multi-body system. Multi-body kinematics are employed to derive the structural and motion relations and the corresponding location error equation。 The motion error chain for the EDM is analyzed to develop a versatile error model. An entire Multiaxial EDM is analyzed as an example to determine its errors. The method provides a reference for Multiaxial EDM precision design.

In the manufacturing process of precision machine tool, the precision of the machine tool can not simply rely on parts design tolerance to achieve, and also need choose parts assemble for different tolerance values to ensure the accuracy of machine tools. Machine tool assembling deviation accumulation model is established by using the homogeneous coordinate transformation matrix, the quality loss function of taguchi methods apply to mechanical products matching activities. Considering the processing deviation of parts, the quality loss function of assembly cumulative deviation as an effective indicator for measure machine tool accuracy, the assembly precision of machine tools are ensured by optimize matching different geometric deviation parts. An example is given to testify the validity of this method.

In this contribution, a chatter detection method is investigated for milling operations. The proposed approach can give not only qualitative condition (stable or unstable), but a quantitative measure of stability. For this purpose, it requires an external excitation of stable machining condition. Transient vibration of the perturbation is captured by means of stroboscopic section, and the corresponding monodromy operator is approximated by its projection to the subspace of the dominant modes. The monodromy matrix is determined with the application of homogeneous coordinate representation. Then, the periodic solution and the dominant characteristic multipliers are calculated and their modulus determines the quantitative measure of stability condition.

In this paper we describe a design to compute an inversion in F p as well as division. Inversion can be used in Elliptic Curve Cryptography systems and pairing-based cryptography, which are becoming popular for Public Key Cryptosystems. For the same level of security, ECC and pairing use much smaller key length than RSA but need modular inversion. In ECC when points are represented in so-called affine coordinates, the addition of two points involves a field inversion. Some pairing require one inversion over F p in order to perform the final exponentiation. Usually, inversions are avoided in Elliptic Curve Cryptography as they are expensive. For example, inversions in affine coordinates are transform into multiplication in Jacobian or projective coordinates. In order to improve performance of Public Key Cryptosystems, we present in this paper an improved algorithm for prime field modular inversion. We demonstrate that affine coordinates can be more efficient than projective or jacobian for the scalar multiplication.

To accurately describe the problem of excavator bucket teeth space trajectory in the mining process, is presented to describe the trajectory of excavator bucket teeth using D-H homogeneous coordinate method. Based on the principle of robotics, the excavator boom arm and bucket as three robot manipulators, through the driving of the boom cylinder and the arm cylinder and bucket cylinder, establish mathematical model of excavator working device pose space, using MATLAB/Simulink simulation to analyze the spatial motion, and fast get excavator mining envelope graph. The ZE-360 hydraulic excavator as an example, verify the scientific D-H homogeneous coordinate method in spatial motion analysis of excavator working device and adaptability, and provide a theoretical basis for the excavator trajectory and work space analysis.

A novel mirror array is proposed to enlarge the range of angular measurement, which is based on the characteristic of the ellipse. The relevant tolerance analysis based on homogeneous coordinate transformation is also carried out.

Compared to conventional circular components such as keys, splices and pins, polyhedron components have many advantages as connecting components in torque transmission systems, including a greater shear strength, an improved fatigue strength and an improved transmission efficiency. However, the performance of such components is critically dependent on the precision of the manufacturing process. Accordingly, this study derives a mathematical model based on the homogeneous coordinate transformation method to facilitate the design, machining and error compensation of generic polyhedron components with n sides. The validity of the proposed approach is demonstrated numerically using polyhedron components with three, four and five sides. The results confirm that the proposed machining and error compensation method provides a simple yet versatile approach for fabricating a wide range of polyhedron components.

The main objective of this study is to provide an effective algorithm of the transmitted solar radiation calculation through window glazing on a clear day. This algorithm would be used in developing a computer program for fenestration system analysis and shading device design. Various simulation methods have been evaluated to figure out the most accurate and effective procedure in estimation of transmitted solar radiation on a tilted surface on a clear day. Characteristics of simulated results of each step have been scrutinized by comparing them with measured results of the site as well as results from other simulation programs. Generally, the Duffie & Beckman’s solar calculation method introducing the HDKR anisotropic model provided the most reliable simulation results. The DOE-2 program usually provided over-estimated simulation results. The estimation of extraterrestrial solar radiation and beam normal radiation were conducted pretty accurately. However, the solar radiation either on horizontal surface or on tilted surface involves complicated factors in estimation. Even though the estimation results were close to the real measured data during summer when solar intensity is getting higher, the estimation provided more error when solar intensities were getting weaker. The convex polygon clipping algorithm with homogeneous coordinates was fastest model in calculation of sunlight to shaded area ratio. It could not be applied because of its shape limitation.

Based on the multi-body system theories and used the homogeneous coordinate transform. Systematically analyzed the geometric error and thermal error of face gear NC grinding machine. Established the face gear NC grinding machine of grinding mathematical model of comprehensive error according with the mechanism grinding errors,To provide a theoretical basis of the error modeling analysis and the error compensation on NC grinding Machine Tool of face-gear.

Despite many alternatives to feature tracking problem, iterative least squares solution solving the optical flow constraint has been the most popular approach used by many in the field. This paper attempts to leverage the former efforts to enhance feature tracking methods by introducing a view geometric constraint to the tracking problem. In contrast to alternative geometry based methods, the proposed approach provides a closed form solution to optical flow estimation from image appearance and view geometry constraints. We particularly use invariants in the projective coordinates generated from tracked features that results in a new optical flow equation. This treatment provides persistent tracking of features even when they are occluded. At the end of each tracking loop the quality of the tracked features is judged using both appearance similarity and geometric consistency. Our experiments demonstrate robust tracking performance even when the features are occluded or they undergo appearance changes due to projective deformation of the template.

In order to improve the reconnaissance efficiency of unmanned aerial vehicle (UAV) electro-optical stabilized imaging systems, a real-time multi-target localization scheme based on an UAV electro-optical stabilized imaging system is proposed. First, a target location model is studied. Then, the geodetic coordinates of multi-targets are calculated using the homogeneous coordinate transformation. On the basis of this, two methods which can improve the accuracy of the multi-target localization are proposed: (1) the real-time zoom lens distortion correction method; (2) a recursive least squares (RLS) filtering method based on UAV dead reckoning. The multi-target localization error model is established using Monte Carlo theory. In an actual flight, the UAV flight altitude is 1140 m. The multi-target localization results are within the range of allowable error. After we use a lens distortion correction method in a single image, the circular error probability (CEP) of the multi-target localization is reduced by 7%, and 50 targets can be located at the same time. The RLS algorithm can adaptively estimate the location data based on multiple images. Compared with multi-target localization based on a single image, CEP of the multi-target localization using RLS is reduced by 25%. The proposed method can be implemented on a small circuit board to operate in real time. This research is expected to significantly benefit small UAVs which need multi-target geo-location functions.

Error detection and compensation technology is an economical and effective method for improving the precision of CNC machine tool. The paper established the geometric errors model of three-axis CNC milling machine based on homogeneous coordinates transformation theory. Error detection is tested by digital ball bar and error compensation software is developed for XK7132 milling machine, the compensation effect is evaluated by a laser interferometer. The results show that the precision of CNC milling machine is improved effectively by the proposed method.

An approach was proposed to calculate the directions of crystal defects in the research of synchrotron radiation topography (SRT). The calculating method was deduced based on the theory of homogeneous coordinates. When spherical coordinates of a crystal defect had been calculated in a radiograph, the directions of the defect on any other radiograph, taken after the specimen had been turned around any axis in the SRT experiments, could be calculated. The directions of crystal defects can be determined by the methods previously been used only if the images of the same defects are similar in the topographs, but it is often not the case in the SRT experiments. With the method proposed in this paper, it is convenient to analyze the defects in different radiographs on which the images of the same defects are dissimilar. An example was taken to show the use of the method.

Conventionally, image object recognition and pose estimation are two independent components in machine vision. This paper presented a simple but effective method KNN-SNG, which tightly couples these two components within a single algorithm framework. The basic idea of this method came from the bionic pattern recognition and the manifold ways of perception. Firstly, the shortest neighborhood graphs (SNG) are established for each registered object. SNG can be regarded as a covering and triangulation for a hypersurface on which the training data are distributed. Then for recognition task, the determined test image lies on which SNG by employing the parameter “k”, which could be calculated adaptively. Finally, the local linear approximation method was adopted to build a local map between high-dimensional image space and low-dimensional manifold for pose estimation. The projective coordinates on manifold can depict the pose of object. Experiment results manifested the effectiveness of the method.

The effect of geometric error on machining accuracy was researched by multi-body system theory, as well as homogeneous coordinate transformation method. Taking a vertical machining center as example, topological structure of the machine tool was described by lower body array. Lower body array of the machining center, motion freedom between adjacent bodies and geometric errors of the vertical machining center were analyzed. Geometric errors of the bodies in the multi-body system were expressed by homogeneous coordinate transformation. Error model for machining accuracy was deduced and geometric errors having influence on the machining accuracy were identified. The research results provide guidance for analyze of geometric errors on machining accuracy.

In order to improve machining accuracy of machining center, the effect of geometric error on machining accuracy was researched by multi-body system theory. Taking a vertical machining center as example, topological structure of the machining center was described by lower body array. Geometric errors of the bodies in the multi-body system were expressed by homogeneous coordinate transformation. Error model for machining accuracy was deduced and geometric errors having great influence on the machining accuracy were identified. The research results show that, straightness errors and linear displacement errors in three directions have direct influence on machining accuracy, and the effect on machining accuracy caused by angle errors are related to the dimensions of the machining center and travel distance of the three axes. The research results provide guidance for analysis on sensitivity of geometric errors.

This article conducts a detailed research on design of specific robot with 4-Dof based on hydraulic driving, using the advanced CATIA to achieve the motion simulation and applying ANSYS to optimize structure of main parts by finite elements analysis. D-H coordinate system and the homogeneous coordinate transformation matrix are used to describe the posture and position of robot, which give the kinematics equations of the robot .With the result of simulation and design by CATIA, interference between each part of the robot is examined and eliminated in advance. ANSYS analysis gives the result of stress and strain, which help optimize the structure design. With careful design and targeted optimization, the result shows that trajectory and stability are in accordance with the work scheduled to meet the design requirements and that designing with CATIA and ANSYS can improve quality and efficiency greatly.

The thermal error of direct driving type A/C axis CNC milling head in the practical processing is analyzed. Based on the theory of homogeneous coordinate transformation and small error hypothesis, the transformation matrixes between the coordinate system of kinematic pairs and the relationship between errors and compensations are obtained. The thermal error compensation model and the thermal error compensation system which embedded into the Siemens 840D system are established, and play an important role in increasing the processing accuracy.

This paper mainly studies the problem of the movement of PRP cylindrical coordinate industrial manipulator. Based on the description of the manipulator position and gesture, the determination of coordinate of the rectilinear joint and rotary joint and the homogeneous coordinate transformation, the kinematical equation and its inverse solution can be deduced subsequently. It provides the theoretical basis for the following study.

Several hardware implementations of elliptic curve cryptography have been recently proposed for resource-constrained applications but few of them considered the power analysis countermeasures. In this paper, a new modular multiplication with zero-value attack countermeasure is proposed. The Montgomery ladder algorithm and randomized projective coordinates method are used to resist simple power analysis and differential power analysis. The circular shift register has been adopted to reduce the area. The overall design has been implemented in binary field. 16.5K Gate Equivalent (GE) area is needed and 10.8ms is required for one scalar point multiplication at 13.56MHz. The implementation result shows that the proposed ECC processor achieves power analysis resistance with low resource cost.

Focusing on the self-localization problems of the seeds sampling robot system during the operation process, this paper proposes a self-calibration method of industrial robot. It is based on geometric constraints of points in the coordinate system of the seed sampling box, which realizes the automatic acquisition of the absolute coordinates of robot target points by using the homogeneous coordinate transformation matrix and solves the self-localization problems. The test results show that the absolute value of the relative difference of theoretical coordinates and the actual coordinates is less than 5%o, which means the method is correct and practicable and can meet the requirements of practical work. It is easy to implement and it has advantages of low cost and high accuracy, which is of great significance to solve the self-localization of the workpiece.

A method for the reconstruction of a vessel centerline from angiographic images is outlined in this work. A typical coronary artery segment with bifurcations was emulated with a 3D printed static phantom and several angiograms were acquired at various angular positions on the C-Arm. The effectiveness of the reconstruction turned out to be largely influenced by the intrinsic parameters of the angiographic system, particularly the homogeneous coordinates system scaling factor λ. Therefore, recourse was made to a heuristic optimization method to estimate the optimal value of λ for each view. We measured the reliability of the reconstruction method by varying the fitness function of the optimization step and measuring the distances of 8 test points in comparison to the corresponding points identified in the μCT centerline. Preliminary results showed that, with an adequate number of views, the adoption of the optimal fitness function allowed the median distance error to be decreased below the acceptance threshold of 10%. As expected, the reliability of the method is improved by increasing the number of processed views.

The paper presents a methodology for modeling profile of two circular-arc cams, which is based on the application of homogeneous coordinate transformation method. Analytical expressions that allow complete determining of all design parameters and coordinates of all the points of two circular-arc cams profile are defined. Also, analytical expressions for determining the kinematic performance such as displacement, velocity, acceleration and jerk are derived. The defined methodology is applied on concrete examples for which the analysis of the kinematic performance is also performed. Additionally, it is shown that a proper choice of the design parameters can significantly affect the improvement of the kinematic performance, especially the reduction of jerk as one of the most unfavorable occurrences in these mechanisms. The given methodology allows very efficient determination of all input data for parametric modeling and production of two circular-arc cams on numerical machines. This approach allows the fulfillment of one of the most important requirements of modern production–reduction of time necessary for design and manufacturing which causes reduction of costs.

We present a novel approach for a rigorous bundle adjustment for omnidirectional and multi-view cameras, which enables an efficient maximum-likelihood estimation with image and scene points at infinity. Multi-camera systems are used to increase the resolution, to combine cameras with different spectral sensitivities (Z/I DMC, Vexcel Ultracam) or – like omnidirectional cameras – to augment the effective aperture angle (Blom Pictometry, Rollei Panoscan Mark III). Additionally multi-camera systems gain in importance for the acquisition of complex 3D structures. For stabilizing camera orientations – especially rotations – one should generally use points at the horizon over long periods of time within the bundle adjustment that classical bundle adjustment programs are not capable of. We use a minimal representation of homogeneous coordinates for image and scene points. Instead of eliminating the scale factor of the homogeneous vectors by Euclidean normalization, we normalize the homogeneous coordinates spherically. This way we can use images of omnidirectional cameras with single-view point like fisheye cameras and scene points, which are far away or at infinity. We demonstrate the feasibility and the potential of our approach on real data taken with a single camera, the stereo camera FinePix Real 3D W3 from Fujifilm and the multi-camera system Ladybug 3 from Point Grey.

Track irregularity is the main disturbance of vibration of wheel-rail system. Combined with the structure of the ramp simulator and the feature of longitudinal ramp, this paper completed the simulation of vehicle longitudinal ramp, and constructed he model of coordinative relations for the slope simulation. Based on the method space transformation of homogeneous coordinate and the expression of space vector of the 21 actuators, three models of inverse displacement analysis of the 6-Dof simulation platform were built. It also implemented the real-time solution by means of simulink, which provided parameters reference for the control of 6-Dof loading platform, and was of important theoretical value and realistic significance.

Gear Measuring Center(GMC) is commonly used to test error of the tooth surface of the gear, whose geometric accuracy directly impacts on the accuracy of measurement. How to quickly and accurately detect space geometric error of the measuring machine and compensate becomes the essential means of high-precision measurements. According to the problem above, in the paper, three-beams laser detection technology is proposed. The detection of the geometric errors of the linear axis was achieved. The accurate measurement for the position and attitude of the plane mirror on measurement seat was achieved based on laser telemetry principle. The positioning error, the pitching angle errors, the deflection angle errors and the straightness errors were separated. And then based on multi-body system theory, by using of homogeneous coordinate transformation, the error compensation model of 4-axis measuring machine which includes three shifting pairs and one revolute pair was established, and the algorithm was given in the paper. The theoretical foundation for real-time compensation of 4-axis GMC was established. The geometric errors of GMC can be improved by the method of the error detection and compensation. The method plays a very important role in high-precision measurements.

An efficient iterative pose estimation method was proposed to improve the accuracy and robustness of monocular vision measurement systems.By using homogeneous coordinates,it avoids the limit of existing algorithms on the selection of reference points for a paraperspective camera model.First,a method to compute the pose of an object under the paraperspective camera model was researched using homogeneous coordinates,and its geometric meaning was expatiated in detail.Then,this method was used to estimate the pose of an object in an iterative way under the full perspective camera model with high precision.Simulation results indicate that the proposed method improves the accuracy,speed and robustness of the paraperspective camera model based iterative pose estimation.Real measurement results show that the translation measurement precision and rotation measurement precision of the proposed method are better than 0.1 mm and 0.1°,respectively,and it can satisfy the requirements of various vision detection systems.Furthermore,the accuracy of the proposed method can be improved further by using the land mark point method and sub-pixel feature locating techniques.

This paper studies the problem of multi-joint robot with four degrees of freedom that is used in the process of loading and unloading, the method of homogeneous coordinate transformation is used to achieve the exchange between the implementation end of the space coordinate and the joint angle. Providing the theoretical reference and a basis of calculating for the follow-up study, and ultimately meeting the actual needs of production.

Five-axis machining, an important processes in precision manufacturing, has been used in defense, aerospace and consumer product industries. Many combinations can be synthesized to generate various five-axis machine tool configurations, in which the linear and rotary axes are normally orthogonal. Since five-axis NC data can only be applied to a specific configuration, the portability of the NC data is inevitably limited. A special purpose five-axis machine with a nonorthogonal linear axis configuration is investigated in this research. The complete analytical equations for NC data are obtained using the homogeneous coordinate transformation matrix and inverse kinematics. A window-based postprocessor system written by Borland C++ Builder was developed according to the proposed algorithm. A roller gear cam was adopted as an example to generate the NC code using the proposed postprocessor system. A trail-cut experiment conducted with this special purpose machine tool confirms the effectiveness of the proposed methodology.

According to the intrinsic and extrinsic parameters of a camera to be needed in some applications for machine vision,a method based on the neural network with embedded orthogonal weight matrix is proposed for camera calibration.Firstly,the neural network with the embedded orthogonal weight matrix is structured,whose weights are corresponding to the camera extrinsic parameters and intrinsic parameters.Thus,the structured neural network coincides with the model of camera.The generation of orthogonal weight matrix is served as the last mutation operator in the iteration of genetic algorithm,and the performance index is the square of 2-norm of the difference between vector consisting of network's outputs and homogeneous coordinate of corresponding feature point projected in image plane.Meanwhile,a hybrid genetic-simulation annealing algorithm is introduced into the solving-programming.When the system comes to the equilibrium,the intrinsic and extrinsic parameters of the camera can be obtained in the light of network's weights.The simulated experiments illustrate that the proposed algorithm is robust,and has the advantages of high calibration precision,simplicity and clarity according to real experiments.It provides an effective solution scheme for camera calibration of intrinsic and extrinsic parameters.