A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-p...A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control(CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument(P, R and S standing for prismatic,revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.展开更多
In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a defi...In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.展开更多
With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） meth...With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.展开更多
A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear syste...A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.展开更多
The linear interpolation of linear system on a family of linear systems is introduced and discussed. Some results and examples on singly generated systems on a finite dimensional vector space are given.
An approach of three-dimensional seismic ray tracing is presented,which is derived from adopting two-dimensional linear traveltime interpolation（LTI）.By adjusting the forward process using the partition of grid inte...An approach of three-dimensional seismic ray tracing is presented,which is derived from adopting two-dimensional linear traveltime interpolation（LTI）.By adjusting the forward process using the partition of grid interface,and backward step by considering more directions,the new approach is suitable for the application of three-dimensional models.The calculation results show that,with the same accuracy,the improved 3-D method is much faster than the method of traditional LTI directly applied in the three-dimensional case.展开更多
Diffusion tensor imaging is a unique method to visualize white matter fibers three-dimensionally, non-invasively and in vivo, and therefore it is an important tool for observing and researching neural regeneration. Di...Diffusion tensor imaging is a unique method to visualize white matter fibers three-dimensionally, non-invasively and in vivo, and therefore it is an important tool for observing and researching neural regeneration. Different diffusion tensor imaging-based fiber tracking methods have been already investigated, but making the computing faster, fiber tracking longer and smoother and the details shown clearer are needed to be improved for clinical applications. This study proposed a new fiber tracking strategy based on tri-linear interpolation. We selected a patient with acute infarction of the right basal ganglia and designed experiments based on either the tri-linear interpolation algorithm or tensorline algorithm. Fiber tracking in the same regions of interest （genu of the corpus callosum） was performed separately. The validity of the tri-linear interpolation algorithm was verified by quan- titative analysis, and its feasibility in clinical diagnosis was confirmed by the contrast between tracking results and the disease condition of the patient as well as the actual brain anatomy. Statis- tical results showed that the maximum length and average length of the white matter fibers tracked by the tri-linear interpolation algorithm were significantly longer. The tracking images of the fibers indicated that this method can obtain smoother tracked fibers, more obvious orientation and clearer details. Tracking fiber abnormalities are in good agreement with the actual condition of patients, and tracking displayed fibers that passed though the corpus callosum, which was consistent with the anatomical structures of the brain. Therefore, the tri-linear interpolation algorithm can achieve a clear, anatomically correct and reliable tracking result.展开更多
This paper analyzes and compares two time interpolators, i.e., time replica and time linear interpolator, for pilot aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems. The mean squar...This paper analyzes and compares two time interpolators, i.e., time replica and time linear interpolator, for pilot aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems. The mean square error (MSE) of two interpolators is theoretically derived for the general case. The equally spaced pilot arrangement is proposed as a special platform for these two time interpolators. Based on this proposed platform, the MSE of two time interpolators at the virtual pilot tones is derived analytically;moreover, the MSE of per channel estimator at the entire OFDM symbol based on per time interpolator is also derived. The effectiveness of the theoretical analysis is demonstrated by numerical simulation in both the time-invariant frequency-selective channel and the time varying frequency-selective channel.展开更多
Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spl...Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.展开更多
Field D* algorithm is widely used in mobile robot navigation since it can plan and replan any-angle paths through non-uniform cost grids. However, it still suffers from inefficiency and sub-optimality. In this article...Field D* algorithm is widely used in mobile robot navigation since it can plan and replan any-angle paths through non-uniform cost grids. However, it still suffers from inefficiency and sub-optimality. In this article, a new linear interpolation-based planning and replanning algorithm, Update-Reducing Field D*, is proposed. It employs different approaches during initial planning and replanning respectively in order to reduce the number of updates of the rhs-values of vertices. Experiments have shown that Update-Reducing Field D* runs faster than Field D* and returns smoother and lower-cost paths.展开更多
In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantag...In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
A modified time domain interpolation method is proposed for orthogonal frequency division multiplexing(OFDM)systems to address the problem that time domain interpolation in the least square(LS)channel estimation metho...A modified time domain interpolation method is proposed for orthogonal frequency division multiplexing(OFDM)systems to address the problem that time domain interpolation in the least square(LS)channel estimation method based on comb-type pilots cannot choose the pilot spacing flexibly.Firstly,the estimated channel frequency response(CFR)at pilot positions in the frequency domain is obtained by LS channel estimation based on comb-type pilots,and the estimated channel impulse response(CIR)in the time domain is obtained by linear interpolation and inverse fast Fourier transform(IFFT).Secondly,the error of the estimated CIR obtained by linear interpolation is analyzed by theoretical deduction,and a method for correcting it is proposed.Finally,an estimated CFR at all subcarrier positions in the frequency domain is obtained by performing zero padding in the time domain and fast Fourier transform(FFT)on the modified CIR.The simulation results suggest that the proposed method gives similar performance to time domain interpolation,yet it does not need to meet the condition of time domain interpolation that the number of subcarriers must be an integral multiple of pilot spacing to use it.The proposed method allows for flexible pilot spacing,reducing the number of pilots and the consumption of subcarriers used for channel estimation.展开更多
A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method a...A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.展开更多
It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem o...It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem of convergence and control the occurrence of real poles.In this paper,we establish a family of linear Hermite barycentric rational interpolants r that has no real poles on any interval and in the case k=0,1,2,the function r^(k)(x)converges to f^(k)(x)at the rate of O(h^3d+3-k)as h→0 on any real interpolation interval,regardless of the distribution of the interpolation points.Also,the function r(x)is linear in data.展开更多
In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate ser...In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate series of pre-processing and elementary corrections and then operate a series of main processing steps for more precise analysis on the images. There are several approaches for processing which are depended on the type of remote sensing images. The discussed approach in this article, i.e. image fusion, is the use of natural colors of an optical image for adding color to a grayscale satellite image which gives us the ability for better observation of the HR image of OLI sensor of Landsat-8. This process with emphasis on details of fusion technique has previously been performed;however, we are going to apply the concept of the interpolation process. In fact, we see many important software tools such as ENVI and ERDAS as the most famous remote sensing image processing tools have only classical interpolation techniques (such as bi-linear (BL) and bi-cubic/cubic convolution (CC)). Therefore, ENVI- and ERDAS-based researches in image fusion area and even other fusion researches often don’t use new and better interpolators and are mainly concentrated on the fusion algorithm’s details for achieving a better quality, so we only focus on the interpolation impact on fusion quality in Landsat-8 multispectral images. The important feature of this approach is to use a statistical, adaptive, and edge-guided interpolation method for improving the color quality in the images in practice. Numerical simulations show selecting the suitable interpolation techniques in MRF-based images creates better quality than the classical interpolators.展开更多
Image morphing is a powerful tool for visual effect. In this paper, a view interpolation algorithm is proposed to simulate a virtual walk along a street from start position to end position. To simulate a virtual walki...Image morphing is a powerful tool for visual effect. In this paper, a view interpolation algorithm is proposed to simulate a virtual walk along a street from start position to end position. To simulate a virtual walking view needs to create new appearing scene in the vision-vanishing point and disappearing scene beyond the scope of view. To attain these two aims we use two enhanced position parameters to match pixels of source images and target images. One enhanced position parameter is the angular coordinates of pixels. Another enhanced position parameter is the distances from pixels to the vision-vanishing point. According to the parameter values, pixels beyond the scope of view can be ＂moved＂ out in linear interpolation. Result demonstrates the validity of the algorithm. Another advantage of this algorithm is that the enhanced position parameters are based on real locations and walking distances, so it is also an approach to online virtual tour by satellite maps of virtual globe applications such as Google Earth.展开更多
Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough hi...Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.展开更多
Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital ste...Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital step before constructing interpolation functions. The most widely used parameterization method is accumulative chord length parameterization. In this paper, we give out a better method based on the interpolation of conics. Based on this method, a sequence of fairer Hermite curves can be constructed.展开更多
基金the CNC Equipment Development for Key Structure Integrated Manufacturing by LAW(No.ZB-ZBYZ-03-11-2190)the Shanghai Aerospace Fund(No.HTJ10-20)
文摘A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control(CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument(P, R and S standing for prismatic,revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.
文摘In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.
基金The National Natural Science Foundation of China(No.60702027)the Free Research Fund of the National Mobile Communications Research Laboratory of Southeast University (No.2008B07)the National Basic Research Program of China(973 Program)(No.2007CB310603)
文摘With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.
基金supported by the National Natural Science Foundation of China （Grant No.10271074）
文摘A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.
文摘The linear interpolation of linear system on a family of linear systems is introduced and discussed. Some results and examples on singly generated systems on a finite dimensional vector space are given.
基金Supported by the National Natural Science Foundation of China (69983005)
文摘An approach of three-dimensional seismic ray tracing is presented,which is derived from adopting two-dimensional linear traveltime interpolation（LTI）.By adjusting the forward process using the partition of grid interface,and backward step by considering more directions,the new approach is suitable for the application of three-dimensional models.The calculation results show that,with the same accuracy,the improved 3-D method is much faster than the method of traditional LTI directly applied in the three-dimensional case.
基金supported by the National Natural Science Foundation of China,No.60703045
文摘Diffusion tensor imaging is a unique method to visualize white matter fibers three-dimensionally, non-invasively and in vivo, and therefore it is an important tool for observing and researching neural regeneration. Different diffusion tensor imaging-based fiber tracking methods have been already investigated, but making the computing faster, fiber tracking longer and smoother and the details shown clearer are needed to be improved for clinical applications. This study proposed a new fiber tracking strategy based on tri-linear interpolation. We selected a patient with acute infarction of the right basal ganglia and designed experiments based on either the tri-linear interpolation algorithm or tensorline algorithm. Fiber tracking in the same regions of interest （genu of the corpus callosum） was performed separately. The validity of the tri-linear interpolation algorithm was verified by quan- titative analysis, and its feasibility in clinical diagnosis was confirmed by the contrast between tracking results and the disease condition of the patient as well as the actual brain anatomy. Statis- tical results showed that the maximum length and average length of the white matter fibers tracked by the tri-linear interpolation algorithm were significantly longer. The tracking images of the fibers indicated that this method can obtain smoother tracked fibers, more obvious orientation and clearer details. Tracking fiber abnormalities are in good agreement with the actual condition of patients, and tracking displayed fibers that passed though the corpus callosum, which was consistent with the anatomical structures of the brain. Therefore, the tri-linear interpolation algorithm can achieve a clear, anatomically correct and reliable tracking result.
文摘This paper analyzes and compares two time interpolators, i.e., time replica and time linear interpolator, for pilot aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems. The mean square error (MSE) of two interpolators is theoretically derived for the general case. The equally spaced pilot arrangement is proposed as a special platform for these two time interpolators. Based on this proposed platform, the MSE of two time interpolators at the virtual pilot tones is derived analytically;moreover, the MSE of per channel estimator at the entire OFDM symbol based on per time interpolator is also derived. The effectiveness of the theoretical analysis is demonstrated by numerical simulation in both the time-invariant frequency-selective channel and the time varying frequency-selective channel.
文摘Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.
文摘Field D* algorithm is widely used in mobile robot navigation since it can plan and replan any-angle paths through non-uniform cost grids. However, it still suffers from inefficiency and sub-optimality. In this article, a new linear interpolation-based planning and replanning algorithm, Update-Reducing Field D*, is proposed. It employs different approaches during initial planning and replanning respectively in order to reduce the number of updates of the rhs-values of vertices. Experiments have shown that Update-Reducing Field D* runs faster than Field D* and returns smoother and lower-cost paths.
基金Project supported by the Second Stage of Brain Korea 21 Projectssupported by Basic Science Research Program through the National Research Foundation of Korea (NRF)funded by the Ministry of Education,Science and Technology (2011-0013902)
文摘In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
基金The National Natural Science Foundation of China(No.51975117)。
文摘A modified time domain interpolation method is proposed for orthogonal frequency division multiplexing(OFDM)systems to address the problem that time domain interpolation in the least square(LS)channel estimation method based on comb-type pilots cannot choose the pilot spacing flexibly.Firstly,the estimated channel frequency response(CFR)at pilot positions in the frequency domain is obtained by LS channel estimation based on comb-type pilots,and the estimated channel impulse response(CIR)in the time domain is obtained by linear interpolation and inverse fast Fourier transform(IFFT).Secondly,the error of the estimated CIR obtained by linear interpolation is analyzed by theoretical deduction,and a method for correcting it is proposed.Finally,an estimated CFR at all subcarrier positions in the frequency domain is obtained by performing zero padding in the time domain and fast Fourier transform(FFT)on the modified CIR.The simulation results suggest that the proposed method gives similar performance to time domain interpolation,yet it does not need to meet the condition of time domain interpolation that the number of subcarriers must be an integral multiple of pilot spacing to use it.The proposed method allows for flexible pilot spacing,reducing the number of pilots and the consumption of subcarriers used for channel estimation.
文摘A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.
基金Supported by the National Natural Science Foundation of China(Grant No.11601224)the Science Foundation of Ministry of Education of China(Grant No.18YJC790069)+1 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.18KJD110007)the National Statistical Science Research Project of China(Grant No.2018LY28)。
文摘It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem of convergence and control the occurrence of real poles.In this paper,we establish a family of linear Hermite barycentric rational interpolants r that has no real poles on any interval and in the case k=0,1,2,the function r^(k)(x)converges to f^(k)(x)at the rate of O(h^3d+3-k)as h→0 on any real interpolation interval,regardless of the distribution of the interpolation points.Also,the function r(x)is linear in data.
文摘In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate series of pre-processing and elementary corrections and then operate a series of main processing steps for more precise analysis on the images. There are several approaches for processing which are depended on the type of remote sensing images. The discussed approach in this article, i.e. image fusion, is the use of natural colors of an optical image for adding color to a grayscale satellite image which gives us the ability for better observation of the HR image of OLI sensor of Landsat-8. This process with emphasis on details of fusion technique has previously been performed;however, we are going to apply the concept of the interpolation process. In fact, we see many important software tools such as ENVI and ERDAS as the most famous remote sensing image processing tools have only classical interpolation techniques (such as bi-linear (BL) and bi-cubic/cubic convolution (CC)). Therefore, ENVI- and ERDAS-based researches in image fusion area and even other fusion researches often don’t use new and better interpolators and are mainly concentrated on the fusion algorithm’s details for achieving a better quality, so we only focus on the interpolation impact on fusion quality in Landsat-8 multispectral images. The important feature of this approach is to use a statistical, adaptive, and edge-guided interpolation method for improving the color quality in the images in practice. Numerical simulations show selecting the suitable interpolation techniques in MRF-based images creates better quality than the classical interpolators.
文摘Image morphing is a powerful tool for visual effect. In this paper, a view interpolation algorithm is proposed to simulate a virtual walk along a street from start position to end position. To simulate a virtual walking view needs to create new appearing scene in the vision-vanishing point and disappearing scene beyond the scope of view. To attain these two aims we use two enhanced position parameters to match pixels of source images and target images. One enhanced position parameter is the angular coordinates of pixels. Another enhanced position parameter is the distances from pixels to the vision-vanishing point. According to the parameter values, pixels beyond the scope of view can be ＂moved＂ out in linear interpolation. Result demonstrates the validity of the algorithm. Another advantage of this algorithm is that the enhanced position parameters are based on real locations and walking distances, so it is also an approach to online virtual tour by satellite maps of virtual globe applications such as Google Earth.
文摘Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.
基金Supported by Shandong Ji'nan College and Institute Independent Innovation Project (No.201303011),Shandong Ji'nan College and Institute Independent Innovation Project(No.201303021),Shandong Ji'nan College and Institute Independent Innovation Project(No.201303016)Scientific Research Foundation of Shandong Province of Outstanding Young Scientist Award (No.BS2013DX039)
文摘Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital step before constructing interpolation functions. The most widely used parameterization method is accumulative chord length parameterization. In this paper, we give out a better method based on the interpolation of conics. Based on this method, a sequence of fairer Hermite curves can be constructed.
