According to the test data of subdivision errors in the measuring cycle of angular measuring system, the characteristics of subdivision errors generated by this system are analyzed. It is found that the subdivision er...According to the test data of subdivision errors in the measuring cycle of angular measuring system, the characteristics of subdivision errors generated by this system are analyzed. It is found that the subdivision errors are mainly due to the rotary-type inductosyn itself. For the characteristic of cyclical change, the subdivision errors in other measuring cycles can be compensated by the subdivision error model in one measuring cycle. Using the measured error data as training samples, combining GA and BP algorithm, an ANN model of subdivision error is designed. Simulation results indicate that GA reduces the uncertainty in the training process of the ANN model, and enhances the generalization of the model. Compared with the error model based on the least-mean-squared method, the designed ANN model of subdivision errors can achieve higher compensating precision.展开更多
Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference...Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.展开更多
A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this met...A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.展开更多
In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new ...In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.展开更多
相位细分技术是提高精密仪器测量分辨率和精度的关键技术。传统的机械、光学等细分技术已难以满足当前高精度测量领域的需求。基于坐标旋转数字计算(Coordinate Rotation Digital Computer,CORDIC)方法的角度计算原理,将输入的正交信号...相位细分技术是提高精密仪器测量分辨率和精度的关键技术。传统的机械、光学等细分技术已难以满足当前高精度测量领域的需求。基于坐标旋转数字计算(Coordinate Rotation Digital Computer,CORDIC)方法的角度计算原理,将输入的正交信号转换为向量(x,y),通过多次旋转迭代使向量最终收敛于X轴,对旋转角度进行求和即可得到目标角度值。基于FPGA用Verilog语言编写CORDIC算法,可以实现相位细分、信号辨向和整周期计数功能,通过扩展数据位宽消除了算法迭代过程中产生的舍入误差。对改进算法进行了仿真与实验验证,结果表明经过20级迭代后其理论分辨率为0.4″,计算角度的误差为±0.5″,光栅测角系统实际测量误差减小了约98.42%。该算法通过对正交信号进行精密细分来计算精密仪器的相角变化量,在工程应用中具有普适性。展开更多
This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon.The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot interval...This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon.The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot intervals under a minor assumption, that λ is the second and third eigenvalues of the subdivision matrix. And then, a million of numerical experiments are tested with randomly selecting positive knot intervals, which verify that our new subdivision scheme satisfies the assumption.However this is not true for the other two existing non-uniform Doo-Sabin schemes in Sederberg, et al.(1998), Huang and Wang(2013). In additional, numerical experiments indicate that the quality of the new limit surface can be improved.展开更多
文摘According to the test data of subdivision errors in the measuring cycle of angular measuring system, the characteristics of subdivision errors generated by this system are analyzed. It is found that the subdivision errors are mainly due to the rotary-type inductosyn itself. For the characteristic of cyclical change, the subdivision errors in other measuring cycles can be compensated by the subdivision error model in one measuring cycle. Using the measured error data as training samples, combining GA and BP algorithm, an ANN model of subdivision error is designed. Simulation results indicate that GA reduces the uncertainty in the training process of the ANN model, and enhances the generalization of the model. Compared with the error model based on the least-mean-squared method, the designed ANN model of subdivision errors can achieve higher compensating precision.
文摘Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.
文摘A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.
文摘In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.
文摘相位细分技术是提高精密仪器测量分辨率和精度的关键技术。传统的机械、光学等细分技术已难以满足当前高精度测量领域的需求。基于坐标旋转数字计算(Coordinate Rotation Digital Computer,CORDIC)方法的角度计算原理,将输入的正交信号转换为向量(x,y),通过多次旋转迭代使向量最终收敛于X轴,对旋转角度进行求和即可得到目标角度值。基于FPGA用Verilog语言编写CORDIC算法,可以实现相位细分、信号辨向和整周期计数功能,通过扩展数据位宽消除了算法迭代过程中产生的舍入误差。对改进算法进行了仿真与实验验证,结果表明经过20级迭代后其理论分辨率为0.4″,计算角度的误差为±0.5″,光栅测角系统实际测量误差减小了约98.42%。该算法通过对正交信号进行精密细分来计算精密仪器的相角变化量,在工程应用中具有普适性。
基金supported by the National Natural Science Foundation of China under Grant No.61872328SRF for ROCS SE+1 种基金the Youth Innovation Promotion Association CASCAS-TWAS president’s fellowship program。
文摘This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon.The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot intervals under a minor assumption, that λ is the second and third eigenvalues of the subdivision matrix. And then, a million of numerical experiments are tested with randomly selecting positive knot intervals, which verify that our new subdivision scheme satisfies the assumption.However this is not true for the other two existing non-uniform Doo-Sabin schemes in Sederberg, et al.(1998), Huang and Wang(2013). In additional, numerical experiments indicate that the quality of the new limit surface can be improved.
