In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system o...In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved, the theorem of fractal dimension of fractal interpolated surface is derived, and the case that practical data are used to interpolate fractal surface is studied.展开更多
In this paper,an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall.This model adopts the maximum positive deviations and maximum negative deviations between ...In this paper,an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall.This model adopts the maximum positive deviations and maximum negative deviations between the measured values and trend values to determine the contraction factors.Hole profiles in 24 directions are measured.Fractal parameters are calculated to evaluate the measured surface profiles.The maximum and minimum fractal dimension of the hole wall are 1.36 and 1.07,whereas the maximum and minimum fractal roughness are 4.05 x 10-5 and 4.36 x 10-10 m,respectively.Based on the two-dimensional evaluation results,three-dimensional surface topographies in five typical angles(0°,45°,90°,135°,and 165°)are reconstructed using the improved model.Fractal parameter Ds and statistical parameters Sa9 Sq,and Sz are used to evaluate the reconstructed surfaces.Average error of Ds,Sa,Sq,and Sz between the measured surfaces and the reconstructed surfaces are 1.53%,3.60%,5.60%,and 9.47%,respectively.Compared with the model in published literature,the proposed model has equal reconstruction effect in relatively smooth surface and is more advanced in relatively rough surface.Comparative results prove that the proposed model for calculating contraction factors is more reasonable.展开更多
Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the origina...Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.展开更多
文摘In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved, the theorem of fractal dimension of fractal interpolated surface is derived, and the case that practical data are used to interpolate fractal surface is studied.
基金This work was supported by the Intelligent Robotic in Ministry of Science and Technology of the People's Republic of China(Grant No.2017YFB1301703)the Young Fund of the Natural Science Foundation of Shaanxi Province,China(Grant No.2020JQ-121)+1 种基金the National Natural Science Foundation of China(Grant No.51975472)the Innovation Capability Support Plan of Shaanxi Province,China(Grant No.2019KJXX-063)。
文摘In this paper,an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall.This model adopts the maximum positive deviations and maximum negative deviations between the measured values and trend values to determine the contraction factors.Hole profiles in 24 directions are measured.Fractal parameters are calculated to evaluate the measured surface profiles.The maximum and minimum fractal dimension of the hole wall are 1.36 and 1.07,whereas the maximum and minimum fractal roughness are 4.05 x 10-5 and 4.36 x 10-10 m,respectively.Based on the two-dimensional evaluation results,three-dimensional surface topographies in five typical angles(0°,45°,90°,135°,and 165°)are reconstructed using the improved model.Fractal parameter Ds and statistical parameters Sa9 Sq,and Sz are used to evaluate the reconstructed surfaces.Average error of Ds,Sa,Sq,and Sz between the measured surfaces and the reconstructed surfaces are 1.53%,3.60%,5.60%,and 9.47%,respectively.Compared with the model in published literature,the proposed model has equal reconstruction effect in relatively smooth surface and is more advanced in relatively rough surface.Comparative results prove that the proposed model for calculating contraction factors is more reasonable.
文摘Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.
