Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affin...Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.展开更多
This paper explains that the terms“horizontal and vertical scales”are not appropriate in map projections theory.Instead,the authors suggest using the term“scales in the direction of coordinate axes.”Since it is no...This paper explains that the terms“horizontal and vertical scales”are not appropriate in map projections theory.Instead,the authors suggest using the term“scales in the direction of coordinate axes.”Since it is not possible to read a local linear scale factor in the direction of a coordinate axis immediately from the definition of a local linear scale factor,this paper considers the derivation of new formulae that enable local linear scale factors in the direction of coordinate x and y axes to be calculated.The formula for computing the local linear scale factor in any direction defined by dx and dy is also derived.Furthermore,the position and magnitude of the extreme values of the local linear scale factor are considered and new formulas derived.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.60972004 and 60402004)
文摘Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.
文摘This paper explains that the terms“horizontal and vertical scales”are not appropriate in map projections theory.Instead,the authors suggest using the term“scales in the direction of coordinate axes.”Since it is not possible to read a local linear scale factor in the direction of a coordinate axis immediately from the definition of a local linear scale factor,this paper considers the derivation of new formulae that enable local linear scale factors in the direction of coordinate x and y axes to be calculated.The formula for computing the local linear scale factor in any direction defined by dx and dy is also derived.Furthermore,the position and magnitude of the extreme values of the local linear scale factor are considered and new formulas derived.
