Tackling of uncertain data is a major problem in analysis, modeling and simulation. Fractal interpolation surface and fuzzy set method are employed to solve the issue of uncertainty in modeling irregular surface. Initial interpolation data grid point is used as the kernel of Gaussian fuzzy membership function and its fuzzy numbers can be calculated by specifying λ of λ-cut set. These fuzzy numbers are used as uncertain data, which are the boundaries of the fluctuation of initial grid, and defined as a new kind of fuzzy interpolation grids. With these interpolation grids fractal interpolation surface algorithm is applied to act on. By these definitions, experimental data for modeling rock surface is illustrated to show that how the interpolation scheme proposed in this paper enhances the controllability for manipulating uncertain data.
Aiming at the problem that rendering 3D Julia sets on CPU is slowly, a method of rendering 3D Julia sets on GPU is presented in this paper. After introducing the advantages of GPU and the operations of quaternion, the generating process of 3D Julia sets is discussed in detail. Ray tracing volume rendering algorithm is applied to obtain high quality 3D Julia sets, and escaping time algorithm is used to generate the discreet data of Julia sets, of which normal is estimated according to the original of ray and accelerated by using unbounding sphere algorithm, and the graphics examples are given to illustrate this algorithm. Finally, the factors of affecting rendering speed and refined effect are summarized. The results show that the speed of 3D Julia sets rendering on GPU is much faster than CPU, and the interactivity of rendering process is also enhanced.
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