Affine And Projective Iterated Function Systems And Fractal Interpolation Surface,

Fractal Interpolation Surface is an important part of the Fractal Geometry Theory. It has broad application in Figure and Image Processing, Material Subject, Geography and Geological Subject, Computer Simulation etc. At the present time, there are many research results on the regular dissection of the rectangle area, the research of irregular dissection on triangle or quadrangle area and the dissection on spatial area are very few. So it is very necessary to introduce the generic affine transformation and project transform methods.Contraposing these problems, this paper do some research on Iterated Function System (IFS) and fractal interpolation surface as follows:1. Dissect the triangle area regularly or irregularly, using generic affine transform to construct affine IFS, and the corresponding fractal interpolation IFS. And using this IFS we simulates the mountain in the nature successfully.2. Dissect the quadrangle area regularly or irregularly, using generic project transform to construct project IFS, and the corresponding fractal interpolation IFS. And using this IFS we simulates the mountain in the nature successfully.3. Dissect the triangle area regularly or irregularly, using generic project transform to construct project IFS, and the corresponding fractal interpolation IFS. And using this IFS we simulates the mountain in the nature successfully.4. Dissect the spatial triangle area regularly or irregularly, construct spatial affine transform. Then introduce the fourth dimension, construct fractal interpolation IFS. And using this IFS we simulates a kind of fractal interpolation surface in space.5. Dissect the spatial quadrangle area irregularly, construct spatial project transform. Then introduce the fourth dimension, construct fractal...