Fractal Graph Metamorphosis Technology

As an important embranchment of the non-linear science, fractal theories is a foreland subject have been applied vastly in the aspects of fractal modeling, nature scene simulating and image compressing. With the rapid development of computer graphics and the technology of software, the study and application of the fractal theories is taken more attention and the technique of fractal morphing have been popular. The research of fractal metamorphosis is an important realm of the computer graphics.Fractal graph morphing requests a progress which is a gradual, smooth and natural transformation from one key shape into another. As a scientific tool, iterated function systems (IFS) put up a good manner to simulate the nature scenery. This thesis studies the approach of the fractals attractors' morphing controlled by a vertex transformed techniques in two-dimensional and three-dimensional space on the iterated function systems (IFS).Firstly, this paper expatiate on fractal theories and some fractal graph generating systems, analyze the disadvantage of some currently algorithm. Analyzing the disadvantage of some currently algorithms, an interactive fractal modeling algorithm -points transformation algorithm is presented ground on the fractal theories, mathematics, computer graphics etc. The algorithm include two-point transformation, three-point transformation (affine transformation in two-dimensional), four point transformation (bilinear transformation in three-dimensional) and their corresponding translation (upgrade). Taking advantage of this algorithm, you can implement the technology of interactive, visualizing and real-time fractal graph generating by using iterated function system based on affine mapping. And then you can morphing the graph to get the object attractors expediently by control the vertex. The interpolation be considered in the thesis include linear interpolation, thrice interpolation, and spline interpolation. The constraint condition be used to keep the connectivity of graphics and corresponding matching to make the scenery more natural and verisimilitude.The results in this thesis are very useful for nature scene simulating, flash making, architecture foiling and virtual reality etc. theoretical research . it will shorten the time of the morphing effectively, keep the connectivity topology of the fractal graphics and enrich the theory and technique of the morphing ulteriorly.