Since the conception of fractal was introduced by Mandelbrot in 1970, as a new nonlinear subject, fractal was attracted by many academic researchers for a very long time.Fractal theory mainly describe irregular,Self-similar geometry of the nature and nonlinear system. Therefore, many natural phenomena such as rolling mountains, floating clouds, dense waterways, and different plants are the main research object of the fractal, and with our daily life.In recent years, with the rapid development of computer graphics, fractal and hardware technique, fractal theory has been widely applied in computer animation, virtual reality, fractal modeling, natural scenery simulating and so on. Fractal animation is an important field of fractal theory, and its control technology is one of the most important issues in computer graphics.The fractal animation control algorithm based on the point transform is mainly researched in the paper. The basic theories of fractal, several typical generating methods of fractal graphs, the fixed point connection, interpolation algorithms and existing fractal animation control algorithm are studied. For the disadvantages of existing fractal animation control algorithm, a novel fractal animation control algorithm based on fixed point connect is presented. The proposed algorithm includes the matching principle of point transform, connectivity control algorithm of attractor and interpolation control algorithm. The problem of mismatch of the number of attractor between two key frames is solved by the matching principle of point transform. Attractor connectivity control algorithm can effectively control the attractor connectivity, avoiding attractor cracking phenomena in the existing algorithms. The Interpolation control algorithm can flexibly change attractor path by nonlinear interpolation, therefore, the problems of attractor disappear and distortion is solved, and more natural and more real fractal animation is achieved.The topology of fractal graph can be effectively controlled in the algorithm, and the theory of fractal animation is enriched. |