Research And Design Of 3D Fractal Parameterized Drawing System Based On ObjectARX

Fractal possesses not only a deep theoretical significance but also a huge value in application; great attention has been paid to its research. The connotation of 2D fractal graph is profound and with a clear hierarchy, and the 3D fractal graph is even more colorful in a rich hierarch, it embodies deeply the orderliness and chaos of various types, thus provided a powerful tool for computer description and treatment of irregular natural scenery. Owing to the theory of fractal, 3D modeling and programming have not been familiarized and grasped by ordinary personnel, its application has been restricted. Let the 3D fractal graph be generated on computer, and using fewer numbered parameters to obtain complicated lifelike graph of natural scenery. The abstract abstruse theoretical research is let to be applied into practical design, and let the designers don't have to be expend time on the programming and the abstruse mathematics, these will make considerable practical value on the pushing forward of simulative emulation techniques.Basic principle and application of 3D fractal graph have been carried out in this paper. On the bases of analyzing the theoretical foundation of the formation of fractal graph, the technique of 3D fractal graph and typical fractal method and graphic example were studied. Its theoretical basis, key elements, principle and method of generation, and range of application were analyzed. The possibility, method, technology, and application of its 3D parameterization were expounded, thus summed up and screened out important parameters of determining its formation, and established the model. On the bases of ObjectARX2000 a 3D modeling method combining the 3D fractal modeling with the solid modeling was put forward for 3D modeling method of Sierpinski triangle. An improved algorithm of 3D fractal curved surface was advanced to substitute the displacement method of triangle midpoint for generating the fractal-curved surface, so as to establish a 3D mathematical model for 3D Caley tree. Main program was compiled by the use of VC++ and ObjectARX language to form a 3D fractal parameterized drawing system, thus provided a convenient condition for introducing the fractal into the domain of CAD design.Under the circumstances of AutoCAD2000, this paper developed a 3D fractal parameterized drawing module. By inputting certain numbered parameters, a wonderful magnificent 3D fractal graph could be generated. The function 3D plotting of AutoCAD2000 was enhanced and let the complicated mathematical problems and issues of programming become a simple and easy using command. Thus convenient conditions were created for realizing the simulation of real object in natural world, the generation of emulative body and the supplied material for designing matched scenery. By the aid of powerful compiling function and coloration with doodle dyeing function of AutoCAD, to make the fractal graph being more true to life and enchanting beautiful.A preliminary research on the principle technique of chaos, which bears a very close relationship with fractal, was also carried out in this paper. Projection drawings in different projective directions of chaos graph formed in AutoCAD were achieved, and the drawings could be observed from arbitrary angle in real time was realized by the aid of 3D display function of AutoCAD. It is convenient for carrying out research and analysis upon the relationship between chaos graph and its mathematical formulae.