The Technology Of Skeleton And Cut-off Set In Fractal Modeling

After Mandelbrot put forward the concept of fractal, the research on fractal geometry had attracted extensive attentions, especially at nature scenery simulation. Fractal modeling displays its unique advantage and become one of the popular topics.Iterated Function System (IFS) is the typical method of fractal modeling. Its attractor usually is fractal. If given an IFS, that its attractor is unique, which is independent with the iterative initial set, and obtained by infinite iteration. But at the process of natural scenery simulation, usually don't need the attractor of IFS, just need the result of the finite iteration.When we simulate the natural scenery, especially on trees modeling, Condensation Iterated Function System is a better method, because the result by finite iteration has relation with initial set. Different modeling were obtained by different initial set.This thesis based on the Condensation Iterated Function System, curve theory and subdivision method, put forward a fractal modeling technology by Skeleton and Cut-set. This technology has two main methods. The one is obtaining shape outline of the IFS' initial set firstly, and then bending the outline; the other one is bending the skeleton firstly, then get the outline of the initial set by using Cut-set. There are two main strategies in the process of bending: Approximation and Interpolation.The thesis take the tree for example, presents different initial set by different bending. The method concludes control-point spline, data-point spline and subdivision. The paper also gives many effect pictures on the result by using this technology. The result show, that by using this technology, we realized the smooth processing of the tree's surface, and make the simulation effect more fidelity. Because different initial set can get by using different bend method, so we can make various forms by iteration and realize the diversification of the fractal modeling.