基于整数维约束的分维形状映射生成方法

把整数维图形研究方法与分数维图形研究方法相结合，提出一种基于整数维规则几何形状的约束的分维形状映射生成方法，有于描述自然界和工程中出现的且具有特定基本形状趋势的随机现象和随机过程，首先，任意选取一个具有调配函数的自由形状构造一个有序参数空间，确定有序参数的取值规律和区域，把有序参数空间与自适应神经网络，随机性相结合，构造一个随机离散参数空间，并建立起有序参数与随机离散参数之间的参数对应关系，最后，通过有序与无序的参数对应关系，建立一个独立于任意规则几何形状的统一的分形映射关系，对相应整数维的任意规则参数几何形状分形映射，生成宏观形态趋势可预见和可控制的分维形状，该提出的方法适有于任意参数几何形状的分形映射，生成分形图形，且方法简明，易于实现。

Generation of Fractal Shape Mapping under Integeral Dimension Constraint

In simulation of natural scenes of virtual reality, the visualization of irregular geometric shape has got very important position. In order to generate irregular geometric shape with specific shape character, a new method of generating fractal shape mapping based on integeral dimension constraint is presented by combining integeral dimension modeling method with fractal dimension modeling method,thus can be used to simulate random natural phenomena of specific basic shape tendency. Firstly, for determining the rule and region of ordered parameter value, an ordered parametric space is constructed by choosing the free shape with mixed function. Then, a random disordered parametric space is constructed by combining the ordered parametric space with adaptive linear neuron networks, and the parametric correspondence relation can be created between the ordered parametric space and the disordered parametric space.Finally, according to the relation of ordered and disordered parametric correspondence, an unique fractal mapping relation is created independent of any regular geometric shape. And the macro conformation tendency of predictable, controllable and adjustable fractal shape can be generated by fractal mapping from any specific regular parametric geometric shape of corresponding integeral dimension. The method of fractal shape mapping generation can be applied to any parametric geometric shape and easy to be realized.