Study Of UTD Method Based On NURBS Modeling

Due to the limitation of traditional UTD method in modeling that objects are always approached with cylinders and cones, a new method of UTD is presented in this thesis which combines NURBS modeling with UTD method. At first, the mathematical expressions and the basic characteristic of Bezier surface and NURBS surface is presented. Then, the ray-tracing algorithm for reflected ray of NURBS-UTD is given. The algorithm is applied to some typical models and good results are achieved compared to analytical results, which proves the validity of the algorithm. Also some examples of ray-tracing on arbitrary surfaces are given. Creeping ray is a special type of ray whose ray-tracing is relatively complex. The ray-tracing algorithm for creeping ray of NURBS-UTD is presented in this thesis. The algorithm is applied to some typical models and good results are achieved compared to analytical results, which also prove the validity of the algorithm. Some examples of creeping ray-tracing on arbitrary surfaces are given too. In the calculation of patterns in UTD method, ray-tracing is the key problem. But after so many preparations like ray-tracing, the calculation of scattering field becomes the kernel in UTD method. At the end of this thesis, the calculation of fields in the lit region which include direct field and reflected field and are given. Results of fields on a cylinder and a cone are given compared to referenced results and the compare shows the validity of the method presented in this thesis. Besides, Result of the fields in lit region when NURBS-UTD method is applied on an arbitrary surface is given.