Improvement And Application Of 2D Vector Field Design Techniques

In the fields of Scientific Visualization, vector field is one of the most important objects. There is so much progress on some theories and technologies relatively and some are applied practically, such as topology, compression or simplification of vector fields. Because of the different conditions of different researches, each needs data with special features. A researcher has to spend more time on pre-processing the data from simulation or sampling. He should take off the noise information and correct the errors to get some data with conditions of features, fields, distribution, etc. If possible, it will be more effective getting data from designing with own purpose. Then, all the procedure of data process can be simpler. For this data demand, some researchers put forward the theory of designing and this proves practical and useful. Additionally, it can be a substitute or a secondary method of the other techniques relevantly. Here we will improve several key techniques for application and show the creative points.The first is defining the elements of topology graphic interactively and quickly. Every element is defined with mathematic description in special features. We can establish certain rules for designing the features and locations, and all of above are based on the ideas of triangulations and piecewise linear.Secondly, in order to preserve the topology configuration, we create an algorithm to get triangulation results from adjusting with constrictions. In this way, we can make the procedure more quickly and effectively.Thirdly, we show the simple methods to correct or adjust the local features. The elements of the topological graphic can be defined with their own controlling polygons. But in the fields with less topological definitions, more other constrictions are needed to insure the texture. Additionally, based on the triangulation results, we can redefine the information of the points and get new or more reasonable results of the vector fields.Above all, this paper includes modeling for visualization and error analysis. We also describe the application of designing vector fields with high-order critical points. Also here are conceptions about Clifford algebra and its applications.