Research On Methods Of Topological Structures Analysis And Visualization For Vector Fields

Data field is a class of discrete dataset,which distributes in the special space area and whose elements interact with each other.It is widely applied in the domains of aerospace,marine meteorology,electromagnetic analysis and so on,such as wind field,flow field,electromagnetic field and so on.Vector field,which is a special class of data field and has both magnitude and direction,can describe the laws of motions and change of the objects.It is of great significance to comprehend and dig the underlying distribution characters of vector field and further to discover the laws of motions and changes for scientific computation and engineering application.The researches of vector field mainly focus on data processing,topological structures analysis and visualization.The vector field data processing is to address the completeness and availability of the dataset and contains data interpolation,smooth and denoising.The topological structures analysis mainly researches the critical structure characters of vector field and contains the topological structures extraction for steady(time-independent)vector field and topological structures tracking for time-dependent vector field.The vector field visualization uses the visual means to describe the global characters of distributions,motions and changes for vector field.This dissertation studies key problems of vector field researches,which contain interpolation,topological structures extraction,topological structures tracking and visualization with streamlines.It aims to break through the key technologies,and support the special applications of vector fields from the theoretical and technical aspects.The main contents and contributions in this dissertation are as follow:There are two shortcomings of inverse distance weighted(IDW)method for vector field interpolation,on the one hand the selection of reference samples lacks of scientific guide,on the other hand the local behavior of the vector field can't be expressed.Considering these two shortcomings,an adaptive IDW interpolation method involving local behavior for vector field is proposed.Firstly,the original sample set is searched based on the distance impact degree.And then,the original set is classified as small sample set or large sample set.In the case of small sample set,it can be used for IDW method directly.However,in the case of the large sample set,the optimal sample set for IDW interpolation method can be acquired by the optimization step based on the assumption of local linear approximation.Theoretical analysis indicates that the proposed method can select the reference samples adaptively,and the interpolation result is more reasonable due to the assumption of local linear approximation.The experimental results show that proposed method improves the interpolation accuracy.To address the problems in the already existing topological structures extraction methods based on Morse decompositions,which contain too many empirical parameters and vague refinement objectives,this paper proposes a novel extraction method for topological structures based on the improved Morse decompositions.Firstly,the critical simplexes are defined and detected by a robust manner.Secondly,the Morse sets can be classified by their regions and the detected critical simplexes.And a new refinement criterion for identifying Morse sets to refine based on the classification of Morse sets is built.Finally,the flow of the proposed method is presented.Experimental results demonstrate the availability and effectiveness of the proposed method.Morse sets are more numerically stable than the conventional topological structures.However,the tracking of Morse sets is a missing part for the analysis of time-dependent vector fields.A novel tracking method of Morse sets for 2D bounded time-dependent vector fields is proposed.The critical triangle is defined and detected by a robust combinatorial way.The forward and backward image of a critical triangle can be acquired by the mapping search strategy.Finally,the tracking method of Morse sets for critical points is proposed based on their images,and the tracking method of Morse sets for closed orbits is proposed based on the tracking of Morse sets for critical points.Experimental results demonstrate the availability and effectiveness of the proposed method.The streamline method is an important one in the visualization of 3D vector fields.In order to solve the problems of streamline occlusion and visual confusion caused by excessive streamlines,meanwhile to ensure the streamlines can present the variation law and important features of vector fields exactly,a view-dependent streamline simplification method for 3D vector fields based on feature-preservation is proposed.Firstly,streamline set of 3D vector fields is generated by particle tracking and mapped under view-dependent.Secondly,feature-preservation computation of the streamline set is implemented.Finally,the streamline set is simplified effectively by computing visual effect metric based on iteration.The experiment results show that the visual effects of the streamlines are enhanced on the basis of valid feature-preservation of vector fields,and the effectiveness of the proposed method is unaffected by the viewpoint transformation.