Data Reconstruction And Topological Analysis For Two-Dimensional Scalar Field Under Continuous Framework

With the rapid development of modern scientific computing and the use of a variety of measuring instruments,the scalar field data collection is more and more convenient,the source of data is becoming more and more widely,such as aerospace,geological exploration,biomedical,fluid mechanics,etc.But data collection is not a final purpose,effectively within the discrete data extraction and analysis of critical information,is the ultimate goal of we get the data,also is one of today's popular science content.And the use of mathematics and computer graphics theory and tools in the field of computing and visual analysis is an effective way to find critical information.This paper take two dimensional scalar field data as the research object,adopt a new method of geometric calculation and topology analysis which base on sequential modeling,visualization of two dimensional scalar field feature point distribution,topology structure,build the Morse-Smale complex shape.The calculation and analysis results can provide the reference for the professional researchers of scalar field data sources.Continuous scalar field topology analysis is based on the Morse theory,in view of the discrete data of the scalar field,the traditional methods are mostly conducted in discrete framework,its theoretical basis is Morse theory after discrete.So the topology structure is only an approximation of discrete data field effect with low precision,poor smoothness,complicated process and other defects.This paper use Double ZP box spline to reconstruct discrete data as continuous model,to satisfy the continuity conditions which Morse theory should have.And directly calculate the critical points,building the integral curve and Morse-Smale complex on continuous model.Experimental results show that,compared with discrete frame method,the method based on continuous framework which accuracy of point extraction is higher,the topological structure more clearly,topological integral curve has better smoothness and Morse-Smale complex simplify more efficient.