Reconstrução de superfícies 3D por aproximação multiquádrica

Abstract

Progress in the wider areas of technology has grown strongly in recent years. Areas such as aeronautics, meteorology, geological modeling, geology, climate patterns, stellar spectra, or human gene distributions, are regularly confronted with problems of surface reconstruction in various applications. The real numerical data is usually difficult to analyze. Any function that effectively correlate the actual data is difficult to obtain and of difficult interaction. There are many methods to reconstruct a continuous surface from scattered data or regularly spaced in the domain. In this thesis, the idea of the basic theory of Hardy multiquadric approach to surface reconstruction has been developed to approximate a given data set. This method is part of a class of methods known as methods of radial basis functions and we show its superiority in terms of accuracy and smoothness desired, and even with the reduced total number of data needed for reconstruction of the surface. The applications examples in this thesis are to digital terrain elevation (DEM), 3D surface reconstruction, but this method is easily extended to other areas in any dimension. We discuss its implementation, its performance and provide numerical simulations.