The Orthogonal Reconstruction Method for Surface Modeling over Triangulated Domains

To apply frequency spectrum analysis method,which is commonly used in signal processing and on digital geometry processing,it is necessary to choose a proper orthogonal function system.This paper first presents the detailed mathematic expressions of orthogonal V-system of degree 2 over triangulated domains,and then proposes a frequency spectrum analysis method to surface models,which is a direct application of the new constructed system.The method is to expand a surface model represented by piecewise polynomial of degree 2 in two variables in a V-series and then get the frequency spectrums,with which the surface model can be precisely reconstructed.Therefore orthogonal decomposition and reconstruction of a geometry object can be realized.Compared with the previous research,the expression of geometry information with the V-system of degree 2 has advantage of significant reduction in the quantity of data involved.The experimental results show that the proposed method is practical and feasible.