Construction of Smooth Biorthogonal Waves on Triangulated Spaces

The article presents the results of the first part of the work on the development of CAD / CAM / CAE systems for the analysis and construction of fiber laying trajectories for 3D printing of structures made of composite materials. The study is devoted to biorthogonal wavelets of the class of smoothness on a triangulable space, which is obtained from closed multidimensional cubes or their homeomorphic formations by gluing edges. The use of wavelet coefficients allows obtaining fairly accurate approximations of the function. The proposed results can be applied for an approximate solution of the problems of the theory of elasticity.