Abstract

In this paper we present a technique for the calculation of the Fourier transform for functions defined on oriented closed 2-manifolds. The objects are given as oriented triangular meshes. Our focus in this paper is on the characteristic function of the model, that is, the function that is equal to one inside the model and zero outside. The advantage of our approach is that it provides an automatic, simple, and efficient method for computing the Fourier coefficients directly from the mesh representation. This avoids the approximation of the mesh by a grid of voxels which leads to a loss of details and error prone in calculation. The main idea is to distribute the calculation of the Fourier coefficients over the elementary shapes composing the mesh. Then we use the divergence theorem to simplify the computation by calculating the coefficients using integrations on simpler domains. The algorithm is simple and efficient, with many potential applications. Some examples are given to demonstrate the effectiveness of our approach.

Key words: Fourier coefficients, partial calculation, voxelization, triangular mesh, divergence theorem.