Reconstructing Low Degree Triangular Parametric Surfaces Based on Inverse Loop Subdivision

Abstract

In this paper, we present an efficient local geometric approximate method for reconstruction of a low degree triangular parametric surface using inverse Loop subdivision scheme. Our proposed technique consists of two major steps. First, using the inverse Loop subdivision scheme to simplify a given dense triangular mesh and employing the result coarse mesh as a control mesh of the triangular Bézier surface. Second, fitting this surface locally to the data points of the initial triangular mesh. The obtained parametric surface is approximate to all data points of the given triangular mesh after some steps of local surface fitting without solving a linear system. The reconstructed surface has the degree reduced to at least of a half and the size of control mesh is only equal to a quarter of the given mesh. The accuracy of the reconstructed surface depends on the number of fitting steps k, the number of reversing subdivision times i at each step of surface fitting and the given distance tolerance ε. Through some experimental examples, we also demonstrate the efficiency of our method. Results show that this approach is simple, fast, precise and highly flexible.