Implicit surface reconstruction based on generalized radial basis functions interpolant with distinct constraints

Abstract

• We propose a generalized radial basis function interpolant with difference constraints. • Various types of constraints are derived to satisfy the interpolation conditions . • An adaptive iterative algorithm is used for approximating gradient and tangent constraints. • The numerical results reveal the improved performance of our method. In this work, we present a new algorithm for reconstruction of implicit surfaces from a set of cloud points with normals (Hermite data), based on the generalized radial basis functions interpolant with various types of constraints. Our key contribution is a novel construction of difference constraints in the interpolant to satisfy certain linear functional data, named as the domain constraints, the difference constraints of the gradient and the difference constraints of the tangent. To avoid ambiguous constraints, we apply an iterative algorithm to determine the adaptive distance in the difference constraints. The extended interpolant can not only provide an exact interpolation to the function values, but also approximate the function's derivatives by constructing a difference operator along the gradient or tangent direction. We interpolate the sampling points using our method by constructing a signed distance field in the geometry domain. Compared to the Hermite–Birkhoff interpolation with RBFs, the interpolant we use has faster solution efficiency. The experimental results of several data sets show the reliability and performance of our method in a variety of practical scenarios.