Sectional discrete curvature estimation based on the parabola

Abstract

The local geometric properties such as curvatures and normal vectors play important roles in analyzing the local shape of objects. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the curvature of vertices, because there is no its exact definition in meshes. In this paper, we indicate the fatal error in computing discrete sectional-curvatures by the previous discrete curvature estimations. Moreover, we present a new discrete sectional-curvature estimation to overcome the error, which is based on the parabolic interpolation and the geometric properties of Bezier curve.