Principal Directions Estimation on Point Set Surfaces

Principal direction is an important geometry feature of 3D surfaces. It can benefit many applications such as surface quadrangulation, surface field design and so on. In this paper, we propose a novel algorithm for estimating principal directions based on normal variations. The proposed algorithm is based on the observation that the principal directions indicate respectively the slowest and the steepest variation of the surface normal. The algorithm is simple yet efficient. It doesn't need any analytic surface fitting procedure. The result shows that our algorithm is correct and suitable for different surface shapes.