Research on 3D medial axis transform via the saddle point programming method

The present paper investigates the 3D medial axis transform of objects bounded by freeform surfaces via the saddle point programming method, a mathematical programming approach used to identify the saddle points of a function. After exploring the local geometry and saddle point property of 3D medial axis transform, the mathematical programming method is employed to construct the saddle point programming models. Based on the optimality conditions that the optimal solutions should satisfy, a generic algorithm for computing various medial axis points is developed. In order to identify the junction points and localize the problem, the boundary and the skeletal curves are divided into skeletal segments, and it is proved to be efficient and accurate by numerical examples.

► The local geometric properties of 3D MAT are detailed.
► We study the saddle point properties of the 3D MAT.
► The medial axis points are solved from the saddle point programming models.
► The medial sheets are obtained by identifying two families of orthogonal curves.