A contact detection algorithm for superellipsoids based on the common‐normal concept

The paper aims to introduce an efficient contact detection algorithm for smooth convex particles.

The contact points of adjacent particles are defined according to the common‐normal concept. The problem of contact detection is formulated as 2D unconstrained optimization problem that is solved by a combination of Newton's method and a Levenberg‐Marquardt method.

The contact detection algorithm is efficient in terms of the number of iterations required to reach a high accuracy. In the case of non‐penetrating particles, a penetration can be ruled out in the course of the iterative solution before convergence is reached.

The algorithm is only applicable to smooth convex particles, where a bijective relation between the surface points and the surface normals exists.

By a new kind of formulation, the problem of contact detection between 3D particles can be reduced to a 2D unconstrained optimization problem. This formulation enables fast contact exclusions in the case of non‐penetrating particles.