Particles in granular matter can have very different and irregular shapes. The computational treatment of nonspherical objects is a major difficulty in the simulation of granular flows. In this paper; two basic strategies for contact resolution between objects described by level surfaces are presented and analyzed. They are based on the iterative solution of systems of nonlinear equations. The major difficulties are pinpointed and necessary steps toward a generic algorithm are proposed. A test case of colliding cardioids in two dimensions is used to demonstrate the algorithms and illustrate common pitfalls.