One challenging and not extensively studied issue in obstacle avoidance is the corner cutting problem. Avoidance constraints are usually imposed at the sampling time without regards to the intra-sample behavior of the dynamics. This paper improves upon state of the art by describing a multi-obstacle environment over a hyperplane arrangement scaffolding, provides a piecewise description of the "shadow" regions and represents them into a combined mixed integer and predictive control formulation. Furthermore, over-approximation constraints which reduce to strictly binary formulations are discussed in detail. Illustrative proofs of concept, comparisons with the state of the art and simulation results over a classical multi-obstacle avoidance problem validate the benefits of the proposed approach.