To solve complex whole-body motion planning problems in near real-time, it is essential to either advance approximate solutions or to incorporate better informed priors. In this paper, we focus on modeling such a prior, by precomputing the feasibility of contact transitions in the context of discrete contact planning. Our contribution is twofold: First, we introduce the contact transition and object (CTO) space, a joint space ofcontact states and geometrical information. Second, we develop an algorithm to precompute the decision boundary between feasible and non-feasible spaces in the CTO space. This boundary is used for online-planning in classical contact-transition spaces to quickly prune the number of possible future states. By using a classical planning setup of A* together with a l2-norm heuristic, we demonstrate how the prior knowledge about object geometries can achieve near real-time performance in highlycluttered environments, thereby not only outperforming the state-of-the-art algorithm by several magnitudes, but also having a significantly lower model sparsity.