In this paper we propose a simple way to formulate geometric contact formation to have an arbitrary intersection shape in a robotic (humanoid) posture generation problem. The contact shape is the outcome of our posture generator that is formulated as a non-linear optimization programming to fulfill a large variety of robot intrinsic limitations (e.g. joint and torque limits) and tasks (e.g. desired contact). Starting by defining convex areas of contact on the robot's body and the environment, that we call contact patches, we can generate contacts with arbitrary intersection of a pair of any of these predefined patches. Our geometric contact modeling writes very simply as additional constraints and variables added to the optimization problem, translating the search for an ellipse inscribed in the intersection of the pair of patches we want in contact. The result of our posture generator is then a configuration where contact patches are not necessarily included in one another. This allows our posture generator to propose contacts of different shapes with a non-predefined number of contact points (used later to compute reaction/contact forces). We illustrate the efficiency of our method in multi-contact posture generation with the HRP-2 and ATLAS humanoid robots with results that can not be generated automatically by existing methods.