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Treating the interactions of soft tissue with rigid user-guided tools is a difficult problem. This is particularly true if the soft tissue has a slender shape, i.e., resembling a thin shell, and if the underlying numerical time-integration scheme employs large time steps. In this case, large mutual displacements of both the tool and the soft tissue occur frequently, resulting in deep interpenetrations or breakthroughs. As a consequence, the computation of spatially and temporally coherent contact spaces turns out to be very challenging. In this paper, an approach is proposed that is tailored to these kinds of interactions. To solve this problem, a novel spatially reduced representation of the soft tissue geometry is employed where the dominant dimensions of the object are approximated by a 2D triangle surface, while the third dimension is given in terms of nodal radii. To construct a feasible, nonpenetrating configuration, a novel manifold projection scheme is presented where the colliding triangles are rasterized into a distance field in order to robustly estimate the contact spaces, even for large intersections. The method produces physically plausible results, albeit it is purely geometric, and the material parameters are neglected at the collision response stage. Various examples, including an interactive prototype arthroscopy simulator, underline the wide applicability of the approach.