We address the problem of representing and processing non-regular, non-manifold two-dimensional simplicial meshes, that we call triangle-segment meshes, at different levels of detail. Such meshes are used to describe spatial objects consisting of parts of mixed dimensions, and with a non-manifold topology. First, we describe a multi-resolution model for non-regular, non-manifold meshes, that we call a Non-manifold Multi-Tessellation (NMT). We consider the selective refinement query, which is at the heart of several analysis operations on multiresolution meshes. Next, we focus on a specific instance of a NMT, generated by a simplification process based on vertex-pair contraction, and we describe a compact data structure for encoding it. We also propose a new data structure for triangle-segment meshes, capable of representing both connectivity and adjacency information with a small memory overhead, that we use to describe the mesh extracted with selective refinement. To this aim, we define algorithms to efficiently perform mesh updates on such a data structure.
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