Tiling Surfaces with Cylinders Using n-loops

Subdividing surfaces into cylinders is a significant question in various applications. Even if specific approaches have been described in several domains, most of the time topological properties are not explicitly handled, and the segmentation remains mainly driven by geometry. We present here an original approach to describe the topological and combinatorial nature of a tiling with cylinders. We first introduce m-cellular complexes, a framework allowing the flexible description of cuttings and tilings. Then we describe n-loops, an extension of the loops for producing tilings with cylinders. Computational issues of n-loops are then addressed, using both topological and geometrical properties of the surface. Finally, we propose two applications, first tiling a surface with large quadrangles patches, and then segmenting surfaces with possible protrusions.