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A pair of pants is a genus zero orientable surface with three boundarycomponents. A pants decomposition of a surface is a finite collection ofunordered pairwise disjoint simple closed curves embedded in the surface thatdecompose the surface into pants. In this paper we present two Morse theorybased algorithms for pants decomposition of a surface mesh. Both algorithmsoperates on a choice of an appropriate Morse function on the surface. The firstalgorithm uses this Morse function to identify handles that are gluedsystematically to obtain a pant decomposition. The second algorithm uses theReeb graph of the Morse function to obtain a pant decomposition. Bothalgorithms work for surfaces with or without boundaries. Our preliminaryimplementation of the two algorithms shows that both algorithms run in muchless time than an existing state-of-the-art method, and the Reeb graph basedalgorithm achieves the best time efficiency. Finally, we demonstrate therobustness of our algorithms against noise.

Segmenting a Surface Mesh into Pants Using Morse Theory