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We extend the two‐dimensional Cartesian shapelet formalism to   d  ‐dimensions. Concentrating on the three‐dimensional case, we derive shapelet‐based equations for the mass, centroid, root mean square radius, and components of the quadrupole moment and moment of inertia tensors. Using cosmological   N  ‐body simulations as an application domain, we show that three‐dimensional shapelets can be used to replicate the complex sub‐structure of dark matter haloes and demonstrate the basis of an automated classification scheme for halo shapes. We investigate the shapelet decomposition process from an algorithmic viewpoint, and consider opportunities for accelerating the computation of shapelet‐based representations using graphics processing units.

Three‐dimensional shapelets and an automated classification scheme for dark matter haloes 1★ [link]