An efficiently packed, low-distortion parameterization with a short boundary can save a great amount of memory and improve both quality and efficiency of rendering. Existing packing methods begin with an input atlas (or parameterization), but the cuts in the input atlas may be not suitable for a high quality result. We propose a simple yet effective approach to cut an input surface and generate an atlas that comprehensively considers the packing efficiency, the mapping distortion and the boundary length. Viewing the desired cuts on the input mesh as the pullback of a low-distortion mapping from a polysquare boundary, we notice that the above three objectives actually imply a small number of cone singularities with angle deficit of pi/2 k, k in Z, and orthogonally intersected short cuts passing through all singularities. Therefore, we first leverage a cross frame-field to identify a set of singularities and cancel some of them to balance their amount and atlas distortion. Then, the singularities remained are heuristically connected by short cuts which intersect with each other nearly orthogonally. Results show that our method produces a low-distortion and polysquare-like atlas with controllable number of singularities. Comparing with other atlas generation methods only focusing on distortion, taking our atlas as the input for the subsequent packing algorithm (Liu et al., 2019) is better than using previous cutting strategies on a benchmark containing 5519 cases, because the conflicts among those desired objectives for packing are alleviated at an early stage.