Provided herein are methods of reconstructing an image from projection data provided by a tomography scanner that is based on geometric optics comprising scanning an object in a cone-beam imaging geometry following a non-standard spiral path or a general piecewise smooth scanning path wherein projection data is generated and reconstructing an image according to a closed-form formula that is either in the filtered backprojection (FBP) or backprojection filtration (or backprojected filtration, BPF) formats. Also provided herein are associated systems and apparatuses for tomographic imaging.