The Freaky Torus

This dataset contains the Python code to compute samples on our shape space Freaky Torus of deformed tori, a synthetic shape space with factors S¹×S¹×T² The first factor, an S¹, controls the deformation of the latitudinal cross-section into a rotated ellipse. The next factor, another S¹, controls the deformation of the longitudinal cross-section into a rotated ellipse. The third factor, a two-dimensional flat torus T², controls the position of a bump on the deformed torus. Above, we visualize our synthetic shape space by demonstrating the effect of moving along the individual factors to the final shape. More details on the construction can be found in the appendix of the ICLR 2023 paper Parametrizing Product Shape Manifolds by Composite Networks. Additional to the code, we also include the exact dataset that we used for the results of our paper in the data folder.