This is a dataset of volumetric mapping problems. It consists of 60 instances, each consisting of a tetrahedral mesh of a genus 0 object together with a prescribed mapping of its boundary onto a cuboid. A standard 3D Tutte embedding fails (i.e. yields inverted/flipped elements and thus a non-bijective map) on every single instance. Also state-of-the-art 3D untangling methods struggle with it, despite the relatively simple convex boundary setting. For instance, the Code of the method "Lifting Simplices to Find Injectivity" succeeds on 35/60, the Code of the method "Foldover-free maps in 50 lines of code" succeeds on 28/60. We therefore hope it can inspire and be of use in further research on this problem.
The instances were encountered during research in the context of the 3D Motorcycle Complex.
Each instance is represented by two tetrahedral meshes in .vtk format, object.vtk and parameter.vtk. Both contain the same mesh structure, object.vtk equipped with the XYZ-coordinates (object space) per vertex, parameter.vtk equipped with UVW-coordinates (parameter space) per vertex (where the boundary vertices' UVW-coordinates represent the prescribed boundary map; the interior vertices' UVW-coordinates represent the (non-flip-free) Tutte embedding solution). The handles.txt file of each instance additionally contains the list of indices of boundary vertices (as required as additional input by one of the above codes).