Datasets:
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README.md
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pretty_name: EuLearn
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size_categories:
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- 10B<n<100B
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---
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# Dataset Description
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This dataset contains 3D objects representing a topologically diverse collection of surfaces, each generated from closed, parameterized curves with varying number of self-intersections (singular knots). The surfaces are organized by topological genus, ranging from 0 to 10, so each genus has its own subdirectory. Each surface comprises four files:
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## Filename Encoding Convention
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- `r0.02_0.029`: Minimum and maximum radius of the tubular neighborhood.
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- `v90`: Voxel resolution per axis. While v90 nominally refers to a 90 × 90 × 90 voxel grid, an offset of 5 voxels per side was added to prevent surface clipping at the bounding box edges.
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As a result, the actual scalar field is discretized into 101 × 101 × 101 = 1,030,301 grid points, yielding 1,000,000 voxels in total.
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- `.stl`: File extension. This denotes the
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Other file variants use suffixes to indicate their content:
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# Acknowledgements
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pretty_name: EuLearn
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size_categories:
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- 10B<n<100B
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---
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# Dataset Description
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This dataset contains 3D objects representing a topologically diverse collection of surfaces, each generated from closed, parameterized curves with varying number of self-intersections (singular knots). The surfaces are organized by topological genus, ranging from 0 to 10, so each genus has its own subdirectory. Each surface comprises four files:
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- __Non-Smoothed STL Mesh__ (`*_ns.stl`): A 3D mesh of the surface with sharp geometry and unmodified vertex positions. This version retains the raw output of the Marching Cubes algorithm.
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- __Smoothed STL Mesh__ (`.stl`): A geometrically smoothed version of the `*_ns.stl` surface, generated using Laplacian vertex smoothing in Blender.
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- This process adjusts vertex positions to reduce sharp edges and improve regularity, modifying surface area and volume while preserving the mesh connectivity and topological features (e.g., genus and Euler characteristic).
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- __Scalar Field__ (`*_sf.txt`): A plain-text file encoding the scalar field used to generate the surface via the Marching Cubes algorithm. The isosurface at level 0 defines the mesh geometry in the `*_ns.stl` file.
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- __Blow-up Profile__ (`*_bup.txt`): A plain-text file containing the radius at each point along the discretized curve. These radii define the thickness of the tubular neighborhood used to generate the scalar field.
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## Filename Encoding Convention
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- `r0.02_0.029`: Minimum and maximum radius of the tubular neighborhood.
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- `v90`: Voxel resolution per axis. While v90 nominally refers to a 90 × 90 × 90 voxel grid, an offset of 5 voxels per side was added to prevent surface clipping at the bounding box edges.
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As a result, the actual scalar field is discretized into 101 × 101 × 101 = 1,030,301 grid points, yielding 1,000,000 voxels in total.
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- `.stl`: File extension. This denotes the __smoothed__ version of the surface mesh.
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As mentioned above, the other file types use the following suffixes to indicate their content:
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- `_ns.stl`: The non-smoothed surface mesh, output directly from the Marching Cubes algorithm (raw geometry).
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- `_sf.txt`: The scalar field used to generate the surface.
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- `_bup.txt`: The blow-up profile, i.e., the radius function discretization for the analytical envelope.
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# Acknowledgements
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