Published June 13, 2023 | Version 2.0
Dataset Open

Expansion Cones Dataset for Robust Tetrahedral Mapping Evaluation

  • 1. University of Bern
  • 2. Osnabrück University


This record stores the dataset used by the "Expansion Cones" paper.
This paper presents a volumetric mapping method called Shrink-And-Expand (SAE for short).
Its robustness was evaluated by mapping ~3'000 ball-topology meshes to 4 different target boundaries (spherical, tetrahedral, "stiff" tetrahedral and random star-shaped). Other tetrahedral mapping methods can be evaluated by using the rest meshes and either of the target boundaries.

The record is structured as follows:

  • `ball_topology_tet_wild_ovm_format`: all input meshes in their original shapes, in .ovm format. These consists of the TetWild dataset, restricted to ball-topology meshes. If you need to convert the meshes to another format, you can use Martin Heistermann's fork of meshio.
    NOTE: Those meshes were pre-processed by splitting all interior edges connecting two boundary vertices and all interior faces connecting three boundary vertices. This was done to satisfy the prerequisites of our method.
  • `input_meshes_with_XXX_mapped_boundary`: all those meshes mapped to 4 boundary shapes: tetrahedral, "stiff" tetrahedral, ball and random star-shape. Please read the related paper for more details about the boundary types.

These meshes are also all in `.ovm` format. The interior vertices are all located at the origin, which is inside of the kernel of their boundary.
The other archives contain data used to compare SAE with two other volumetric mapping methods called Total Lifted Content (TLC) and FoldOver-Free (FOF)

  •  `SAE_results/expansion_data`: All `.json` files corresponding to executions of our method (SAE) on those meshes.
  •  `SAE_results/quality_stats`: conformal and volumetric distortion values for _all_ cells of _all_ meshes.
  • `TLC_FOF_results`: For each mesh and each competitor method (and each boundary map), there are 1 to 3 files, depending on the results of running those methods.
    • `TLC/FOF_timing_s.txt` gives the number of seconds it took to run
    • `TLC/FOF_stats.txt` stores the following data: `[mesh name, #vertices, #edges, #faces, #cells, #degenerate cells after running the method, #flipped cells after running the method]`. This file only exists if the method terminated within the 12hours time limit.
    • `TLC/FOF_quality_stats.txt` lists the conformal and volumetric distortion of each individual cell in the resulting map produced by the competitor methods (one line per cell), This file only exists if the method produced a valid map.


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Additional details


AlgoHex – Algorithmic Hexahedral Mesh Generation 853343
European Commission


  • Nigolian et al. (2023), Expansion Cones: A Progressive Volumetric Mapping Framework, doi:10.1145/3592421