Robust discretization of implicit geological surfaces by piecewise-linear approximation on a simplicial mesh.

@inproceedings{Mézerette2026RM,
 abstract = {Implicit geological modeling generates networks of implicit surfaces that must be discretized into conforming meshes for visualization and physics-based simulation. This discretization is challenging because geological interfaces often exhibit discontinuities, truncations, and finite extensions that classical surface-extraction methods do not handle. We present an increasing-dimension algorithm for the piecewise-linear discretization of discontinuous implicit surface networks on a planar simplicial mesh. Surfaces are organized in a directed acyclic dependency graph and processed in topological order, so that when a surface is discretized, every interface across which it is discontinuous has already been handled. The algorithm proceeds by increasing dimension over the mesh elements (vertices, edges, faces) so that each element is treated only once, independently of how many higher-dimension elements share it. First, intersections with each mesh edge are computed and ordered: continuous functions are linearly interpolated from vertex samples, while discontinuous functions are estimated near discontinuities by linear extrapolation from valid nearby samples. Second, the surface network is reconstructed independently within each triangular face: surfaces are inserted sequentially in topological order, and each inserted segment splits the current polygon into sub-polygons in which subsequent surfaces are reconstructed. Ambiguous and inconsistent cases are resolved by local mesh refinement. Experiments on synthetic networks of continuous, truncated, and discontinuous implicit circles yield conforming piecewise-linear reconstructions that preserve the dependency relations of the input model. The method is implemented in C++ on top of the CGAL library and currently handles planar sections of discontinuous implicit surface networks. Extending it to full three-dimensional tetrahedral meshes is left for future work.},
 author = {Mézerette, Ronan and Clausolles, Nicolas and Lopez Simon and Loriot, Sébastien},
 booktitle = {2026 {RING} meeting},
 language = {en},
 pages = {279--292},
 publisher = {ASGA},
 title = {Robust discretization of implicit geological surfaces by piecewise-linear approximation on a simplicial mesh.},
 year = {2026}
}