{
  "abstract": "Triangulated irregular networks (TINs) are widely used to represent topography and bathymetry, but their quali-ty control is usually dominated by geometric criteria such as minimum angle and aspect ratio, which do not test whether connectivity errors have changed the topology of the mesh. We present a topology-aware quali-ty-control framework based on a local Euler-curvature identity and on lower-star Euler characteristic curves (ECCs). For a triangular two-manifold with boundary we classify the affine local functionals of vertex degree, incident-face count and boundary indicator whose total is invariant under mesh refinement and boundary dis-cretization, and reduce them to the canonical normalization κχ(v) = 1 − d(v)/2 + t(v)/3, whose sum equals the Euler characteristic of any finite triangular complex. Across 32 valid meshes built from four triangulation rules and four resolutions on two real Earth-surface benchmark arrays, the largest static residual was 1.74 × 10⁻¹¹. Injecting 1 to 40 missing facets, duplicated facets or orphan vertices returned a residual equal to the number of defects, whereas topology-preserving diagonal remeshing left it at machine precision. A coordinate-only sliver collapsed the minimum plan-view angle from 38.75° to 0.28° without changing the topological residual. ECCs additionally exposed representation uncertainty, with maximum inter-triangulation spreads of 25 and 20 Euler units and raster 4- versus 8-neighbour differences of 80 and 70. The framework separates mesh topology, ele-ment geometry and representation-induced uncertainty in an auditable way.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Bekarys Tashmukhanbet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2w0hdcvzhd9f6.bib",
  "cited_by": 0,
  "doi": "10.31223/x52r5h",
  "fulltext_url": null,
  "id": "2w0hdcvzhd9f6",
  "issns": [],
  "landing_url": "https://eartharxiv.org/repository/view/15094/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/legalcode",
  "metadata_licence": null,
  "native_subjects": [
    [
      "bepress",
      "Digital Elevation Model"
    ],
    [
      "bepress",
      "Earth Sciences"
    ],
    [
      "bepress",
      "Environmental Sciences"
    ],
    [
      "bepress",
      "Euler Characteristic"
    ],
    [
      "bepress",
      "Geomorphology"
    ],
    [
      "bepress",
      "Mathematics"
    ],
    [
      "bepress",
      "Mesh Quality"
    ],
    [
      "bepress",
      "Physical Sciences and Mathematics"
    ],
    [
      "bepress",
      "Topological Data Analysis"
    ],
    [
      "bepress",
      "Triangulated Irregular Network"
    ],
    [
      "bepress",
      "Trinagulated Irregulat Network"
    ],
    [
      "openalex",
      "1704|Computational Geometry and Mesh Generation"
    ]
  ],
  "openalex": "W7213619831",
  "pdf_url": "https://eartharxiv.org/repository/object/15094/download/26195/",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2w0hdcvzhd9f6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "15094",
      "source": "eartharxiv",
      "url": "https://eartharxiv.org/repository/view/15094/"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "bepress:Environmental Sciences",
      "subfield": "environmental-science"
    },
    {
      "field": "earth",
      "origin": "bepress:Geomorphology",
      "subfield": "geology-geochemistry"
    },
    {
      "field": "mathematics",
      "origin": "bepress:Mathematics",
      "subfield": "general"
    }
  ],
  "title": "Topology-Aware Quality Control of Triangulated Terrain Models Using Local Euler Curvature and Elevation-Filtration Curves",
  "title_text": "Topology-Aware Quality Control of Triangulated Terrain Models Using Local Euler Curvature and Elevation-Filtration Curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:36Z",
  "url": "https://research.draconitic.com/paper/2w0hdcvzhd9f6",
  "venue": "EarthArXiv",
  "versions": []
}