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ToPos: Automated Optimal Positioning on Topographic Manifolds using Constrained Geodesic Voronoi Decomposition — arXiv:2609.05084

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05084
License (as archived): CC0-1.0
Archived: 2026-10-16T23:49:41.069Z
SHA-256 of the archived text: 676a748d0b763395d76126069cbb1421eff8b4bf62db5d0e2df3ae3ec030733b
Stable URL of this page: https://metraipolis.com/documento/dc_e496cfd4d5fe

How to cite

ToPos: Automated Optimal Positioning on Topographic Manifolds using Constrained Geodesic Voronoi Decomposition — arXiv:2609.05084 — arXiv (en), https://arxiv.org/abs/2609.05084 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e496cfd4d5fe (Metraipolis archive dc_e496cfd4d5fe, sha256 676a748d0b763395d76126069cbb1421eff8b4bf62db5d0e2df3ae3ec030733b)

BibTeX

@misc{dce496cfd4d5fe,
  title = {ToPos: Automated Optimal Positioning on Topographic Manifolds using Constrained Geodesic Voronoi Decomposition — arXiv:2609.05084},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05084},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e496cfd4d5fe; sha256 676a748d0b763395d76126069cbb1421eff8b4bf62db5d0e2df3ae3ec030733b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05084. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Reliable autonomous mapping, environmental sampling, last-mile logistics, and infrastructure deployment depend on the optimal surface area-balanced distribution of Spatial Reference Sites (SRS). Conventional 2D Euclidean methods often fail in high-relief environments by neglecting topographic variations and physical obstructions. This leads to significant planimetric distortion, spatial clustering, and the placement of targets in inaccessible or shadowed regions, compromising both data integrity and operational safety. This paper introduces ToPos, an automated framework for TOPography-aware Optimal Sampling on topographic manifolds. We treat the terrain as a discrete 2-dimensional manifold embedded in 3D Euclidean space and replace standard flat-map distances with non-Euclidean geodesic distances that follow the actual surface geometry. The point distribution is formulated as an optimization problem using a Constrained Geodesic Voronoi Decomposition, solved via a Riemannian Nesterov Accelerated Gradient (NAG) engine. Our approach restricts target locations to a feasible "safe zone," accounting for non-traversable slopes, vegetation, environmental occlusions, etc. Through evaluations on non-convex sinusoidal manifolds, we show that ToPos mitigates planimetric distortion by utilizing geodesic metrics. This approach results in a $\sim$74% improvement in optimal surface area-balanced distribution, as measured by the coefficient of variation (CV) of the Voronoi cell areas. The framework is architected as a Geographic Information System (GIS)-ready micro-service to bolster the mentioned applications. Index Terms: Topographic Manifolds, Geodesic Voronoi Decomposition, Infrastructure Deployment, 3D Mapping, Spatial Sampling, and Non-Euclidean Optimization.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-07 in cs.RO).
Categorie arXiv: Robotics (cs.RO).
Pagina del lavoro: https://arxiv.org/abs/2609.05084 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T23:21:38.640Z dalla pagina https://arxiv.org/catchup/cs.RO/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).