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Open Access | Just Accepted

An Accurate and Time-Efficient Algorithm for Computing Isoline Sourced from Polylines on Triangle Meshes

Wenlong Meng1( )Hang Yu1Yixuan Geng1Yanbo Pu1Shiqing Xin2

1 School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China

2 School of Computer Science and Technology, Shandong University, Qingdao 266237, China

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Abstract

Geodesic isolines derived from polylines constitute a crucial element within geographic information systems (GIS), playing a pivotal role in enhancing the understanding of geographical terrains. Current methods for delineating isolines sourced from polylines on discrete meshes often rely on simplistic linear interpolation. However, these methods fall short in accuracy due to the complex, non-linear nature of geodesic distance fields, thereby inadequately capturing intricate topological features present in real isolines. To tackle this challenge, we demonstrate that Apollonius diagrams can effectively encode the geometric attributes of isolines on meshes and extract the isolines using the Apollonius diagrams with geodesic metric. Moreover, exact geodesic computation is computationally intensive and memory-demanding. In response, we introduce a graph-based approach enhanced by Steiner point insertion, offering a practical method for computing geodesic distances. Drawing on these strategies, we introduce an accurate and efficient algorithm for polyline-sourced isoline computation on triangle meshes. Comprehensive evaluations indicate that our approach yields significantly more accurate geodesic isolines compared to the commonly employed linear interpolation.

Tsinghua Science and Technology
Cite this article:
Meng W, Yu H, Geng Y, et al. An Accurate and Time-Efficient Algorithm for Computing Isoline Sourced from Polylines on Triangle Meshes. Tsinghua Science and Technology, 2024, https://doi.org/10.26599/TST.2024.9010181

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Received: 03 June 2024
Revised: 10 August 2024
Accepted: 25 September 2024
Available online: 19 November 2024

© The author(s) 2025

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

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