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

Geodesic isolines derived from polylines constitute a crucial element within geographic information systems, 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.