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Terrain trees: a framework for representing, analyzing and visualizing triangulated terrains

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Abstract

We propose a family of spatial data structures for the representation and processing of Triangulated Irregular Networks (TINs). We call such data structures Terrain trees. A Terrain tree combines a minimal encoding of the connectivity of the TIN with a hierarchical spatial index. Connectivity relations are extracted locally at run-time, within each leaf block of the hierarchy, based on specific application needs. Spatial queries are performed by exploring the hierarchical data structure. We present a new framework for terrain analysis based on Terrain trees. The framework, implemented in the Terrain trees library (TTL), contains algorithms for morphological features extraction, such as roughness and curvature, and for topology-based analysis of terrains. Moreover, it includes a technique for multivariate visualization, which enables the analysis of multiple scalar fields defined on the same terrain. To prove the effectiveness and scalability of such framework, we have compared the different Terrain trees against each other and also against the most compact state-of-the-art data structure for TINs. Comparisons are performed on storage and generation costs and on the efficiency in performing terrain analysis operations.

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Availability of data and material

The LiDAR datasets used in this manuscript are publicly available data provided by the OpenTopography Facility with support from the National Science Foundation under NSF Award Numbers 1833703, 1833643, and 1833632. The experimental results reported in this manuscript are collected in the same hardware environment and with the standard process.

Code availability

The source codes of the Terrain trees library and the Indexed data structure with Adjacencies (IA data structure) are available in public domain.

Notes

  1. https://opentopography.org/

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Acknowledgements

This work has been mainly developed while Riccardo Fellegara was with the University of Maryland at College Park, USA. This work has been supported by the US National Science Foundation under grant number IIS-1910766. It has also been performed under the auspices of the German Aerospace Center (DLR) under Grant DLR-SC-2467209. The big creek, canyon lake gorge, great smokey mountain, and sonoma county point clouds are kindly provided by the OpenTopography Facility [56] with support from the National Science Foundation under NSF Award Numbers 1833703, 1833643, and 1833632. We also acknowledge NASA Grant NNX13AP69G for the collection of sonoma county dataset, NSF Award number 1043051 for the collection of big creek, canyon lake gorge, and great smokey mountain datasets

Funding

This study was funded by the US National Science Foundation under grant number IIS-1910766.

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Authors and Affiliations

  1. German Aerospace Center (DLR), Braunschweig, Germany

    Riccardo Fellegara

  2. Clemson University, Clemson, SC, USA

    Federico Iuricich

  3. University of Maryland, College Park, MD, USA

    Yunting Song & Leila De Floriani

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  1. Riccardo Fellegara
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  2. Federico Iuricich
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  3. Yunting Song
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  4. Leila De Floriani
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Correspondence to Yunting Song.

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Appendix A

Appendix A

Figures 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31.

Fig. 20
figure 20

The storage costs for storing the hierarchical index of the Terrain trees on canyon lake gorge dataset using different values of \(k_v\) and \(k_t\). The x-axis shows the threshold value on the vertices

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Fig. 21
figure 21

Timings for generating the spatial decomposition of Terrain trees and extracting the VT relation in Terrain trees on canyon lake gorge dataset using different values of \(k_v\) and \(k_t\). The x-axis shows the vertex threshold value

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Fig. 22
figure 22

The storage costs for storing the hierarchical index of the Terrain trees on sonoma county 1 dataset using different values of \(k_v\) and \(k_t\). The x-axis shows the threshold value on the vertices

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Fig. 23
figure 23

Timings for generating the spatial decomposition of Terrain trees and extracting the VT relation in Terrain trees on sonoma county 1 dataset using different values of \(k_v\) and \(k_t\). The x-axis shows the vertex threshold value

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Fig. 24
figure 24

The storage costs for storing the hierarchical index of the Terrain trees on sonoma county 2 dataset using different values of \(k_v\) and \(k_t\). The x-axis shows the threshold value on the vertices

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Fig. 25
figure 25

Timings for generating the spatial decomposition of Terrain trees and extracting the VT relation in Terrain trees on sonoma county 2 dataset using different values of \(k_{\textit{v}}\) and \(k_t\). The x-axis shows the vertex threshold value

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Fig. 26
figure 26

The storage costs for storing the hierarchical index of the Terrain trees on big creek dataset using different values of \(k_{\textit{v}}\) and \(k_t\). The x-axis shows the threshold value on the vertices

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Fig. 27
figure 27

Timings for generating the spatial decomposition of Terrain trees and extracting the VT relation in Terrain trees on big creek dataset using different values of \(k_{\textit{v}}\) and \(k_t\). The x-axis shows the vertex threshold value

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Fig. 28
figure 28

The storage costs for storing the hierarchical index of the Terrain trees on sonoma county 3 dataset using different values of \(k_{\textit{v}}\) and \(k_t\). The x-axis shows the threshold value on the vertices

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Fig. 29
figure 29

Timings for generating the spatial decomposition of Terrain trees and extracting the VT relation in Terrain trees on sonoma county 3 dataset using different values of \(k_{\textit{v}}\) and \(k_t\). The x-axis shows the vertex threshold value

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Fig. 30
figure 30

The storage costs for storing the hierarchical index of the Terrain trees on sonoma county 4 dataset using different values of \(k_{\textit{v}}\) and \(k_t\). The x-axis shows the threshold value on the vertices

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Fig. 31
figure 31

Timings for generating the spatial decomposition of Terrain trees and extracting the VT relation in Terrain trees on sonoma county 4 dataset using different values of \(k_v\) and \(k_t\). The x-axis shows the vertex threshold value

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Fellegara, R., Iuricich, F., Song, Y. et al. Terrain trees: a framework for representing, analyzing and visualizing triangulated terrains. Geoinformatica 27, 525–564 (2023). https://doi.org/10.1007/s10707-022-00472-3

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