Representation of 3-D elevation in terrain databases using hierarchical triangulated irregular networks: a comparative analysis

1998 ◽  
Vol 12 (8) ◽  
pp. 853-873 ◽  
Author(s):  
MAHDI ABDELGUERFI ◽  
CHRIS WYNNE ◽  
EDGAR COOPER ◽  
LADNER ROY
Keyword(s):  
Comparative Analysis ◽  
Triangulated Irregular Networks ◽  
Irregular Networks

Comparative analysis of hierarchical triangulated irregular networks to represent 3D elevation in terrain databases

1997 ◽  
Author(s):  
Mahdi Abdelguerfi ◽  
Chris Wynne ◽  
Edgar Cooper ◽  
Roy V. Ladner ◽  
Kevin B. Shaw
Keyword(s):  
Comparative Analysis ◽  
Triangulated Irregular Networks ◽  
Irregular Networks

Boundary Problem for Triangulated Irregular Networks

1993 ◽  
Vol 20 (4) ◽  
pp. 244-250 ◽  
Author(s):  
Steven T. Bower ◽  
Carlton M. Newton
Keyword(s):  
Boundary Problem ◽  
Triangulated Irregular Networks ◽  
Irregular Networks

The Radial Sweep Algorithm for Constructing Triangulated Irregular Networks

1982 ◽  
Vol 2 (3) ◽  
pp. 11-21 ◽  
Author(s):  
Mirante ◽  
Weingarten
Keyword(s):  
Triangulated Irregular Networks ◽  
Sweep Algorithm ◽  
Irregular Networks

scholarly journals FAST ROBUST ARITHMETICS FOR GEOMETRIC ALGORITHMS AND APPLICATIONS TO GIS

2021 ◽  
Vol XLVI-4/W2-2021 ◽  
pp. 1-8
Author(s):  
T. Bartels ◽  
V. Fisikopoulos
Keyword(s):  
Code Generation ◽  
Computational Cost ◽  
Floating Point ◽  
Data Sets ◽  
Delaunay Triangulations ◽  
Triangulated Irregular Networks ◽  
Gis Data ◽  
Irregular Networks ◽  
Meta Programming ◽  
Point Arithmetic

Abstract. Geometric predicates are used in many GIS algorithms, such as the construction of Delaunay Triangulations for Triangulated Irregular Networks (TIN) or geospatial predicates. With floating-point arithmetic, these computations can incur roundoff errors that may lead to incorrect results and inconsistencies, causing computations to fail. This issue has been addressed using a combination of exact arithmetics for robustness and floating-point filters to mitigate the computational cost of exact computations. The implementation of exact computations and floating-point filters can be a difficult task, and code generation tools have been proposed to address this. We present a new C++ meta-programming framework for the generation of fast, robust predicates for arbitrary geometric predicates based on polynomial expressions. We show examples of how this approach produces correct results for GIS data sets that could lead to incorrect predicate results for naive implementations. We also show benchmark results that demonstrate that our implementation can compete with state-of-the-art solutions.

scholarly journals A Modified Methodology for Generating Indoor Navigation Models

2019 ◽  
Vol 8 (2) ◽  
pp. 60 ◽  
Author(s):  
Elżbieta Lewandowicz ◽  
Przemysław Lisowski ◽  
Paweł Flisek
Keyword(s):  
Spatial Data ◽  
Medial Axis ◽  
Indoor Navigation ◽  
Medial Axis Transformation ◽  
Triangulated Irregular Networks ◽  
Modeled Structure ◽  
Irregular Networks ◽  
Thiessen Polygons ◽  
Automatic Methods ◽  
Traditional Approaches

Automatic methods for constructing navigation routes do not fully meet all requirements. The aim of this study was to modify the methodology for generating indoor navigation models based on the Medial Axis Transformation (MAT) algorithm. The simplified method for generating corridor axes relies on the Node-Relation Structure (NRS) methodology. The axis of the modeled structure (corridor) is then determined based on the points of the middle lines intersecting the structure (polygon). The proposed solution involves a modified approach to the segmentation of corridor space. Traditional approaches rely on algorithms for generating Triangulated Irregular Networks (TINs) by Delaunay triangulation or algorithms for generating Thiessen polygons known as Voronoi diagrams (VDs). In this study, both algorithms were used in the segmentation process. The edges of TINs intersected structures. Selected midpoints on TIN edges, which were located in the central part of the structure, were used to generate VDs. Corridor structures were segmented by polygon VDs. The identifiers or structure nodes were the midpoints on the TIN edges rather than the calculated centroids. The generated routes were not zigzag lines, and they approximated natural paths. The main advantage of the proposed solution is its simplicity, which can be attributed to the use of standard tools for processing spatial data in a geographic information system.

An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks

2001 ◽  
Vol 27 (8) ◽  
pp. 959-973 ◽  
Author(s):  
Gregory E. Tucker ◽  
Stephen T. Lancaster ◽  
Nicole M. Gasparini ◽  
Rafael L. Bras ◽  
Scott M. Rybarczyk
Keyword(s):  
Object Oriented ◽  
Triangulated Irregular Networks ◽  
Irregular Networks

Embedding rivers in triangulated irregular networks with linear programming

2010 ◽  
Vol 25 (4) ◽  
pp. 615-631 ◽  
Author(s):  
Marc van Kreveld ◽  
Rodrigo I. Silveira
Keyword(s):  
Linear Programming ◽  
Triangulated Irregular Networks ◽  
Irregular Networks

QuadTIN: quadtree based triangulated irregular networks

2003 ◽  
Author(s):  
R. Pajarola ◽  
M. Antonijuan ◽  
R. Lario
Keyword(s):  
Triangulated Irregular Networks ◽  
Irregular Networks

scholarly journals 3D Simplification Methods and Large Scale Terrain Tiling

2020 ◽  
Vol 12 (3) ◽  
pp. 437
Author(s):  
Ricard Campos ◽  
Josep Quintana ◽  
Rafael Garcia ◽  
Thierry Schmitt ◽  
George Spoelstra ◽  
...  
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Level Of Detail ◽  
Web Based ◽  
European Area ◽  
Levels Of Detail ◽  
Triangulated Irregular Networks ◽  
Large Scale Dataset ◽  
Irregular Networks ◽  
Elevation Data

This paper tackles the problem of generating world-scale multi-resolution triangulated irregular networks optimized for web-based visualization. Starting with a large-scale high-resolution regularly gridded terrain, we create a pyramid of triangulated irregular networks representing distinct levels of detail, where each level of detail is composed of small tiles of a fixed size. The main contribution of this paper is to redefine three different state-of-the-art 3D simplification methods to efficiently work at the tile level, thus rendering the process highly parallelizable. These modifications focus on the restriction of maintaining the vertices on the border edges of a tile that is coincident with its neighbors, at the same level of detail. We define these restrictions on the three different types of simplification algorithms (greedy insertion, edge-collapse simplification, and point set simplification); each of which imposes different assumptions on the input data. We implement at least one representative method of each type and compare both qualitatively and quantitatively on a large-scale dataset covering the European area at a resolution of 1/16 of an arc minute in the context of the European Marine Observations Data network (EMODnet) Bathymetry project. The results show that, although the simplification method designed for elevation data attains the best results in terms of mean error with respect to the original terrain, the other, more generic state-of-the-art 3D simplification techniques create a comparable error while providing different complexities for the triangle meshes.

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