1. Department of Geoinformation Science Technische Universität Berlin WS 2006/07 Geoinformation Technology: lecture 9a Triangulated Networks Prof. Dr. Thomas H. Kolbe Institute for Geodesy and Geoinformation Science Technische Universität Berlin Credits: This material is mostly an english translation of the course module no. 2 (‘Geoobjekte und ihre Modellierung‘) of the open e-content platform www.geoinformation.net.www.geoinformation.net

2. 2 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 Triangulated Networks

3. 3 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 Overview  triangle networks – “Triangulated Irregular Networks“ (TINs)  modelling of the relief by TINs  Delaunay TINs: ‘especially good‘ TINs  break lines in the relief: Constrained Delaunay TINs  triangulated networks and hydrography

4. 4 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 Triangulated Networks and Terrain Models  given: n irregularly distributed points with planimetric coordinates and height values  wanted: a data model for the terrain‘s relief  observation: 3 (linear independent) points define a plane  solution: construction of a triangle network

5. 5 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 Triangulated Networks and Contour Lines

6. 6 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 Categorisation of TINs  triangulated networks are: a special tesselation of the plane with the height as an additional attribute special simplicial complexes special maps (all internal faces are triangles) discrete, finite approximate representatives of fields  TINs as terrain models: it applies: z = f(x,y)  Digital Terrain Models (DTM) are often called a “2,5D representation“

7. 7 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 “Bad“ and “Good“ Triangulated Networks usual triangulation may generate sharply peaked triangles Delaunay- Triangulation with minimum (interior) angles

8. 8 T. H. Kolbe – Geoinformation Technology: lecture 9 Department of Geoinformation Science WS 2006/07 Delaunay Triangulation  for a set of n points the Delaunay TIN is the TIN, in which the smallest occurring angle is maximised  Delaunay TINs fulfill the circle criterion: no fourth node lies inside the perimeter of a triangle exercise: how to design an algorithm to transform a TIN into a Delaunay TIN ?