Geoinformation Technology: lecture 9a Triangulated Networks

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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.
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Triangulated Networks
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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

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Triangulated Networks and Terrain Models

• given n irregularly distributed points with
  planimetric coordinates and height values
• wanted a data model for the terrains relief
• observation 3 (linear independent) points define
  a plane
• solution construction of a triangle network

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Triangulated Networks and Contour Lines
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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

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Bad and Good Triangulated Networks

• usual triangulation may generate sharply peaked
  triangles
• Delaunay-Triangulation with minimum (interior)
  angles

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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 ?