GEM 3390

1
Lecture 16 Content

• Geographic Information Systems (GIS)
• Data Structures and Data Management
• (Continued)

2
Lecture content

• Representation of continuous surfaces
• definition
• general nature of surfaces
• data structures
• spatial interpolations

3

• Representation of continuous surfaces
• Definition
• A continuous surface is a representation of a
  phenomena where the data is space filling
• Typical examples of continuous surfaces are
• Elevation (as part of topographic data)
• Rainfall, pressure, temperature
• Population density
• General nature of surfaces
• Critical features peaks, pits, ridge lines,
  valley bottom, passes, etc. The critical points
  controls the formation of the continuous surface
• Faults they show sharp discontinuities in
  elevations such as the occurrence of cliffs
• Fronts sharp discontinuities of slope
• Slope and aspect which will be discussed later in
  detail

4

• Continuous surface data structure
• Points grid of elevation (regular and
  heterogeneous)
• Lines digitized contours
• Areas TIN (Triangular Irregular Network)
• Spatial Interpolations
• Polynomials (first, second, or higher orders)
• Moving average (simple, weighted with various
  types of functions). This is the use of a
  neighboring raster cells determine the mean value
  which will be applied to the center cell for a
  pre-defined search window
• Kriging (family of linear prediction) Kriging is
  based on the assumption that the parameter being
  interpolated can be treated as a regionalized
  variable.
• The following slide shows elevation represented
  by a set of pixels

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Elevation represented by a set of points
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A topographic map and a corresponding TIN
representation
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• A TIN is constructed by triangulating a set of
  vertices. The vertices are connected with a
  series of edges to form a network of irregular
  triangles. The resulting triangulation satisfies
  the Delauney criterion. The Delauney criterion
  ensures that the three vertices of a triangle
  lies within the circumference of a circle as
  shown below. A triangle must form only in one
  circle.

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Elevation represented as areas
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Triangulation of a terrain surface
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• The End