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Introduction

Introduction. Last day we looked at global and local interpolators. Today we will look at: Digital Elevation Models Density Surfaces Software options. Digital Elevation Models.

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Introduction

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  1. Introduction • Last day we looked at global and local interpolators. • Today we will look at: • Digital Elevation Models • Density Surfaces • Software options

  2. Digital Elevation Models • Originally developed as part of the process used to create ortho photos, but now widely used in other calculations (slope, aspect, line of sight, viewsheds, watersheds, etc.) and visualisation.

  3. Methods Of Representation • Three main methods: • Altitude matrices (raster) • Isolines - e.g. contours (vector) • Triangulated Irregular Networks – TINs (vector) • Isolines were the main method in traditional cartography, but do not very flexible for GIS.

  4. Altitude Matices • Very flexible for calculating contours, slope, aspects, etc. • Disadvantages: • Data redundancy if terrain is flat. • Do not adjust to relief complexity. • Exaggerated emphasis along lines of the grid.

  5. TINs • TINs represent a surface using contiguous, non-overlapping irregular triangles. • The areas inside each triangle have approximately the same slope and elevation. • The corners of each triangle are generally at different altitudes. • Edges form breaks of slope. • Complex terrain can be accommodated using smaller triangles. • Known features can be recorded accurately (not interpolated as in a raster).

  6. Conversion Methods • TINs to altitude matrices. Grid superimposed. Height in each cell is a distance weighted average of the three corner points of the triangle within which the centre of the grid falls. • Altitude matrix to TIN. Three stages: • 1. Identify minimum number of corner points for the triangles; • 2. Decide which points should be joined to form the triangles; • 3. Convert to a data structure.

  7. TIN Conversion Algorithms • At least four methods can be used to decide on the corner points: • Skeleton method • Very important point method • Hierarchy transform method • Drop heuristic method • At least two methods can be used to determine ‘joins’: • Minimum distance • Delauney triangles

  8. TIN Data Structure • The data stucture used to record this information includes: • A node list – i.e. list of the corner points • A pointer list – for each node a list of the other nodes to which that node is connected (in clockwise direction) • A trilist – lists the triangle on either side of each link.

  9. Isoline To Altitude Matrix • Would appear to be very simple – identify a number of sample points along each contour and then apply a local interpolator to estimate value for each grid cell. • However, can produce a terraced effect. • If used to calculate slope, can produce a tiger stripe effect. • Photogrammetric measurements much better. • If must convert from a contour map: • Use sparse sample on contour lines. • Use known values for other points (e.g. peaks). • Interpolate using a wide search radius.

  10. Density Surfaces • The density of discrete objects (e.g. people) is sometimes modelled as a 3D-surface. • Underlying logic may appear similar to interpolation: i.e. you start with points and end up with a surface. • Important differences: • Interpolation estimates values for points on a surface from known points; density surfaces create a surface by counting discrete objects. • It would make sense to estimate the altitude of Carton using data for Maynooth and Leixlip, but it would not make sense to estimate its population density.

  11. Construction Of A Density Surface • One simple way to construct a density surface is: • Define a regular lattice of points. • For each point draw a circle with a specified radius. • Count the number of objects (e.g. people) within each circle, and hence the density for the circle. • Use interpolation to construct a surface using the density measures for each point. • User must decide on: • Spacing of points • Size of circles • Different decisions produce different results.

  12. Kernel Estimation • Kernel estimation provides a preferable approach. • This uses a weighted count or average of the points in each circle.

  13. Kernel Estimation(2) • Results will be dependent on: • The distance between the lattice points. • The radius of the circles, referred to as the bandwidth. • The choice of kernel weighting function. • Can be used to compare two surfaces calculated from different sets of discrete points (possibly using different bandwidths). • Can divide one surface by the other to create a third surface showing relative risk.

  14. ArcGIS Options • ArcGIS provides several interpolation options: • The Spatial Analyst extension provides: • IDW • Spline • Kriging • The Geostatistical Analyst extension provides the above plus: • Trend surface • Local polynomial • Radial basis function • Addition kriging and cokriging options

  15. Idrisi Options • Idrisi provides most of the options provided by ArcGIS plus a few others. • Idrisi provides an interface to open-source software called GSTAT developed in Utrecht. It also available at http://www.gstat.org/.

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