3D and Surface/Terrain
Prepared by:
George McLeod
With support from:
NSF DUE-0903270
in partnership with:
Geospatial Technician Education Through Virginia’s Community Colleges (GTEVCC)
Digital Terrain Models
• A digital terrain model is a model providing a
representation of a terrain relief on the basis
of a finite set of sampled data
• Terrain data refers to measures of elevation at
a set of points V of the domain plus possibly a
set E of non-crossing line segments with
endpoints in V
Data Sampling
• Regular
• Irregular
Sampling effects resolution
Our three Primary terrain Models
• Digital Elevation Models (DEMS) – aka Regular
Square Grids (RSGs)
• Triangulated Irregular Networks (TINS) – aka
Polyhedral terrain models
• Contour Maps – aka “topo” maps
The Data…
(LIght Detection And Ranging)
Introduction to the Data
• Terrain mapping
• Land surface is 3-D
• Elevation data or
z-data is treated as a
cell value or a point
data attribute rather
than as a coordinate.
• Digital Elevation Model (DEM)
– Gridded array of elevation points obtained from a
variety sampling methods
A constant function can be associated with each
square (i.e., a constant elevation value). This is called
a stepped model (it presents discontinuity steps
along the edges of the squares)
• The function defined on each square can also be
a bilinear function interpolating all four elevation
points corresponding to the vertices of the
• Triangulated Irregular Network (TIN)
– Series of non-overlapping triangles
– Elevation values are stored at nodes
– Sources: DEMs, surveyed elevation points, contour
lines, and breaklines
– Breaklines are line features
that represent changes of
the land surface such as
streams, shorelines, ridges,
and roads
• Example of a TIN based on irregularly
distributed data
Data for Terrain Mapping and Analysis
• Triangulated Irregular Network (TIN)
– Not every point in DEM is used
– Only points most important
– VIP (Very Important Points) algorithm
– Maximum z-tolerance algorithm
– Delaunay triangulation: all nodes are connected to
their nearest neighbor to form triangles which are
as equi-angular as possible.
Tins vs. Grids
• Needs larger storage capacity
• Needs smaller storage capacity
• Computationally difficult
• Computationally simpler
• Flexibility of data sources
• Fixed with a given cell size
• Can add points
• Cannot add sample points
• Better display
• Raster display
• More efficient
• Less efficient
Contour Mapping
• Contouring is most common
method for terrain mapping
• Contour lines connect points
of equal elevation (isolines)
• Contour intervals represent the
vertical distance between
contour lines.
• Arrangement of contour lines
reflect topography
Digital Contour Maps
Contours are usually available as sequences of points
A line interpolating points of a contour can be obtained in different ways
Examples: polygonal chains, or lines described by higher order equations
Digital Contour Maps: properties
They are easily drawn on paper
They are very intuitive for humans
They are not good for complex
automated terrain analysis
Contour Profile Mapping
• Vertical profile shows changes in elevation along a line, such as a hiking
trail, road or stream.
Cartographic Terrain Mapping
Hill shading is also known as a shaded relief or simply shading
Attempts to simulate how the terrain looks with the interaction between sunlight
and surface features.
Helps viewers recognize the shape of land-form features on a map.
• Four factors control the visual effect of hillshading
– Sun’s azimuth is direction of incoming light (0 to
– The sun’s altitude from horizon (0-90°)
– Surface slope (0-90°)
– Surface aspect (0 to 360°)
Hypsometric Tinting
Hypsometric tinting
– Applies different color symbols to represent elevation or depth zones.
Methods of Analysis
Slope measures the rate of change of elevation at a surface location
Aspect is the directional measure of the slope (degrees- 4 or 8 directions)
Hillshade, refer to previous slides
Line of sight refers to the straight line visibility from an observer to a feature
Viewshed analysis refers to the areas of the land surface that are visible
from an observation point or points.
Watershed analysis refers to an area that drains water and other substances
to a common outlet.
Area and volume calculations
Connectivity Function Example:
Viewshed Analysis
Image Source: Chrisman, Nicholas.(2002). 2nd Ed. Exploring Geographic Information Systems. p 198. fig. 8-14
Line of Sight Analysis
Setting a hypothetical light source and calculating the illumination values for each
cell in relation to neighboring cells. It can greatly enhance the visualization of a
surface for analysis or graphical display.
Azimuth 315°, altitude 45°
Viewshed identifies the cells in an input raster that can be seen from one
or more observation points or lines.
It is useful for finding the visibility. For instance, finding a well-exposed
places for communication towers
hillshaded DEM as background
Surface Area and Volume
Application: Environmental Impact Analysis
3D landscape model impact on natural beauty
Application - Flood Risk
3D height data changing water levels-danger areas
The 3rd Dimension: Height Analysis – combining
several methods together
Hill shading
Spot height symbols
Cliff & slope symbols
Viewpoint symbols
3D Terrain Analysis: Summation
• GIS does not always provide exact answers to
problems, but by identifying trends based on
geography, GIS can reveal patterns that can
help us make informed decisions.
• A GIS can improve decision-making; it cannot
make decisions for us.

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