3d GIS fundamentals, GIS technologies, TIN modeling, Surface Creation, DEM,

1. GIS moving to 3rd-Dimension
The application of GIS is limited only by the imagination of those who use it
Dr. Nishant Sinha

2. Journey Expectations
• 3D Data representation and
visualization
– Real world objects
(buildings, towers, etc.) and rendering
on Google Earth
– Digital Elevation Model (DEM)
– Walk through / fly through

3. 3D GIS
▪ The earth is not flat. In the real
world, surfaces with vertical dimensions
exist
• True 3D
– Store data in structures that actually reference
locations in 3D space (x,y,z)
– Here z is not an attribute but an element of the
location of the point
– If z is missing, object does not exist!
▪ 3D enable interactive perspective
viewing and navigation, including
pan, zoom, rotate, tilt, fly-through
simulations, and export utilities for
display on the Web
▪ 3D GIS assist
– Construction of surface models such asTINs and
raster from any data
– Extrude buildings and vector features from a
surface
– Aerial photography can be draped onto a 3D
model to project more realistic look
– Supply analytical functions to calculate
slope, aspect and hill shading
The Eagle map of the United States engraved for rudiments of National Knowledge. 1833.

4. 3D Prevue: “Coastal Terrain Model”
… a surface that integrates topography and bathymetry
+ =
Integrated Topo-Bathy Model
BathymetryTopography

5. Why do we need 3D GIS?
▪ Simulation of complex systems provide
understanding on how the system
operates different perspectives aided by
high quality visualization and interaction
▪ Observation of system features that would
be too small or too large to be seen on a
normal scale system
▪ Access to situations that would otherwise
be dangerous or too remote or
inaccessible
▪ Enable high degree of interaction
▪ Provide a sense of immersion of the
environment
– Where the user can appreciate the scale of change
and visualise the impact of building design on the
external environment and the inhabitants

6. Why do we need 3D GIS?
▪ To offer consensual reading, with which
people will have an immediate perception
of relief, orientation, slope and visibility
▪ Allow to export to popular multimedia
formats such as video (.avi or .mpeg) or
VRML (.vrl or .vrml) that provide the
following benefits
– No prior knowledge of 3D GIS required
– Only require intuitive and easy to use
interface to operate the 3D model
– Inherent flexibility/adaptability – these
multimedia are 3D cross-platform display
and non-browser specific which enable
expensive data to be used more widely
– Fast and slow time simulation – Ability to
control timescale by incorporating a
sequence of captured events into the key
frames of the motion videos

7. Surface defined...
▪ Surfaces involve a third 'z' dimension
(height/elevation/magnitude, quantity) in addition to x,y planimetric
location
▪ Any type of continuous data can be represented as a
surface, whether it be ground elevation, barometric
pressure, rainfall, crop yield, noise levels, population density, sales
intensity, land value, income, crime rates, etc.
▪ 3 basic methods for representing a surface
– DEM (digital elevation model)
– TIN (Triangulated Irregular Network)
– Contour lines

8. Digital Elevation Model (DEM)
▪ Set of regularly spaced sampled ground
points in the x and y dimensions (although
spacing not necessarily the same in each)
accompanied by an elevation measure (z
dimension)
▪ Terminology introduced by USGS
▪ General term digital terrain model (DTM)
may be used to refer to any of the above
surface representations when in digital form
▪ Two concepts used for determining elevation
at points within the grid cells:
– Lattice: each mesh point represents a value on
the surface only at the center of the grid cell.The
z-value is approximated by interpolation
between adjacent sample points; it does not
imply an area of constant value
– Surface grid considers each sample as a
square/rectangular cell with a constant surface
value

9. Triangulated Irregualr Network (TIN)
▪ A set of adjacent, non-overlapping triangles
computed from irregularly spaced
points, with x, y horizontal coordinates and z
vertical elevations
▪ Terminology introduced by USGS
▪ General term digital terrain model (DTM)
may be used to refer to any of the above
surface representations when in digital form
▪ Two concepts used for determining elevation
at points within the grid cells:
– Lattice: each mesh point represents a value on
the surface only at the center of the grid cell.The
z-value is approximated by interpolation
between adjacent sample points; it does not
imply an area of constant value
– Surface grid considers each sample as a
square/rectangular cell with a constant surface
value

10. Triangulated Irregular Network (TIN)
Irregular set of points Irregular set of points connected
through triangulation
Triangulation to create surface
• TIN
– A set of adjacent, non-overlapping triangles computed from
irregularly spaced points, with x, y horizontal coordinates and z
vertical elevations.
• Why triangulation?
– Can capture significant slope features (ridges, etc)
– Efficient since require few triangles in flat areas
– Easy for certain analyses: slope, aspect, volume
– Avoids “weak” geometry and “thin” triangulation
– Creates a unique network (barring a minor exception)

11. Contour (isolines) Lines
▪ Contour lines, or isolines, of constant
elevation at a specified interval,
▪ Advantages
– Familiar to many people
– Easy to obtain mental picture of surface
• Close lines = steep slope
• UphillV = stream
• DownhillV or bulge = ridge
• Circle = hill top or basin
▪ Disadvantages
– Poor for computer representation: no formal
digital model
– Must convert to raster orTIN for analysis
– Contour generation from point data requires
sophisticated interpolation routines, often
with specialized software such as Surfer from
Golden Software, Inc., or ArcView Spatial
Analyst extension

12. Spatial Interpolation
▪ Critical component for raster surface creation
▪ Used to create surface which contain equally spaced cells from
irregularly spaced point data
▪ Five basic methods of interpolation
– Inverse Distance Weighting
– Spline
– Trend
– Natural Neighbor
– Kriging

13. Spatial Interpolation
▪ Critical component for raster surface creation
▪ Used to create surface which contain equally spaced cells from
irregularly spaced point data
▪ Five basic methods of interpolation
– Inverse Distance Weighting
– Spline
– Trend
– Natural Neighbor
– Kriging

14. Inverse Distance Weighting
▪ Inverse DistanceWeighting (IDW): assumes that each input point has a local influence that diminishes
with distance, which is achieved by weighting the points closer to the processing cell greater than those
farther away.
▪ Output values for each cell may be based on
– Nearest neighbor option which weights a specified number of points (the “k" nearest neighbors). If k=n then all points
are included.
– or Radius option which uses all points within a specified radius.
▪ A Power Parameter controls the significance of the surrounding points upon the interpolated value: the
higher the value the less influence from distant points.
– In essence, this is the rate of attenuation with distance; a higher value means a steeper slope for attenuation
▪ A barrier input line theme can be specified to represent a cliff, ridge, or some other interruption in a
landscape; points beyond the barrier are excluded from the weighting. A choice of No Barriers will use all
points specified in the No. of Neighbors or within the identified radius.
▪ Use IDW, for example, to interpolate a surface of consumer purchasing. More distant locations have less
influence, because people are more likely to shop closer to home; a barrier could be railroad lines assuming
nobody "crosses the tracks" to shop.
▪ An IDW surface passes through the measured points (referred to as an “exact interpolation”), and
interpolated surface is never above or below the highest/lowest measured points

16. Spline
▪ Spline is a general purpose interpolation method that fits a minimum-curvature surface exactly
through the input points.
▪ Conceptually, it is like bending a sheet of rubber to pass through the points, while minimizing the
total curvature of the surface.
▪ The Regularized option yields a smoother surface
▪ the weight parameter defines the “weight of the third derivatives of the surface in the curvature minimization
expression.”The higher its value the smoother the surface
-The Tension option tunes the stiffness of the surface according to the character of the modeled
phenomenon.
▪ the weight parameter defines the “weight of the tension”.The higher its value the coarser the surface
▪ The number of points parameter identifies the number of points per region used for local
approximation. Higher values produce smoother surfaces.
▪ The spline method is best for gently varying surfaces such as elevation, water table heights, or
pollution concentrations. It is not appropriate if there are large changes in the surface within a
short horizontal distance, because it can overshoot estimated values.
▪ Like IDW it is an “exact interpolation” in that the surface passes through the measured
points, but unlike IDW the surface can extend above or below measured points

17. Interpolation with cubic "natural" splines between three points
Note how smooth the curves of the terrain are; this is because
Spline is fitting a simply polynomial equation through the points

18. Trend
▪ Trend: Uses a polynomial regression to fit a least-squares surface to the input points.The surface is chosen so that
the sum of the squared differences (vertical distances on the z axis) between the original points and their estimate
on the surface is minimized for the entire surface.
▪ The resulting surface seldom passes through the original points since it performs a best fit for the entire
surface, thus it is an “inexact interpolation.” The lower the RMS error, the more closely the interpolated surface
represents the input points.
▪ Order of the polynomial used to fit the surface is specified by user.The most common order of polynomials is 1
through 3.
– A first-order linear trend surface interpolation simply performs a least-squares fit of a plane to the set of input points.
– When an order higher than 1 is used, the interpolator may generate a Grid whose minimum and maximum might exceed the
minimum and maximum of the input points.
– As the order of the polynomial is increased, the surface being fitted becomes progressively more complex. A higher order
polynomial will not always generate the most accurate surface, it is dependent upon the data.
▪ A logistic option is available for generating a trend surface for prediction of presence/absence of certain
phenomena (in the form of probability) for a given set of locations (x,y) in space.The z value is a categorized
random variable with only two possible outcomes, for instance, the existence of an endangered species or the lack
of existence of that species. These two values of z can be coded as 1 and 0, respectively. It creates a continuous
probability Grid with cell values between 1 and 0. A maximum likelihood estimation is used to calculate the logistic
probability surface model. Trend surface interpolation creates smooth surfaces. (see Interp MakeTrend Discussion in
AV Help)

20. Natural Neighbor
▪ Natural neighbor: similar to IDW in that it applies weights to a set of neighbor
points, so it is a local rather than global interpolation
– However, point selection is based on delauney triangles, and weighting is based on area of
thiessen polygons
▪ “robust” and “conservative, artifice free”
– interpolated heights will be within range of sample heights (none above or below) and it will
not produce peaks, ridges, etc. that are not in the sample data
▪ Exact in that surface passes through all input points
▪ Requires no user input such as search radius, sample count, etc..
▪ Can handle large numbers of points that may crash other methods
▪ Works with regularly and irregularly distributed points
▪ Also known as Sibson interpolation

21. Natural neighbor interpolation.The colored circles. which represent the interpolating weights, wi, are generated using the ratio of the shaded area to that of the cell area
of the surrounding points.The shaded area is due to the insertion of the point to be interpolated into the Voronoi tessellation

22. Kriging
▪ Kriging is an advanced procedure that assumes the distance or direction
between sample points shows spatial correlation that describes the surface.
▪ Kriging assumes that the same pattern of variation can be observed at all
locations on the surface.
▪ This pattern is estimated by constructing Variograms based on sets of n
points or all points within a specified radius.
▪ The best estimation method for generating the output surface is then based
on an interactive examination of theVariogram.
▪ This approach is most useful when you already know about spatially
correlated distance or direction bias within the data. It is most commonly
used in geology and soil science.

23. Example of one-dimensional data interpolation by kriging, with confidence intervals. Squares indicate the location of the data.The kriging interpolation is in red.The
confidence intervals are in green.

24. Data sampling
▪ Method of sampling is critical for subsequent interpolation...
Regular Random Transect
Stratified random Cluster Contour

25. Systematic sampling pattern
Easy
Samples spaced uniformly at fixed
X,Y intervals
Parallel lines
Advantages
Easy to understand
Disadvantages
All receive same attention
Difficult to stay on lines
May be biases
Systematic sampling

26. Random Sampling
Select point based on random
number process
Plot on map
Visit sample
Advantages
Less biased (unlikely to match pattern
in landscape)
Disadvantages
Does nothing to distribute samples
in areas of high
Difficult to explain, location of
points may be a problem
Random Sampling

27. Cluster Sampling
Cluster centers are established
(random or systematic)
Samples arranged around each
center
Plot on map
Visit sample
(e.g. US Forest Service, Forest
Inventory Analysis (FIA)
Clusters located at random then
systematic pattern of samples at
that location)
Advantages
Reduced travel time
Cluster Sampling

28. Adaptive sampling
Higher density sampling where
feature of interest is more variable.
Requires some method of
estimating feature variation
Often repeat visits (e.g. two stage
sampling)
Advantages
Efficient in large homogeneous
areas with higher spatial variation.
Disadvantages
If no method of identifying where
features are most variable then
several you need to make several
sampling visits.
Adaptive Sampling

29. 3D GIS in action: DMRC
GPS Control: 5 cm accuracy Digital Elevation Model: 50 cm accuracy
triangulation

30. 3D GIS in action: DMRC
3D Topology
Texturing 3D Visualization
3D Rendering

33. Acknowledgement
These slides are aggregations for better understanding of GIS. I acknowledge the
contribution of all the authors and photographers from where I tried to
accumulate the info and used for better presentation.

34. Author’s Coordinates:
Dr. Nishant Sinha
Pitney Bowes Software, India
mr.nishantsinha@gmail.com