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3d GIS fundamentals, GIS technologies, TIN modeling, Surface Creation, DEM,
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GIS moving to 3rd-Dimension
The application of GIS is limited only by the imagination of those who use it
Dr. Nishant Sinha
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
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 as
TINs 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.
3D Prevue: “Coastal Terrain Model”
… a surface that integrates topography and bathymetry
+ =
Integrated Topo-Bathy Model
BathymetryTopography
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
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
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
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
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
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)
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
• Uphill V = stream
• Downhill V or bulge = ridge
• Circle = hill top or basin
▪ Disadvantages– Poor for computer representation: no
formal digital model
– Must convert to raster or TIN 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
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
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
Inverse Distance Weighting
▪ Inverse Distance Weighting (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
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
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
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)
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
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
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 the Variogram.
▪ 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.
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.
Data sampling
▪ Method of sampling is critical for subsequent interpolation...
Regular
Random
Transect
Stratified random
Cluster Contour
Systematic sampling pattern
EasySamples spaced uniformly at fixed X, Y intervalsParallel lines
AdvantagesEasy to understand
DisadvantagesAll receive same attention Difficult to stay on lines
May be biases
Systematic sampling
Random Sampling
Select point based on random number processPlot on mapVisit sample
AdvantagesLess biased (unlikely to match pattern in landscape)
DisadvantagesDoes nothing to distribute samples in areas of highDifficult to explain, location of points may be a problem
Random Sampling
Cluster Sampling
Cluster centers are established (random or systematic) Samples arranged around each centerPlot on mapVisit sample
(e.g. US Forest Service, Forest Inventory Analysis (FIA)Clusters located at random then systematic pattern of samples at that location)
AdvantagesReduced travel time
Cluster Sampling
Adaptive sampling
Higher density sampling where feature of interest is more variable. Requires some method of estimating feature variationOften repeat visits (e.g. two stage sampling)
AdvantagesEfficient in large homogeneous areas with higher spatial variation.
DisadvantagesIf no method of identifying where features are most variable then several you need to make several sampling visits.
Adaptive Sampling
3D GIS in action: DMRC
GPS Control: 5 cm accuracy
Digital Elevation Model: 50 cm accuracy
triangulation
3D GIS in action: DMRC
3D Topology
Texturing 3D Visualization
3D Rendering
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.
Author’s Coordinates:Dr. Nishant SinhaPitney Bowes Software, [email protected]
