Modeling%20Surfaces%20Using%20Triangulated%20Irregular%20Network%20Raster%20Interpolation%20From%20Points

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Modeling Surfaces Using Triangulated Irregular
Network Raster Interpolation From Points
The C.W. Post College of Long Island University,
ArcGIS 3-D Analyst, http//www.esri.com (
307-acre campus located 25 miles east of
Manhattan , Brookville, New York)
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Surface terrain model for city of Austin,
TXArcGIS 3-D Analyst
Shoal creek
Waller creek
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Triangulated Irregular Network (TIN)Algorithm
for interpolating irregularly-spaced data to
represent terrain heights for terrain modeling
UT Campus
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TIN

• Digital representation of the terrain
• Preserves details of a shape on the terrain, more
  accurate representation of urban area
• Break lines represent significant terrain
  features like a lake or cliff that cause a change
  in slope
• Relatively few points are required to represent
  large, flat, or smoothly continuous areas
• Requires a much smaller number of points than a
  gridded DTM (The digital terrain model) in order
  to represent the surface terrain with equal
  accuracy

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Steps to Form a Surface From TIN

• A triangular mesh is drawn on the control and
  determined data points
• A perimeter around the data points is
  established.
• The points are connected in a manner that
  smallest triangle formed from any three points is
  constructed (convex hull)
• To connect the interior points, Delaunay
  triangulation is used (lines from one triangle do
  not cross lines of another)
• A surface is created by integrating all of the
  triangles over the domain
• Additional elevation data such as spot elevations
  at summits and depressions and break lines are
  also collected for the TIN model

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A Mesh of Triangles in 2-D
Points
Face
Edge
Triangle is the only polygon that is always
planar in 3-D
Lines
Surfaces
Points
Each triangle defines a terrain surface, or facet
assumed to be of uniform slope and aspect over
the triangle
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TIN Triangles in 3-D
(x3, y3, z3)
(x1, y1, z1)
(x2, y2, z2)
z
y
Projection in (x,y) plane
x
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Delauney Triangulation

• Developed around 1930 to design the triangles
  efficiently
• Geometrically related to theissen tesselations
• Maximize the minimum interior angle of triangles
  that can be formed
• No point lies within the circumcircle of a
  triangle that is contained in mesh

Yes More uniform representation of terrain
No
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Inputs for Creating a TIN

• Mass Points define points anywhere on landscape
• Hard breaklines define locations of abrupt
  surface change (e.g. streams, ridges, road kerbs,
  building footprints, dams)
• Soft breaklines are used to ensure that known z
  values along a linear feature are maintained in
  the tin.

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TIN with Linear Surface Features
Classroom
UT Football Stadium
Waller Creek
City of Austin digitized all the buildings to get
emergency vehicles quickly
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A Portion of the TIN in Large View
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Input data for this portion
Mass Points not inside building
Soft Breaklines along the hills
Hard Breaklines along the roads
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TIN Vertices and Triangles
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ESRI TIN Engine Integrated Terrain Model, ARCGIS
9.2

• Creates varying levels of conditions and points
  to produce pyramid style TINs on the fly
• Provides an efficient methodology for working
  with mass data
• Results in a single dataset that can rapidly
  deploy and visualize TIN based surfaces at
  multiple scale

Courtesy, http//gis.esri.com
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TIN Surface Model
Waller Creek
Street and Bridge
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Data Sources to Develop TINs

• LIDAR (Light Detection and Ranging or Laser
  Imaging Detection and Ranging)
• Aerial photogrammetry

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LIDAR

• An optical remote sensing technology
• Masures properties of scattered light to find
  range and/or other information of a distant
  target
• LIDAR sensor was mounted on-board
• During the flight, the LIDAR sensor pulses a
  narrow, high frequency laser pulse toward the
  earth through a port opening in the bottom of the
  aircraft's fuselage
• The LIDAR sensor records the time difference
  between the emission of the laser beam and the
  return of the reflected laser signal to the
  aircraft
• Range to an object is determined by measuring the
  time delay between transmission of a pulse and
  detection of the reflected signal to the aircraft
• Points are distributed across the space,
  push-broom sensor
• Amazing degrees of details. Resolution is 1/9 arc
  second
• 1 arc second DEM 30 m
• 1/3 arc second DEM 10 m

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LIDAR Terrain Surface for Powder River, Wyoming
Source Roberto Gutierrez, UT Bureau of Economic
Geology
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NCALM National Center for Airborne Laser Mapping

• Sponsored by the National Science Foundation
  (NSF) (http//www.ncalm.org)
• Operated jointly by the Department of Civil and
  Coastal Engineering, College of Engineering,
  University of Florida (UF) and the Department of
  Earth and Planetary Science, University of
  California- Berkeley (UCB)
• Invites proposals from graduate students seeking
  airborne laser swath mapping (ALSM) observations
  covering limited areas (generally no more than 40
  square kilometers) for use in research to earn an
  M.S. or PhD degree.
• Proposals must be submitted on-line by November
  30, 2006

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Aerial photogrammetry (Stereo photographic
coverage)

• The aerial photos are taken using a stereoscopic
  camera
• Two pictures of a particular area are
  simultaneously taken, but from slightly different
  angles, overlapping photographs
• The overlapping area of the two resulting photos
  is called a stereo pair
• Using a computer, stereoplotter, the stereo pair
  can be viewed as a single image with the
  appearance of depth or relief

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Aerial photogrammetry (Stereo photographic
coverage)

• The aerial photos are taken using a stereoscopic
  camera
• Two pictures of a particular area are
  simultaneously taken, but from slightly different
  angles, overlapping photographs
• The overlapping area of the two resulting photos
  is called a stereo pair
• Using a computer, stereoplotter, the stereo pair
  can be viewed as a single image with the
  appearance of depth or relief
• Ground control points are established based on
  ground surveys or aerial triangulation and are
  viewed in the stereoplotter in conjunction with
  the stereo pair
• The image coordinates of any (x,y,z) point in
  stereoscopic image pair can be determined and
  randomly selected and digitized

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3-D ArcScene, Austin, TXAerial photogrammetry
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3-D Scene with Buildings
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Some advantages of TINS

• Fewer points are needed to represent the
  topography---less computer disk space
• Points can be concentrated in important areas
  where the topography is variable and a low
  density of points can be used in areas where
  slopes are constant.
• Points of known elevation such as surveyed
  benchmarks can easily be incorporated
• Areas of constant elevation such as lakes can
  easily be incorporated
• Lines of slope inflection such as ridgelines and
  steep canyons streams can be incorporated as
  breaklines in TINS to force the TIN to reflect
  these breaks in topography

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Geostatistics
Why interpolate?

• Analogy Spatially distributed objects are
  spatially correlated things that are close
  together tend to have similar characteristics

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Interpolation using Rasters

• Interpolation in Spatial Analyst
• Inverse distance weighting (IDW)
• Spline
• TOPOGRID, Topo to Raster (creation of
  hydrologically correct digital elevation models)
• Kriging (utilize the statistical properties of
  the measured points quantify the spatial
  autocorrelation among measured points )
• Interpolation in Geostatistical Analyst

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ArcGIS Spatial Analyst to create a surface using
IDW interpolation
IDW weights assigned arbitrarily
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Example for a linear IDW interpolation
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Using the ArcGIS Spatial Analyst to create a
surface using IDW interpolation

• Each input point has a local influence that
  diminishes with distance
• It weights the points closer to the processing
  cell greater than those farther away
• With a fixed radius, the radius of the circle to
  find input points is the same for each
  interpolated cell
• By specifying a minimum count, within the fixed
  radius, at least a minimum number of input points
  is used in the calculation of each interpolated
  cell
• A higher power puts more emphasis on the nearest
  points, creating a surface that has more detail
  but is less smooth
• A lower power gives more influence to surrounding
  points that are farther away, creating a smoother
  surface. Search is more globally

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Topo to Raster interpolation
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ArcGIS Spatial Analyst to create a surface using
Topo to Raster interpolation

• Designed for the creation of hydrologically
  correct digital elevation models
• Interpolates a hydrologically correct surface
  from point, line, and polygon
• Based on the ANUDEM program developed by Michael
  Hutchinson (1988, 1989)
• The ArcGIS 9.x implementation of TopoGrid from
  ArcInfo Workstation 7.x
• The only ArcGIS interpolator designed to work
  intelligently with contour inputs
• Iterative finite difference interpolation
  technique
• It is optimized to have the computational
  efficiency of local interpolation methods, such
  as (IDW) without losing the surface continuity of
  global interpolation methods, such as Kriging and
  Spline

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Using the ArcGIS Spatial Analyst to create a
surface using Spline interpolation

• Best for generating gently varying surfaces such
  as elevation, water table heights, or pollution
  concentrations
• Fits a minimum-curvature surface through the
  input points
• Fits a mathematical function to a specified
  number of nearest input points while passing
  through the sample points
• The REGULARIZED option usually produces smoother
  surfaces than those created with the TENSION
• For the REGULARIZED, higher values used for the
  Weight parameter produce smoother surfaces
• For the TENSION, higher values for the Weight
  parameter result in somewhat coarser surfaces but
  with surfaces that closely conform to the control
  points
• The greater the value of Number of Points, the
  smoother the surface of the output raster

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Example for a 2-D Spline interpolation
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Interpoloation using Kriging

• Things that are close to one another are more
  alike than those farther away spatial
  autocorrelation
• As the locations get farther away, the measured
  values will have little relationship with the
  value of the prediction location

Kriging weights based on semivariogram
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SemiVariagram
Captures spatial dependence between samples by
plotting semivariance against seperation distance

• Sill The height that the semivariogram reaches
  when it levels off.
• Range The distance at which the semivariogram
  levels off to the sill
• Nugget effect a discontinuity at the origin
  (the measurement error and microscale variation )

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SemiVariagram
h separation distance between i an j
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Case study
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