Title: Modeling%20Surfaces%20Using%20Triangulated%20Irregular%20Network%20Raster%20Interpolation%20From%20Points
1Modeling 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)
2Surface terrain model for city of Austin,
TXArcGIS 3-D Analyst
Shoal creek
Waller creek
3Triangulated Irregular Network (TIN)Algorithm
for interpolating irregularly-spaced data to
represent terrain heights for terrain modeling
UT Campus
4TIN
- 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
5Steps 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
6A 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
7TIN Triangles in 3-D
(x3, y3, z3)
(x1, y1, z1)
(x2, y2, z2)
z
y
Projection in (x,y) plane
x
8Delauney 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
9Inputs 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.
10TIN with Linear Surface Features
Classroom
UT Football Stadium
Waller Creek
City of Austin digitized all the buildings to get
emergency vehicles quickly
11A Portion of the TIN in Large View
12Input data for this portion
Mass Points not inside building
Soft Breaklines along the hills
Hard Breaklines along the roads
13TIN Vertices and Triangles
14ESRI 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
15TIN Surface Model
Waller Creek
Street and Bridge
16Data Sources to Develop TINs
- LIDAR (Light Detection and Ranging or Laser
Imaging Detection and Ranging) - Aerial photogrammetry
17LIDAR
- 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
18LIDAR Terrain Surface for Powder River, Wyoming
Source Roberto Gutierrez, UT Bureau of Economic
Geology
19NCALM 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
20Aerial 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
21Aerial 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
223-D ArcScene, Austin, TXAerial photogrammetry
233-D Scene with Buildings
24Some 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
25Geostatistics
Why interpolate?
- Analogy Spatially distributed objects are
spatially correlated things that are close
together tend to have similar characteristics
26Interpolation 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
27ArcGIS Spatial Analyst to create a surface using
IDW interpolation
IDW weights assigned arbitrarily
28Example for a linear IDW interpolation
29Using 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
30Topo to Raster interpolation
31ArcGIS 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
32Using 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
33Example for a 2-D Spline interpolation
34Interpoloation 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
35SemiVariagram
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 )
36SemiVariagram
h separation distance between i an j
37Case study
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