Topic Series 11
Map Projections, Grids, Image Rectification, Planimetric Mapping
I. Map Projection
A map projection is a system by which the curvature of the earth's surface can be transformed
in order to display the spheroid surface to a flat surface. There are no mathematical or geometric
functions which can be used to transform points from a spherical to a flat surface and still keep the
distances between points correct. Every map projection is therefore a compromise of distortions.
Most map projections in use today adopt one of two compromises:
1. At each point on the map, the scale of distance is kept the same in all directions. Such a
map is conformal because a small figure on the spheroid is transformed into a figure of the
same shape on the map. The size may be different but the angle translation for small regions
will be transformed correctly. Angles are important in photogrammetry.
2. At each point on the map, the area of transformed objects remain constant, but not the
shape or size. Such a map is called an equal-area map.
Map projections attempt to maximize one or more of the following attributes while minimimizing
the negative effects of the others:
Attribute
size
shape
distance
direction
Map Property
equal-area (true relative size)
conformal (true relative shape)
equidistant (scale is uniform)
azimuthal (correct compass bearings)
Many map projection systems have been developed, but they are variations of only three
cartographic (i.e. geometric) surfaces:
1. Plane - the simpliest form of map projection is onto a plane, tangent to the earth's surface
at a point. Scale distortion increases rapidly with distance from the point of tangency.
2. Cylinder - a plane is wrapped around the earth to form a cylinder and a narrow belt of the
earth's surface around the cylinder is projected onto it. The cylinder may then be unrolled into
a plane to form a projection that can be extended, almost without limit, in one direction only
along the longitudinal axis of the cylinder. Different forms of the Mercator projects use the
cylinder surface.
3. Cone - a cone is tangent to the earth at a parallel of latitude. When the cone is cut along
an element and "unrolled", the resulting projection may be extending indefinitely in one
direction, but limited in the other.
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Figure 11-1: Geometric surfaces used for cartographic mapping.
2
Tangent vs. Secant placement of geometric figures: The geometric solids may be placed tangent to
the sperhoid surface or secant to it.
Figure 11-2: Tangent vs. secant sections of geometric solids.
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Figure 11-3: Tangent and secant placement of cartographic surfaces on geometric figures.
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II. Commonly Used Map Projections
The most commonly used map projections are:
Orthographic - projects mapping area onto a plane that is tangent to the earths
surface.
Mercator - projects points onto the surface of a cylinder that is wrapped around the
equator (i.e tangent at) with the axis of the cylinder perpendicular to the equator. May
be extended in the east-west direction. Considerable distortion is introduced at high
latitudes, but relatively little distortion in E-W direction.
Transverse Mercator - projects points onto the surface of a cylinder that is wrapped
around the poles (i.e. tangent at) of the earth with the axis of the cylinder parallel to
the equator. May be extended in the north-south direction with little distortion.
Polyconic - the projection surface touches the globe along a small circle or parallel.
Accuracy is perfect in zone along the common line, but deteriorates rapidly with
distance from the zone.
Lambert Conformal Conic - the cone cuts the spheroid along two parallels of lattitude
such that the axis of the cone is the polar axis of the spheroid.
For example, a state such as Tennessee could use a Mercator for its East-West qualities but
Mississippi would be better off using a Transverse Mercator or a Polyconic projection because they
minimize error in a N-S direction.
The following figures are presented to acquaint you with the array of possible projections that
are used for global projections because the same concepts work for smaller areas. No matter what
projection is used for large areas, some distortion will occur in converting a spherical surface to a
two-dimensional representation.
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Figure 11-4: Projection of earth's surface onto geometric surfaces.
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Figure 11-5: Commonly used map projections.
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Figure 11-6: Orthographic projection.
The orthographic projection is one of the oldest projections because the increase in distortion toward
the edges matches the normal perspective when someone views something spherical. The
orthographic projection presents a realistic view of a globe. Although it can only show one
hemisphere at a time, matched pairs do display the whole earth.
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Figure 11-7: Mercator projection.
The mercator projection is conformal and has the unique characteristic that any rhumb is shown as
a straight line. It exaggerates sizes and distorts shapes away from the equator. Direction is not true,
because all great circles, other than meridians and the equator, plot as complex curves. The mercator
projection should not be used for a base map.
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Figure 11-8: Illustration of the Transverse Mercator projection.
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III. Map Grid Systems
Each map projection system has associated with it a grid system of parallels and meridians
to represent the corresponding reference system on the spheroid. Every point on the projection has
a corresponding latitude/longitude location designation.
A rectangular grid can be superimposed on a map projection so that there will be a a fixed
pair of x,y coordinates corresponding to each pair of geographic coordinates. Examples of
rectangular grid systems include UTM's, and State Plane Coordinates. Interconversion between the
two systems (lat/longs and rectangular coordinates) can be computed through known mathematical
relationships.
The dimensions and orientation of grids vary, but three properties are common to most grid
systems, particularly those adopted by mapping and military agencies. These common properties
of most grid systems are:
1. They are true rectangular grids.
2. They are superimposed on the geographic projection.
3. They permit linear and angular measurements.
The two most common grid systems used for/on base maps are the Universal Transverse
Mercator grid and the State Plane Coordinate System. Each of these systems can be referenced
(mathematically) to Latitudes and Longitudes, which are true geographic location coordinates.
Differences between Lat/Longs, UTM's/State Plane Coordinates, and GLO
Lat/Longs
= geographic location coordinates for all projection systems
= represent known geographic locations of points on the earth spheroid.
UTM's/State Plane Coordinates = artificial grid system for specific projection system.
GLO = systematic land partitioning system; not a point location system.
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Latitude-Longitude (Lat/Long)
Lat/Longs are the geographic location coordinates for all projection systems; they represent
known geographic locations on the earth spheroid. There are parallels of latitude (lines parallel to
equator) and meridians/lines of longitude (perpendicular to equator and converging at the poles).
Longitude is measured from the prime meridian.
Universal Transverse Mercator Grid (UTM grid)
Starting at the 1800 meridian of longitude and progressing East, the globe is divided into
zones that are 60 of longitude in width which are numbered 1 to 60, N and S. Each zone is defined
by an east and west meridian of longitude and has a central meridian passed through the center of
the grid zone; i.e. 30 each side of central meridian. Each zone has its own origin, located at the
intersection of the equator and its own central meridian. A false origin for the north half of the zone
lies 500,000 meters west of the origin. This false origin makes it difficult to cross zone lines.
Mississippi Transverse Mercator (MSTM)
With the UTM grid system, Mississippi is split between UTM zones 15 and 16 and this
causes problems when crossing between zones. The MSTM is grid system that has a false origin
west of the state’s central meridian so that all MSTM easting-coordinates are positive.
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Figure 11-9: Grid zones for the Universal Transverse Mercator Grid system.
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Figure 11-10: Example of UTM and State Plane Coordinates on 7.5 minute quadrangle sheet.
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The UTM is a 10,000 meter grid based on a Transverse Mercator projection. Unfortunately,
Mississippi is split between two UTM zones; Zone 16 on east side, and Zone 15 on west side. UTM
tick marks for 1,000 meter intervals appear along the margins of USGS Quad Sheets. Examples of:
Eastings = 325 is 325,000 meters E
Northings= 3625 is 3,625,000 meters N
Figure 11-11. Determining UTM coordinates on a quad sheet.
To calculate the UTM coordinates of a point on a quad sheet:
1. Connect the easting tic marks on the top and bottom of the quad sheet and draw a
coordinate line near the point.
2. Connect the northing tic marks on both sides of the quad sheet and draw a coordinate line
near the point.
3. Measure the x distance (easting) from easting coordinate line to the point using the 60th's
scale, convert the distance to meters and add to easting coordinate distance.
example: (24/60")*(2000ft/inch scale)/3.2808 meters/ft.
= 243.84 meters + 325,000 = 325,243.8 meters
or,
[(24/60")*(24,000)*(2.54cm/")]/100m
= 243.84 meters + 325,000 = 325,243.8 meters
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4. Measure the y distance (northing) from northing coordinate line to the point using the 60th's
scale, convert the distance to meters and add to northing coordinate distance.
example: (48/60")*(2000ft/inch scale)/3.2808 meters/ft.
= 487.69 meters + 3,625,000 = 3,625,487.69 m
or,
[(48/60")*(24,000)*(2.54cm/")]/100m
= 487.69 meters + 3,625,000 = 3,625,487.69 m
Coordinates of UTM Grid are denoted in the following order:
false easting in meters
false northing in meters
the zone number
the zone hemisphere, north/south
Practical Problems with UTM Grid System
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State Plane Coordinate System (SPC)
In 1933 the U.S. Coast and Geodetic Survey introduced the idea of state plane coordinate
systems for civilian surveying. Single no one map projection system was suitable for every state
because of its shape and orientation, a rectangular coordinate system was established for each state.
The transverse Mercator, oblique Mercator, and Lambert conformal conic projection systems were
used. The transverse Mercator is used for states with long N-S axis and the Lambert conformal conic
for states with long E-W axis. Alaska is the only state to use the oblique Mercator.
The U.S. was eventually divided into 125 SPC zones, each having its own projection surface.
Zone boundaries follow state and county boudaries. Each zone has its own centrally located origin
through which passes it own central meridian. A false origin is established to the west and south of
the zone, usually 2,000,000 feet west of the central meridian.
Coordinates of SPC are denoted in the following order:
false easting in feet
false northing in feet
the state
the zone
The Mississippi state plane coordinate system uses a rectangular 10,000 ft. grid. The grid ticks
appear along the margins of USGS Quad Sheets. See Figure 11-10.
Government Land Office Survey (GLO)
The GLO is actually a systematic, land partitioning system established by the Land Ordinance
of 1785. The initial point of the GLO survey is the intersection of a parallel (called base line) and the
principal meridian.
Range lines were surveyed at 6 mile intervals north and south of the base line.
Township lines were surveyed along parallels at 6 mile intervals east and west of the principal
meridian.
The 6 x 6 mile squares bounded by intersecting township and range lines are called survey or
congressional townships.
In order to reduce the problem of unequal township dimension as the distance east or west of
the principal meridian increased, standard parallels were established every 4th township line and
guide meridians were established every 4th range line to form an "idealized" grid cell that is 24 miles
square (contains 16 townships).
Each township is divided into 36 sections, numbered 1 to 36, each containing 640 acres. A
section can be divided into quarters, halves, and other fractional parts.
Examples of legal descriptions: E1/2, NW1/4, Sec 18, T18N, R13E = ?? acres
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Figure 11-12: Illustration of the GLO Survey system.
IV. Map Ground Control
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The objective of ground control is:
to locate the ground positions of the points which can be accurately identified on
aerial photos. The ground position of a point may be identified by its horizonal
position with respect to a horizontal datum or its elevation with respect to a level
datum.
The purpose of ground control is:
to establish the position and orientation of each photo in space, relative to the ground,
so that planimetric and topographic maps can be compiled from the photos.
National Map Accuracy Standards (NMAS)
Map accuracy is a very complex topic since all maps involve some type of distortion during
the representation from a projection system and transfer of map detail. Any condsideration of map
accuracy must include references to both the vertical and horizontal aspects of position accuracy.
The U.S. National Map Accuracy Standards were issued by the Bureau of the Budget in 1941
and revised in 1943 and 1947. According to NMAS, map accuracy is treated in a statistical condition,
map accuracy decreases progressively as map scale decreases, and horizontal accuracy pertains only
to "well defined points." Since map accuracy is statistically defined and pertains to only a few points,
the standards say nothing about the accuracy with respect to a specific point.
National Map Accuracy Standards are:
A. All first, second, and third order geodetic map control points are to appear on the final map
product:
1. within 1/10 contour interval on vertical control, or
2. within 1/200 inch of true horizontal position
B. 90% of supplementary map control points tested must be:
1. within 1/2 contour interval of true position for vertical control, or
2. within 1/30 inch of true horizontal scale for final map scales of 1:20,000 and larger,
or
3. within 1/50 inch of true horizontal scale for final map scales smaller than 1:20,000.
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Required Control Points (CPs)
Error in Published Map Scale (em):
for Published map scales larger than 1:20,000
em = (1/30 inch)(25.4 mm/inch) = 0.84/2 = +/- 0.42 mm
for Published map scales smaller than 1:20,000
em = (1/50 inch)(25.4 mm/inch) = 0.508/2 = +/- 0.25 mm
Error in Control Point Position (ep):
Remember that ep is the average error in position of a graphical control point at the photo
scale, in mm.
ep = em (Map RF)/(Photo RF)
Combining the errors for Published Map Scale and Control Point Position into the control point
equation, we obtain:
thus, we only need to remember the em's for 1:20,000 larger/smaller as 0.42mm/0.25mm
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Examples of SCP Determination
A. If 250 photos area obtained at a scale of 1:25,000 and a map is to be produced at 1:50,000,
how many SCP's are needed to meet FMAS?
em = error in published map scale for NMAS
= +/- 1/50" for scale smaller than 1:20,000
= (0.02")(25.4mm/")= 0.508mm/2 = +/-0.25mm
ep = ave. error of CP at photo scale, mm
= em (Map RF)/(Photo RF)
= 0.25mm (50,000/20,000)
= 0.50mm
B. Twelve flight lines of 30 photos each will be taken at a scale of 1:18,000 for a published
map of 1:12,000. If 4 well placed CP's are used,
1. Does the map meet NMAS?
t = 12 x 30 = 360
CP = 4
k = 0.16
2. How many CP's would be required?
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V. Planimetric Mapping
Establishment of Primary/Secondary Map Contol Points
Generally, the greater the number of primary control points, the higher the accuracy. But, the
distribution of the control points has a significant effect on mapping accuracy; i.e. error.
A study with 233 photographs of scale 1:12,000 covering 155 square miles in Maryland tested
the various methods of assembling different systems of 273 control points.
#Control Points
4
11
13(1)
8
Location
1 in each corner
all on eastern flight strip
bottom edge, 1 in each line
1 in each corner, 1 midway
down each side
Eror(ft.)
Ave
Max
43
125
350
1300
60
380
18
90
Further experimentation showed that other additions did not greatly increases the accuracy. The
author of this experiment concluded that in constructing maps with photos of scale 1:20,000 from
photos of scale 1:15,840, that if proper control is used, the average error in feet should not exceed the
average number of photos used between control. Naturally, these points will have to be scattered over
the area correctly.
Control points are points on the map that have ground measurements and can be easily located
on the ground and on the map or photo. The points must be identifiable as to position and identity.
Road intersections are easily identified, but tips of islands, intersections of small creeks/streams
would be easy to locate on a photo, but difficult to location on the ground or on a map.
Wing or pass points are also used to set up our photos. If the photos in adjoining flight lines
do not coincide with those of the first flight strip, tie points will be used to "tie" the flight lines
together.
Image and Base Map Preparation
Location of Principal and Conjugate Principal Points
Locate, prick, and ink (with 0.2 inch diameter circle) the principal (red) and conjugate
principal (black) points on each photo. The PP and CPP points will become secondary control points
on the base map.
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Base Map
The paper used to construct the base map should be of sufficient size to allow the mapping
of the desired area at a prescribed base map scale. The paper should reasonably thick. The long
dimension of the map should be oriented North-South. Connect the diagonals to locate the center of
the base map sheet.
Identifying and Locating Primary Control Points
A control point is a point that can be accurately identified on the photo and on the ground in
terms of its horizontal and vertical position. The purpose of control points is to establish the position
and orientation of each photo in space, relative to the ground, so that planimetric and topographic
maps can be compiled from imagery transferred from the photos.
Identify and locate "identifiable" control points (i.e road intersection, stream across highway,
etc.) within your photo mapping area on both the photos and the USGS quadrangle sheet. Calculate
the UTM coordinates of each control point from the quad sheet.
The primary control points to be used are identified by UTM coordinates in meters and must
be plotted on the base map at the desired scale. Always double check your calculations and
measurements before plotting on the base map. Locate the desired number of control points on each
photo of the mapping area. Recall that approximately 8 control points on each photo (1 in each corner
and 1 midway down each side) has been determined to produce the minimum average mapping error.
Locate the primary control points on the base map and on all the photos on which they appear.
If a point appears on more than one photo, mark it on all the photos on which it appears.
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Calculating UTM Coordinates of Control Points from a Quad Sheet
To determine primary control point UTM coordinates, connect the UTM tick marks on both
sides of the quad sheet for the easting and on both top and bottom tics for northing coordinates. Use
the 60th scale to determine the x,y (i.e. easting, northing) distances in meters from the known UTM
coordinate to the control point. See Figure 9-1 below.
Quad Sheet Scale: 1/24,000 = 1 inch = 24,000 inches * 2.54 cm/in./100 cm/m = 609.6 m/in.
or, 1/60 inch = 10.16 m.
1. Connect the easting tic marks on the top and bottom of the quad sheet and draw a
coordinate line near the point.
2. Connect the northing tic marks on both sides of the quad sheet and draw a coordinate line
near the point.
3. Measure the x distance (easting) from easting coordinate line to the point using the 60th's
scale, convert the distance to meters and add to easting coordinate distance.
example: (24/60")*10.16 m/in. = 243.84 m
243.84 meters + 325,000 = 325,243.8 meters
4. Measure the y distance (northing) from northing coordinate line to the point using the 60th's
scale, convert the distance to meters and add to northing coordinate distance.
example: (48/60")* 10.16 m/in = 487.68 m
487.69 meters + 3,625,000 = 3,625,487.69 m
Figure 11-13. Determining UTM coordinates on a quad sheet.
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Establishing Control Points on Base Map
All control points are referenced to the center point of the base map.
base map scale RF = 1:36,000, or
1" = 3,000 ft. or 60/60" = 914.41 meters or 1/60" = 15.240 meters
base map origin =
327,000m E
3,686,250m N
Zone 16N, Mississippi
Control points: 1= 324,170m E, 3,681,748m N
2= 330,963m E, 3,688,811m N
X,Y Distance of control points 1 and 2 from origin:
1: X=easting = 324,170-327,000 = -2,830m/15.24 = -185.7/60ths
Y=northing= 3,681,748-3,686,250 = -4,502m/15.24= -295.4/60ths
2: X=easting = 330,963-327,000 = +3,963m/15.24 = +260.0/60ths
Y=northing= 3,688,811-3,686,250 = +2,561m/15.24= +168.0/60ths
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Figure 11-14. Plotting control points to scale on base map using UTM coordinates.
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Supplementary Control Points
The purpose of supplementary control points (SCP's) is to extend and densify the control
network; the constraints on selection of a SCP are:
1.
A point must appear on at least two (2) photos. (Why is this?)
2.
The point cannot obscure or be obscured by another control point; 2 points cannot
occupy the same radial line. Be careful about obscuring the PP or CPP on the same
or another photo.
3.
A point cannot fall within 0.5", and preferably 0.75", of the edge of a photo.
4.
The location of the point extends the network, or fills in a hole in the network.
When the primary control points (PCP's) have been plotted on the map and located and
marked on the photos, and the SCP's have been marked on the photos, the next step is to utilize the
radial triangulation principle to locate the points on the base map.
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VI. Transfer of Planimetric Imagery
Radial Triangulation
The procedure for transferring SCP's to the base map is based on the radial line assumption:
Assuming vertical or nearly vertical photos, true horizontal angles can be measured from the principal
point because scale change and relief distortions are radial from the principal point. That is, the
horizontal angle, measured from the principal point, remains the same even though the object points
shift along the radial line. See Figure 9-2
Radial triangulation from aerial images is a graphic method of photogrammetric triangulation
which establishes the true horizontal position of image points. Recall that a precision aerial mapping
camera is an angle recording instrument, thus:
1. The basic principle of the radial assumption is that true and constant angles will be formed
at the center of a vertical aerial image between the flight line and a radial line to the base of
the image.
2. More specifically, in a truly vertical image, with nadir point as the vertex, these angles will
remain constant regardless of general scale change and within a wide range of topographic
relief.
The production of planimetric maps with radial triangulation procedures has been a
photogrammetric practice since the 1940's (see Aerial Photos in Forestry by Spurr, 1948), and perhaps
longer.
Since radial triangulation is a graphic method of transferring angles that is based on the
assumption of constant angles from the center of the imagery from the flight line to the object, a brief
review of photo "centers" and their significance is in order.
1. Principal Point (PP) - the geometric or optical center of the film plane from which any
displacement due to camera or lens distortion is radial.
2. Nadir Point (NP) - the "plumb line" point of the camera lens system from which
topographic displacement is radial.
3. Isocenter (IC) - the intersection of the axis of tilt and the line between the NP and PP from
which displacement from tilt and tip are radial.
On a truly vertical photograph (i.e less than 3 degrees tilt), these centers are coincident.
However, if tilt is excessive, the isocenter must be located and used as the center of measurement. In
theory, photos will excessive tilt (greater than 3 degrees) can be used, but in practice, they seldom are
used. The nadir point must be located and used if terrain variation (dissection) is excessive.
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Because of image displacement, a photograph is NOT a map. But, since image displacement
is radial from a known photo center, a precision aerial camera is an angle recording instrument.
Figure 11-15: Illustration of radial line triangulation.
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The application methods for transferring angles from photo imagery to base maps include:
1. transparent templets - mylar or tracing paper.
2. slotted templets - cardboard, plastic, thin strips of metal.
3. mechanical templates - prepared slotted arms of differing lengths; e.g. The Lazy Daisy
Mechanical Triangulator.
Tracing Paper Templet or graphical method is very inexpensive and is the most accurate of readily
available methods commonly used in forestry work. A paper templet (tracing paper) is placed over
each of the photos and a series of lines, radiating from the principal point, is drawn from the principal
point across each CPP, PCP, and SCP. Each line is labeled. Each templet is then placed on the base
map and adjusted until the labeled, radiating lines cross the PCP's. When all templets are in place,
the intersection of the crossing, radial lines is pricked and labeled. Three intersecting lines establishes
a PCP on the base map.
Lazy Daisy Mechanical Triangulator probably hasn't been used commercially since 1965, but it does
serve to illustrate the principle underlying all mapping devices--the elimination of topographic
displacement. One template will be constructed for each of only two photos. Each point on the photo
(CPP's, PCP's, and SCP's) will have a metal arm radiating from the PP to the point. The arm should
extend beyond the base for at least 0.5"--WHY? Make sure that each arm is properly labeled with
grease pencil. When each template has been completed and tightened, begin transferring to the map.
Use the template with the greatest number of PCP's first. As two arms to the same point cross, place
a brass base in the intersection. If you have three crossing arms, you will have established a new PCP.
When all templates have been transferred, prick through each base, and as you remove the templates,
label each point on the base map. Make sure you wipe the arms clean (benzene) and replace in the
correct slot in the container.
Errors in Radial Assumption
The sources of error in radial triangulation are:
1. Excessive tilt
2. Excessive terrain variation
3. incorrect location of appropriate photo center.
Radial triangulation can be accomplished, with minimum error, from unrectified photos if:
1. relief variation does not exceed +/- 500 ft. from average datum.
2. tilt is less than 2 degrees.
3. map scale is not larger than 1:24,000.
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If the map scale is as small as 1:62,500 (roughly 1 inch = 1 mile), terrain variation as large as 1,000
ft. can be accommodated. However, it is always best to select control points which are not at
elevational extremes.
Application of Radial Triangulation
All applications of radial triangulation require:
a. stereoscopic overlap greater than 50 percent.
b. sidelap greater than 15 percent
c. primary control points that are clearly identifiable on photos and map. Primary
control may appear on only one photo, but all control points must be labeled on the
photo on which they appear.
d. secondary control points (wing or pass points) must be located at relatively
permanent landscape features, must appear on at least 2 photos, must not be obscured
by each other or by primary control points, and must be clearly marked and labeled on
each photo in which they appear. Road intersections can be used, but non-permanent
points such as water levels, stream intersections or curves, etc. should not be used.
Summary of Preparing and Assembling a Radial Line Plot
A. Select map projection and prepare base map.
1. Compute scale of base map in linear measure per 1/60th of a inch.
example: base map scale = 1:36,000
thus, 1 inch = 60/60 = 914.41 meters
and, 1/60 = 15.24 meters.
B. Plot primary control points on base map (i.e. to proper scale)
1. Determine the UTM coordinates of the base map center.
example: 327,000m E, 3,686,000m N
2. Calculate the x,y location of each control point (from base map center) by
subtracting the UTM coordinate of the base map center from each control point
coordinate and then dividing by the linear scale per 60th of an inch.
Coordinate distance = (CP UTM - Center UTM)/scale
example: control point = 328,400m E, 3,686,500m N
x =(328,400-327,000)/15.24 = -91.86/60th
y =(3,686,500-3,686,000)/15.24=+32.8/60th
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3. Carefully plot the x,y map scale distance and plot the control point; number it.
C. Mark primary and secondary control points on each photo. Remember that PP and CPP are
both secondary control and that the template assembly radiates from the NP (PP). Locate,
prick, circle and ink on each photo in which they appear:
1. PPs and CPPs (secondary control)
2. Primary control points
3. Wing and/or pass points that appear on at least 2 photos and do obscure the CPPs
or primary control points. Wing points should be used to extend the network of
control, i.e. fill in the gaps, but should not be located at the edges of the image
(distortion); i.e. 0.5 inches.
D. Prepare template assemblies from photo locations/images.
1. Draw/establish radial lines from the NP to all primary and secondary control points
on the photo; label each line with a name/number. If using a paper template, be sure
to extend the lines well beyond the point.
2. Prepare template for each photo.
E. Transfer template assemblies to base map and mark location of the intersection of two
lines/arms. This is the horizontal location of that point.
F. Rectify photo image points (i.e. PPs, CPPs, CPs, etc.) to corresponding map points and
transfer phot image detail to base map via Vertical Sketchmaster.
There will probably be some discrepancy to the fit of the image points to map points.
Try to get primary control points to match as closely as possible and distribute residual
error among secondary points.
Sketch only the center of the photo image zone (i.e. half way between CPP and PP and
half the sidelap).
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Transfer of Image Detail
When a planimetric map is to be constructed, the simplest and least-cost method of
transferring detail from an aerial image to a map is by use of Single Print Transfer Devices. There
are a variety of such instruments for producing planimetric maps.
Single Print Transfer Instruments
1. Reflecting Projectors - The image (transparency or print can be projected unto a back-lit
viewing screen, and the image traced on a suitable mapping medium such as frosted mylar or
tracing paper. The Krones will accommodate a variety of image formats, from 35mm to 9,"
and accommodates a wide scale range, 3X - 72X. Expensive. Another type of Reflecting
Projector is the horizontal version; this type must also be used in a darkened room, and has
the dis-advantage of the hand obscuring part of the projected image. 1/5 reduction to 5X
enlargement, no compensation for tilt/tip.
The normal procedure is to map, for example, stand condition classes - composition, size, density,
and then transfer the mapped form to a 7.5 min. quadrangle or other suitable base map for later
digitizing. However, with the advent of video-scanning, it is possible to digitize directly from the
imagery without the intermediate step of transfer to a suitable base map -- however, because of image
distortions (tilt, scale, etc.) it is necessary to have a relatively large number of control points on
image and ground in order to rectify the image into real space and obtain a reasonable RMS error
(residual mean square). The video camera converts the colors/tones to electronic signals, just like
your camcorder. The data is captured digitally and thus can be displayed on a CRT - display screen.
Control points recognizable and definitive on both image and map are registered, and the image is
rectified by a "RubberSheeting" algorithm. EXPLAIN!
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Figure 11-16: Single print transfer instruments
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2. Camera Lucida Instruments - Any mapping device that superimposes two images by means
of a semi-transparent mirror or prism is a Camera Lucida instrument. In this case the
photographic image is projected and superimposed on the map - by matching images of
control points with the map location of the control. Residual Mean Square = based on the
average squared distance of selected control points on the image to the "real space" map
position.
The common camera lucida instruments include:
a. vertical and oblique sketchmasters
b. universal sketchmaster
c. rectoplanagraph
In all of the above, the operator can adjust the two superimposed images (map and aerial
image) so that the image control points and the map control points are coincident. When this
occurs, detail within the control network on the image can be transferred to the base map.
Figure 11-17: Camera lucida instruments for superimposing two images.
a
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a. Vertical Sketchmaster - image is transmitted from the image surface to a semi-transparent
mirror by a reflecting mirror. The image is transmitted to the base map, and scale, tilt and tip
inherent in the image can be compensated for by manipulating the leg adjustments.
Oblique - not much used today; limited to about 60 deg. tilt and 6" focal length.
b. Universal Sketchmaster - uses a Split Prism, and can be rectified for tilt between 0 and 70
deg.; limited range of focal lengths.
c. Rectoplanagraph - see Forestry Suppliers Catalog. Uses a double prism to transfer image;
0 - 70 deg. tilt and focal lengths from 3 - 12".
Stereo Transfer Instruments
All topographic mapping instruments utilize the basic formula
dh = (H-h)dp/(APb + dp) (floating Dot Principle)
1. Baplex (PG 89) MULTIPLEX
They operate by projecting stereoimages (glass diapositives or positive transparencies) in
complementary colors (anaglyph) or polarized light to a base map (VU-GRAPH). The
operator adjusts X,Y and Z functions of the projectors to rectify the image control to the map
control - using color glasses or polarized glasses. When the 3-D model is obtained, the
operator sets the delta parallax for a given contour and finds the point on the model where
the floating dots are fused. This particular line is traced - if the dots split, you have moved
off of that elevation.
For example --- Given an absolute parallax of the base of 80.00mm, a flying height of 6000
ft., and a 300 ft. contour, what is the delta parallax at which the tracing table is to be set?
dh/(H-h) = dp/(APb + dp)
300/6000 = dp/80 + dp
24,000 + 300 dp = 6000 dp
5700 dp = 24,000
dp = 4.21 mm
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VII. Heads Up Mapping
See topic on “Digitizing with ArcView”
1. Requires ortho-rectified and geo-referenced images
Orthographic images - distortion and scale variances have been removed.
Geo-referenced images - referenced to geographic coordinate system.
2. Advantages
On-screen, easy
No need for control points
Creates shape files for ArcView themes
Ease of editing
3. Disadvantages
No stereo image... thus type/stand lines are difficult; no height differences.
Costs for ortho-rectified images
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VIII. Orthophotography and Mosaics
Orthophotography
Orthophotography shows land cover, cultural, and, to some extent, terrain features in their
true horizontal positions; again employs the line-scanning of a stereo-model where the scanning
device acts as a floating dot and rectifies the image. The road is curved on the left image due to terrain
differences, the ortho treatment corrects this - right image.
U.S.G.S., and DOD in foreign countries, utilizes this technique to produce ORTHOPHOTO
QUADS - an advance copy of a 7.5 min quad, but without contours.
Mosaics
1. ortho-images can be utilized in a mosaicing process whereby 2 or more images are "fitted" together
to form a composite view of an area - that are well controlled in terms of scale and positional accuracy
- expensive!
2. controlled mosaics - normally ratioed (brought to a common scale) and rectified (eliminates tilt),
and matched as closely as possible to plotted control points using only the central portion of the
images. Largely replaced by ORTHO TECHNIQUES.
3. semi-controlled mosaics - use unratioed, but have base map control points to orient;
4. uncontrolled mosaics - just match features and work out from center of assembly; special case =
photo index sheets - assemble photos in uncontrolled fashion and shoot with a large reduction - Demo
index sheet and cutting procedure!!!!
What is the advantage of orthophotos over conventional images and maps??? features shown
in true horizontal position = better scaling --- over maps because you can see "today's" look of the
land - updates maps.
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