2008d
FOREST SURVEY MEMO 08:12:31
Robin Bell 2007
Promotion of pre-digital forest survey procedures
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MANUAL RADIAL LINE PLOTTING
for
FOREST MAPPING
Summary
Radial line plotting (RLP) is a (low order) form of plotting from stereo air photos:
it corrects only for primary distortion / displacement due to elevation - which
displacement is radial about the principal point of an air photo and can be major at
the photo scale of 1:10,000. The formal method, with dedicated instrumentation,
has been historically used for mapping ’from scratch’ extensive areas of Africa
(Directorate of Overseas Surveys). Courses were taught at Edinburgh University
Ecology & Natural Resources, which was fully equipped (Hilger Watts /
Cartographic Engineering).
Small scale Manual RLP – similar to plain tabling – has an application in the
mapping of :
 small areas of steeper sloping / irregular terrain in otherwise gentle
topography;
 any place where there is also a lack of pre-existing map control / mapped
ground framework features, such as is necessary for detail transfer
mapping (Bell, 2007 / Bell, 2009a).
Other indications for manual RLP are :
 lack of formal plotting facilities;
 truly vertical / commercial quality air photography with negligible tilt;
 shortage of time / cash to procure a formal plot from a third party;
 availability of a pains-taking surveyor;
 forest areas distant from the base line of the photo (but less control is in
any case required near the principal point).
A proven manual methodology (impressive results) for manual RLP using a
stereoscope (Bell, 2008b) and simple tools, is described - for work at or around map
scale and photo contact scale of 1:10 000. Brief access to an A3 photocopier with
calibrated enlargement / reduction facility is recommended for final scaling of the
plot.
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With
practice, plotting a single photo overlap, yielding about 10 new control points,
Copyright
Robin Bell
2007 – Manual radial
plotting for forest mapping
page 1 of 9
can
be achieved
in approximately
oneline
hour.
Promotion of pre-digital forest survey procedures – [email protected]
08/02/2014
MANUAL RADIAL LINE PLOTTING
Devised by Robin Bell (with acknowledgement to Stephen H Spurr, 1948)
Definitions
The base map has in practice been the British Ordnance Survey (OS) 1:10 000
scale topographic map.
The principal point (PP) of a truly vertical photograph is effectively the dead
centre. (For a full definition see Bell, 2008b.)
The conjugate principal point (CPP) of the left hand photo of a stereopair is the
PP of the right hand photo as seen on the left hand photo, and vice versa.
The base line for the purposes of the present procedure is the imaginary or
inked line joining the PP and the CPP, the effective line of flight on the photo.
Active Control Points (ACPs) are points of known map location (and altitude in
the case of stereoplotting). To be used in this process they must be recognisable
on the base map and the photo. They are used for the geometric reference to
which all the plotted detail is related.
Proposed control points (PCPs) are the planned new CPs to be formed through
Radial Line Plotting, as extra control for Transfer Mapping (Bell, 2009a).
Radial line plotting Plotting that removes from the photo only the displacement
caused by altitude, which displacement is radial to the PP.
Formal stereoplot / High order plotting (Not covered here) Accurate plotting
by sophisticated and expensive plotter requiring a trained operator, which
removes all significant distortion / displacement in the photos, needing no base
map but only control points (planimetric and altitudinal) per overlap. These
control points may be derived with care from an OS base map.
Objective of manual radial line plotting
To provide and locate additional control points where these are lacking,
especially in variable / steep topography - making use of the principle that
altitudinal displacement on the photo is radial from the PP. The method is very
similar to the traditional terrestrial survey process of plain tabling.
Scope
For indications see summary, Page 1.
In these situations manual radial line plotting can where possible offer a method
generally superior to approximate field methods of survey in terms of cost and
accuracy.
Main equipment and materials /
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Main equipment and materials
 Good mirror stereoscope, ideally with scanning facility (Bell, 2008b), see
page 9;
 Air photos, truly stereoscopic (minimum 60% overlap) and vertical;
 ‘Crystal’ clear acetate overlay for photo enhancement (Bell, 2008c);
 Photocopyable acetate if possible (at least as large as the map area of the
overlap). (Ordinary acetate may melt in the copier);
 Transparent drafting film overlay (eg single mat) about the size of two air
photos;
 Technical pens - red Rotring c 0.2mm, black 0.18mm, Rotring FP 300 or
400 ink
 Very sharp and tough sewing needle (with home-made finger-gripping
device for extensive use);
 Brief access to a (commercial?) Zoom photocopier (1% interval)
Accuracy
Accuracy is mainly dependent on




True verticality of the photo
Meticulous care by the operator / surveyor
Accuracy of the OS base map / map control points
Identification of control points
The main test of accuracy is achieved at the end of the process. If the existing
active control points (ACP’s) on the final plot (see below) did not fit the base
map closely, then it is likely that there would have been a similar error in the
new proposed control points (PCP’s) (see Base length and base line, Page 4 /
5.) Conversely, good fit of ACP’s gives high confidence in the PCP’s. The
surveyor must decide if any error in fit is acceptable in the circumstances,
bearing in mind the likely cost and accuracy of the alternative approximate field
survey methods (See Bell, 2009a, Page 5). Experience has shown over many
years that the fit of plot with ACP’s is always excellent.
It cannot be over-stressed that the whole operation of manual radial line plotting
requires extreme patience and care, especially:
 correct identification of control points
 precise location of the points with pin and ruler (Fig 2) and thus
 maximisation of precision of intersection of the radii. Accidental errors in
individual radii can theoretically be combined and seriously multiplied at
the radius intersections / control points – see Fig 6.
Time required
An experienced surveyor will take about one hour to treat one photographic
overlap, providing about ten new control points / PCP’s. A much larger job
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(multiple overlaps) may more efficiently be managed by using formal
stereoplotting. (But see Fig 8, Page 8)
Method
Test photos for their verticality
Severe lack of verticality in one or other of a stereopair is shown by:
o Need for excessive adjustment of y-parallax on the stereoscope
when scanning from top to bottom of the field of vision. (The
photos must be properly base-lined.) (Bell, 2008b)
o Eye strain (remediable by frequent y-parallax adjustment).
A further indication is:
o Evidence of the aircraft turning significantly and thus banking
between two photographs, shown by significant divergence of the
two base lines of adjacent photographs - or irregularity in the flight
path on flight diagram (as supplied with the air photos).
Existing overlay from photo enhancement (Bell, 2008c)
Any (‘Crystal’) acetate overlay already stuck to the photo from the photo
enhancement process may help protect the photo from the pin, but there should
be no ink obscuring or distorting the view of the desired control points, and this
acetate might best be set aside till the time of transfer mapping (Bell, 2009a).
Choosing control points
Choose the proposed (new) Control Points (PCP’s) / “landmarks” in the area
lacking map control. (To be useful new control points will not appear on the
base map.) In the surrounding area choose Active Control Points (ACP’s) which are suitable reference points visible on both map and photograph ie the
usual type of existing ‘map control’. Choose all the control points as far from
the baseline as possible, since accuracy is poorer the closer one gets to the base
line (Fig 6). Twenty control points is probably the combined practical
maximum of PCP’s and ACP’s. Twelve to fourteen and may be easier to
handle, especially at first (but see Fig 8).
Marking the control points on the photos
Mark all control points with great care on both photos, using stereovision to
ensure that exactly corresponding points are spotted in red on both photos. Use
the red pen and make a small mark prominent enough to be visible through the
drafting film overlay. Number the control points neatly on one photo (to be
visible through the overlay, Fig 1.) In stereo vision, number the points on the
other photo in exactly the same order.
Base length and base line/
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Base length and base line
Cut the drafting film overlay (sufficient to cover two photos side by side – Fig
1).
Base length (the distance on the photo between PP and CPP) can be measured
from either photo. This base length is then scaled up / down to 1:10, 000, and
this is done at first approximately by multiplying by the same factor as used in
transfer mapping (Bell, 2009a Page 3/4). The factor is found by choosing two
points at approximately the same
altitude as the base line, and
measuring the distance on the map
a mm - and the distance on the
photo - b mm. The factor is
expressed as a / b. The length of
this approximately scaled base
line is reproduced on the overlay
as in Fig 1, running between the
overlay principle point (OPP) and
Fig 1
the overlay conjugate principal
point (OCPP) for the left photo.
(Note that when working on the
right photo, the OPP and the
OCPP will change places.) This
overlay will become the ‘plot of
indeterminate scale’. If the control
points lie on either side of the
Fig 2
base line, the base line should be
represented appropriately near the
centre of the overlay as in Fig 7 .
Drawing the first radius, left hand photo
*Fixing the drafting film overlay onto the left photo
Locate the OPP exactly over the principal point of the left photo. This can most
precisely done with a pin if that principle point is also previously marked with a
pin prick. (But beware ‘damaging’ somebody else’s photos.) The overlay is then
rotated until the approximately scaled up / down base line on the overlay is
exactly coincident with the photo base line. Fix the overlay firmly to the photo
(masking tape),
*Marking radii from the OPP to the PCP’s on the left photo /
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*Marking radii from the OPP to the PCP’s on the left photo
Hold the pin into the pricked OPP
on the drafting film overlay. Hold
the ruler against the pin and rotate
it until the edge meets the centre
of the red mark (PCP) number one
on the left photo (Fig 2). Draw
the first radius with the (0.18mm)
black pen, and label the line in the
position shown (Fig 3). Check
Fig 3
that the correct control point has
been used. Repeat for all control
Labelling the first radius, left hand photo
points, finishing with a complete
set of labelled radii for the left
photo cf Fig 8. Remove the drafting film overlay from the left photo,
preparatory to fixing it to the right one. The OPP now becomes the OCPP and
vice versa.
Repeat the operations described in the last 2 paragraphs above both marked
with an asterisk, as in Fig 4, except this time do not draw the complete radius as
shown by the dashed line, but only a small portion of the radius where it
intersects the corresponding radius from the left photo, and label at the
intersection, rather than at the end of the radius. Repeat for all control points.
Enhance each intersection with a black dot centralised precisely on the
intersection (Fig 8). Check that the black dots lie in the correct configuration
relative to the red dots on one of the photos (to prevent identification error at
this stage).
Accurate scaling and scale correction
The black dots / control points on the drafting film overlay / plot now lie in
their correct physical configuration but at an indeterminate scale. (If it had been
possible to accurately scale the
base line itself then the drafting
film overlay would be the final
product / plot.)
To accurately scale the drafting
film overlay / plot, choose two
ACP’s on the acetate at
maximum difference apart distance x mm. Measure the
equivalent distance on the
Ordnance Survey base map distance y mm. The scale
Fig 4
Marking the first intersection via the right hand photo.
OPP & OCPP have interchanged
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factor is y / x. Repeat this operation for other similar pairs of points to ensure
the best average figure in case of slight variation. Scale up / down the drafting
film plot using the zoom photocopier, (scale factor y/x) copying onto
photocopyable acetate (not ‘Crystal’ acetate).
This produces the final transparent plot of PCP’s at 1:10 000 scale.
Transfer of new control points (PCP’s) to OS base map and assessment of
accuracy
Enhance and number lightly the ACP’s on the base map. Match one ACP with
its equivalent on the final plot,
overlay exactly, pricking
through with the pin. With the
pin in position, rotate the final
plot until the other ACP’s on
the plot are as near as possible
Fig 5
coincident with their opposite
numbers on the map. Consider Possible configuration, acute angle, imprecise
adequacy of accuracy
(paragraph on Accuracy, Page
3).
If all final plot ACP’s ‘fit’ the
base map, prick the PCP’s
through onto the map with the
pin. Enhance points on base map
preparatory to detail transfer. Be
Fig 6
prepared to reject any ACP’s
close to the base line (obtuse
Obtuse angle intersection, imprecise location
angle - Fig 6) or other situations
(Fig 5) where the intersection of the two radii is more prone to error due to the
exceedingly acute angle of intersection. Again consider adequacy of accuracy
of ACP’s generally. Be prepared to be suitably impressed by the coincidence of
the ACP’s, giving you confidence in your new control points, the PCP’s
Fig 7
The control points can lie either side of the base
line. Note the labelling
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Transfer mapping (Bell, 2009a)
Before the process of transfer mapping, transfer by eye the PCP’s onto the
‘Crystal’ acetate carrying the enhanced crop detail (mark them ideally neatly in
red), so that in the transfer process they can next be matched to the newly
provided control PCP’s) on the OS base map.
ACP’s or PCP’s can lie either side of the base line (Fig 7 / Fig 8).
Fig 8. Example of a drafting film plot with 28 control points (life size). This is
the eventual form of a drafting film overlay, at indeterminate scale, prior to
accurate scaling and scale correction (Page 6).
PS Stephen Spurr (Spurr, 1948), describes manual radial line plotting using
pins for all control points, and threads for all lines, making for mechanical
adjustment of scale. It would probably not be practicable to use his method for
so many as 28 control points at one time.
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Copyright Robin Bell 2007 – Manual radial line plotting for forest mapping
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References
Bell, R J 2007
Theoretical Forest photointerpretation and detail
transfer mapping service.
Robin Bell 2007, Forest Survey Memo 07:12:31
Bell, R J 2008a
Stratification of conifer crops with particular
reference to inventory and acquisition of even-aged
Sitka spruce in upland areas in Northern Britain.
Robin Bell 2007, Forest Survey Memo 08:01:29.
Bell, R J 2008b
Base-lining & initial stereoscopic viewing of vertical
air photos for forestry.
Robin Bell 2007, Forest survey memo 08:11:01
Bell, R J 2008c
Manual forest air photo enhancement with acetate
overlay
Robin Bell 2007,
Forest survey memo 08:12:25
Bell, R J 2008d
Manual radial line plotting for forest mapping.
Robin Bell 2007,
Forest Survey Memo 08:12:31
Bell, R J 2009a
Detail transfer mapping for forest survey.
Robin Bell 2007,
Forest Survey Memo 09:01:29
Spurr, S H 1948
Aerial photography in forestry. New York.
--ooo0ooo---
Robin Bell achieved 1st class honours in Forestry at Edinburgh University in 1971. He was the
founder of Robin Forestry Surveys, and principle for 20 years. On his retirement in 1998 he
was a Fellow of the
Institute of Chartered
Foresters.
Please get in touch if you
have queries or other
comments.
Robin Bell 2007
Woodlea
Minto
Hawick
Scottish Borders
TD9 8SG
Tel 01450 870 336
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Copyright Robin Bell 2007 – Manual radial line plotting for forest mapping
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