The frecjuency and length of the lines, the linearity and dimensions of the frames
are adjusted with knobs to dränge sizes and forms of the image on the screen within
a wide ränge. The image on the screen may be compressed or extended, and changed
for curvature (transformations of the second and higher Orders)In this way the rather
complex transformations of one projection into another are performed.
Photo transformation
Affine transformation, underlying photomechanical methods of transferring the model
from the material to the original is much simpler. It is done with the aid of a photo-
transformer. Let me note three specific features of affine transformation:
the straight lines of the cartographic material correspond only to straight lines of
the original under compilation;
sections of the corresponding lines are proportionalin other words, the scale along
the lines is constant;
the points and the line are incident. i
Having selected corresponding points for the origins of the co-ordinates, and duly
orientated the two fields (the original and the material) we shall have
X alX; Y b]X b2y; (3)
In these formulas coefficients al5 b1; and b2 express the compression and extension in
directions perpendicular to each other and, in addition, the so-called pure displacement.
The more complex formulas are based on linear fractional functions expressing colli-
near transformation.
Phototransformation may be easily performed using instruments of the F.T.B, type.
After a calculation is made of the elements to be transformed by means of formulas
(or tables), the parts of the instrument are set in the required positions by means of
scales. Then the negative, inserted in the adapter, the lens and the screen of the instru
ment take a position in which the image of the cartographic material is transformed in
the, projection of the map under compilation.
The transformation of the cartographic material with the aid of check points is much
simpler and consists in the alignment of the points of the negative with the corres
ponding points of the cartographic base on the screen. This can be done in case of
similarity transformation.
The formulas are:
X kx, Y =ky (4)
Here the coefficient of similarity shows how the linear dimensions are changed in
the copying. These elementary relations are the basis of many technical methods of map
compilation when there is no need to transform the image in transferring it to the ori
ginal. The most widely spread is the photomechanical method described below.
Essentially, it consists of high precision photography of base materials and super-
imposing their copies upon the cartographic base of the original. The copies are mounted
on a rigid base in accordance with the check points, the points of intersection of the
co-ordinates and the Vertexes of the trapezium angles. Before the mounting, two mu-
tually perpendicular lines are drawn through each check point, on the copies. Folded
notches are made around the check points of the copy to facilitate superimposition. Their
number depends on the State of the material and the Scale of the map being made. The
greater the number of check points on the material the fewer notches are made at the
intersection of the co-ordinates.
207
1 A point on a line of the cartographic material is expressed as a point on the corresponding
line of the original.
