PHOrOGRAMMETRIC ENGINEERING 
lation than from a model-by-model triangu 
lation. However, for the latter he employs 
the modified Herget method in which the strip 
coordinates of points in the preceding model 
are enforced during the orientation of a photo 
graph. Besides, his conclusion is based upon 
the size of systematic errors and not upon the 
residuals after polynomial strip adjustments. 
It is claimed as an advantage of triplet 
orientation that it is here possible to recog 
nize and eliminate errors in the x-coordinates 
of points in the triplet overlap. In the two- 
photo orientation recognition is possible by 
comparing the heights of these points in the 
two models in which they occur. Errors are 
more evident than in the triplet orientation 
because here the least squares adjustment 
does not minimize them. Points with such 
errors are here simply eliminated from use 
in the scale transfer and, if the x-error causes 
F-parallax, also from the relative orienta 
tion. 
On balance, the triangulation by means of 
independent relative orientation of each two 
successive photographs and scaling of the 
resulting models has the advantage that it 
uses simpler formulas and requires only half 
the computation time [69] of the triplet tri 
angulation. The latter, in the version used by 
Tewinkel and in the version recommended 
by McNair, has the advantage that a 
smoother fit between models is obtained 
automatically. 
3. RADIAL TRIANGULATION 
Numerical radial triangulation is discussed 
in ref. [70] to [76]. Roelofs and Timmerman 
describe results and the influence of errors if 
the classical rhomboid triangulation is used. 
Van den Hout describes the use of triangles 
in a block adjustment by the Anblock method. 
The lack of general availability of the exten 
sive literature on the rhomboid triangulation 
may explain recent interest in the numerical 
formulation of the old graphical radial tri 
angulation by means of alternate resection 
and intersection (ref. [74] to [76]). 
Polynomial Adjustment of Strips 
References [17], [36], [38], [39], [69], and 
[77] to [94] deal with the adjustment of strips, 
individually or in blocks, by means of poly 
nomial transformations. The adjustment 
serves to correct the strips for deformation 
and to obtain a reasonable fit of the trans 
formed strips at the ground-control points 
and at the tie points. 
Reference [84 a to f] have made it gradually 
clear that conformal transformations by 
means of polynomials of higher than the first 
degree do not exist. Therefore, in practice the 
adjustment of a strip is performed by means 
of various nearly conformal transformations. 
It can be performed as a sequence of two- 
dimensional transformations (see e.g. [85], 
[86]) or of transformations of planimetry and 
of heights (see e.g. [82], [88]), in each case 
with appropriate correction of the remain 
ing coordinate or coordinates. Alternatively, 
after an initial positioning, it can be per 
formed as one three-dimensional transforma 
tion (see e.g. [36] and [84a]). A proper correc 
tion for strip deformation cannot be guaran 
teed if independent polynomials are used for 
all three coordinates [99] or for planimetry 
and heights [69]. 
Before a block adjustment is performed, 
the strips must first be positioned approxi 
mately. In this positioning, a second-degree 
correction for longitudinal curvature should 
be included. This makes it possible to perform 
the block adjustment of planimetry and that 
of heights separately. 
The transformation of planimetrie ground 
coordinates of control points to the axis-of- 
flight system of a strip is rather common 
(see e.g. [82]) but is rather awkward if a 
block adjustment is performed. It can be 
avoided either by using the known param 
eters in the formulas for the initial position 
ing directly in the correction equations and 
applying the polynomial transformations to 
axis-of-flight coordinates [36] or by applying 
a conformal transformation to the coordinates 
obtained after the initial positioning [85, 86]. 
As in the cases of block adjustment of 
photographs and of models, normal equations 
can be formed for the simultaneous adjust 
ment of all strips. The direct solution of the 
equations is here rather simple [85], [87]. Al 
ternatively, the iterative procedure can be 
used in which strip after strip is transformed 
and tie points from overlapping strips are 
used as additional control points [36], [78], 
[85]. The iterative procedure is simpler to 
program than the simultaneous solution but 
it consumes more computer time. With the 
amount of control that is commonly available 
in topographic mapping, as a rule a sufficient 
convergence of the iterative procedure is ob 
tained after about ten iterations of the plani 
metrie adjustment and five iterations of the 
height adjustment [35], [85]. Tewinkel [9] 
and Jacobs [80] even state that after careful 
positioning of the individual strips there is 
often little need for a block adjustment. 
Practice as well as theory have long since 
shown that it is advisable to keep the degrees