# Aerial Triangulation Types: Radial Triangulation and Spatial Aerial Triangulation (Especially for GATE-Geospatial 2022)

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Apart from the ground controls, all other types of supplementary planimetric and height controls can be established photogrammetrically by a method called aerial triangulation, using the geometric relationships between successive aerial photographs, by means of which the points so established are tied to the ground control to give them geodetic significance. Therefore, with the use of aerial triangulation, the number of control points determined by ground survey methods is drastically reduced.

## Types of Aerial Triangulation

Essentially, there are two types of aerial triangulation:

- Radial aerial triangulation in which measurements are made on the plane of the photograph itself without considering the third dimension, thus giving rise only to planimetric controls (i.e.. minor control points) as pairs of X՚s- and Y-coordinates; and
- Spatial aerial triangulations in which the three-dimensional stereomodel is reconstructed, usually in an analogue instrument or by computation using an analytical approach, thus capable of giving to both height and planimetric controls (i.e.. X-, Y- and Z-coordinates of a point) .

### Radial Triangulation

This method is based on the so-called radial line assumption which states that angles measured from the principal point in a near-vertical aerial photograph are equal to the angles at the terrain corresponding to the principal point of the photograph. This, in fact, is not true, because, as we have seen in an earlier section, displacements on an aerial photograph taken with a tilted camera axis are radial from the isocentre whilst those caused by the relief are radial from the nadir point. Such an assumption has been found to be responsible for some systematic errors in photo directions which are functions of tilts and the degree of variations of relief in the terrain.

A graphical approach to this method of radial triangulation is quite commonly employed. A mechanical approach called slotted template triangulation is also possible (Plate 2) . A full account of the procedures can be found in any photogrammetry textbooks, e. g. Kilford and Moffitt. Accuracy depends on the relief of the terrain and the amount of tilting present in the aerial photographs.

### Spatial Aerial Triangulation

This is more complex than radial triangulation since the third dimension is also involved. The analogue procedure requires the use of a slightly more sophisticated stereo-photogrammetric instrument equipped with a series of projectors by which stereomodels can be set up one after another so that individual models in one strip are connected together. The setting up of the first model requires proper relative and absolute orientation. Hence, the main principle of spatial aerial triangulation is the transfer of the elements of the orientation of the first model from model to model. The actual procedures involved vary from one type of machine to another. Thus, the aero polygon Method is generally employed for Multiplex-type and universal machines, whilst the Method of Independent Models is favoured for precision or topographic plotter.

Basically, the result from spatial aerial triangulation is a list of coordinates of points of interest in the coordinate system of the first model in a strip. Discrepancies (called ‘cracks’ ) may occur between successive models, which produce greater and greater errors as one model after another is connected. A statistical adjustment has to be carried out to eliminate these discrepancies. The accuracy of aerial triangulation by the method of independent models carried out on topographic plotter is about 0.2m at model scale after adjustment.

An analytical method of spatial aerial triangulation involving the use of the digitiser and the computer is also possible, which considerably speeds up the whole operation.