4.14.1.3. Analytical aerial triangulation

Graphical radial triangulation is performed with simple instruments, such as mirror stereoscope, a ruler, a pencil and a tracing sheet. The steps are given below:

1. The photographs are laid out in strips and all GCPs are identified on the photographs and their numbers marked on the photographs.
2. The principal point is obtained for each photograph. The principal points are then stereoscopically transferred to the adjoining photographs as conjugate principal points.
3. Now two points, called minor control points (MCPs), also called pass points or wing points, are selected on both sides of the principal point of photo, fulfilling the following conditions: a. The two points should be as nearly at the same elevation as the principal point. b. The points should be at a distance from the principal point, which is equal to twice the mean base of the adjoining photographs. c. The points should lie approximately on the bisector of the base angle on either side, and d. The point should serve as lateral point as well.
4. The MCPs are selected and transferred stereoscopically to adjoining photographs.
5. The lateral control points (LCPs) are selected in the centre of lateral overlaps of adjacent strips to serve as connecting points between different the strips. These LCPs are selected at least at the beginning and the end of the strip and on every third photo of the strip. These are then stereoscopically transferred to photographs of adjoining strips.
6. The radial directions from the principal point to all minor control, lateral control and ground control points appearing on the photograph are drawn, through the points.

In graphical radial triangulation, we begin by laying out photographs in strips and identifying Ground Control Points (GCPs), which are key reference points. Next, we determine the principal point for each photograph, which is essentially the focal center. This principal point is then transferred between photographs for consistency. We also establish two MCPs near this principal point, ensuring they are nearly the same height as the principal and spaced according to certain criteria. Additionally, we select LCPs that connect adjacent strips. Finally, we draw radial lines from the principal point to all control points on each photo, which aids in creating accurate spatial relationships between the images.

Imagine you're piecing together a big puzzle. Each photograph represents a puzzle piece. Just as you would start by identifying the corner pieces (the GCPs), you need to identify these key points on your images. The principal point acts like the center of the puzzle, guiding where other pieces should go. When you choose your points carefully, like ensuring they are at the same height and properly spaced, it's similar to ensuring your puzzle pieces fit together nicely. Drawing lines to connect points is like marking paths between similar pieces to help complete the picture.

Due to elevation differences of terrain and variations in the flying height of aircraft, the scale of photographs generally varies considerably. The photographs of a strip are required to be brought to a common scale through graphical triangulation. The plot of the strip where all the photographs, having uniform scale, are fixed in their correct relative position is called as MCP.

Different elevations of terrain and flying heights can cause variations in the scale of aerial photographs, making it essential to standardize them to a common scale. This is done through graphical triangulation, which helps to align the photographs uniformly. The resulting plot, which maintains this consistency across all images, is known as the Minor Control Plot (MCP). This process ensures that measurements taken from the photographs remain accurate and representative of the actual distances.

Think of it as adjusting the volume on several different audio speakers. Each speaker might have varying output levels, similar to how photographs might have different scales due to elevation. To create a balanced sound (or accurate representation), you adjust each speaker until they all operate at the same level. In aerial photography, this adjustment is crucial for ensuring that when you look at the combined images, everything fits together harmoniously.

Each strip is plotted on a transparent sheet to facilitate the drawing. The photographs are laid out in their correct relative directions so that the plotting is carried out in the right direction. With the first photograph in position below the tracing sheet, principal point base is transferred. The base line is extended up to the edge of the photograph on either side. The position of principal points of the first photograph and one of the two adjacent photographs is then transferred on the tracing sheet. The radial directions to all the points appearing on the photograph are also drawn.

Once the photographs are arranged correctly, each strip is plotted on a transparent sheet, which allows for easier and more accurate drawing of reference lines. The process begins with placing the first photograph and transferring the principal point to the tracing sheet. This establishes a base line that will be extended further to include adjacent photographs. By doing this, you ensure that all parts of the photographs are represented accurately and in their true orientation before further measurements and adjustments are made.

Envision laying a piece of fabric down to cut a pattern; you want the fabric to lay flat without wrinkles to ensure that your cutting is precise. In this case, laying down each photograph on the transparent sheet is akin to making sure that fabric is smooth and correctly oriented. Just as the pattern pieces must align with the fabric, the photographs must line up accurately before any adjustments or cutting (measuring) take place.

The scaling is then carried out by plotting the actual distance AB between the two ground control points, between which the scaling is to be done, on a straight line drawn on a separate sheet. A semicircle is drawn taking B′ as centre and distance BB′ as radius. The scaled position of any other point C′ on minor control plot is obtained by coinciding A′ with A and C′ falling on the line AB.

To scale the photographs accurately, you first determine the actual distance between two known ground control points (A and B). A straight line represents this, and a semicircle is drawn from one of these points to help locate other points on the plot. By aligning points correctly, you ensure that all features in the photo match their real-world locations accurately. This process is crucial in ensuring that the scaled positions of points derived from the minor control plots are consistent with ground reality.

Consider trying to create a scale model of a building. You'd start with measurements of the foundation (the distance AB), and then use those dimensions to map out the entire structure accurately. Just like you’d use a compass to ensure your angles are right, the semicircle helps maintain the correct relationship between points in the photography process, ensuring every feature is proportionally accurate as you work from a small model to reality.

After scaling all the points of minor control plots, these points are pricked through the tracing sheet. The positions of principal points, minor control points and lateral control points of all the strips are likewise pricked on the graph sheet and adjusted so that all ground control points fall over their plotted positions and lateral control points give positions of least error.

Once all points are scaled, they are marked (or pricked) through the tracing sheet, creating reference points on the graph sheet. This helps to closely align every control point on the maps to their actual positions. The adjustments made ensure minimal errors between the measurements taken in the photographs and the actual ground locations, making the outputs more reliable and accurate for analysis and mapping.

It's similar to creating a pointillist painting where each dot (control point) has to be carefully placed to create an overall image. Just like in painting, you may step back to see how well the image comes together, you need to make sure each of those points is accurately placed to reflect what you see in real life. This fine-tuning ensures that when you look at the final output, it reflects the actual landscape correctly, without significant discrepancies.

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