Photogrammetry is a technique that allows you to take measurements from the photographic image. Considering that photography represents the effort made by man to memorize in a complete and objective way all that information received by the eye, photogrammetry should represent the easiest way to document the territorial reality. The man performs the photogrammetric survey from the first years of life: every time he has to take an object, he must first detect the position of the object with the simple aid of sight and, judging by the safety with which he brings his hand on the 'object, we must take note of the great precision of the survey performed. A child, when he has to grab a toy, does not always succeed in the relief operation: in fact the first attempts are not successful and he must practice abundantly before succeeding in his intent. Photogrammetry takes advantage of man's ability to make precision measurements of everything he can grasp, putting at his fingertips the three-dimensional photographic image of objects, in the most suitable scale. Therefore, the reasons why such an extremely simple and ergonomic relief technique is so infrequent seem incomprehensible. In the following chapters, these reasons will be carefully examined, but at the basis of all there is the poor cultural preparation of those who should be users of the survey. In this paragraph we will examine the geometric bases on which the photogrammetric technique is based, starting with fixing the following hypotheses:
- any point on the surface of an object emits a beam of light rays;
- theoretically one of these rays, through the camera lens (identified with the projection center), according to a rectilinear trajectory, projects the image of the point on the sensitive surface;
- reversing the projection process (ie imagining to transform the camera into a projector and keeping the position of the sensitive sensitive surface fixed) the image of the point is projected onto the real point;
- repeating the experience with two cameras placed at a certain distance (which we will call "base") the rays, projecting the images of the point, intersect at the same point.
The figure on the following page shows the geometric scheme of what is commonly called "normal case" (adopted by us), in which the sensitive surfaces are coplanar and the optical axes of the objectives are perpendicular to them (therefore parallel to each other) . Just as it is easy to deduce from the figure, taking advantage of the similarity of the triangles determined by the rays projecting the point P, represented on the three reference planes, there is a two-way correspondence between the coordinates (x, y, z) of the same point P and the two pairs of coordinates (x1, z1) and (x2, z2) with which the images P1 and P2 are identified in the reference systems existing on the two frames.
It should be noted immediately that:
- the origin of each of the two systems is at the intersection of the perpendicular from the center of projection to the surface. This point is called "main point" and the relative ray is called "main ray";
- the abscissa (x1 and x2) and ordinate (z1 and z2) axes of the same systems, being the image upside down, are directed respectively to the left and down;
- the distance of the center of projection from the surface of the frame is called the "main distance" and is measured with the precision of the hundredth of a millimeter;
- during projection (restitution), the coordinates (x, y, z) of the intersection point are linear functions of B (base). Basically, if the other variables remain unchanged (C = main distance, x1 = abscissa of the left image point, z1 = ordinate of the left image point, x2 = abscissa of the left image point, z2 = ordinate of the left image point ), the return model has the same scale of representation as the base.