how to find what might be called "focal distance", taking the words borrowed from the camera head, the problem is to direct a reference system with origin at the point of view and with the axes passing through the points drain on the projection plane, which is to say a system equally oriented with respect to that object.
consider the reference system or projection plane of the plate, namely the XL and ZL axis of Fig. 4. We translate the measure of this system, bringing about the origin O. YL axis coincides with the optical axis and "pit" the plan at the point P, which is the center of the photographic plate.
summary, the necessary elements are:
1) the center of the 'image
2) at least two pairs of segments that contribute to the escape of the same plan.
As already seen, is not necessary to know a priori the focal length, even though its known true value can be used as an additional check on the calculations. In fact we tried to minimize the necessary a priori, raise the deductible from the image itself.
report back to the fi. 4, to guide a system parallel to the object, we need to bring the optical axis coincides with the y-axis of the system, passing through f. This is equivalent to find two angles, called alpha and beta, which are those vertical and horizontal rotation. The angle beta can be calculated from the D and C legs "of the right triangle. Similarly, we can find the angle alpha, using the catheter, and the hypotenuse of the triangle above, taken this time also as the catheter.
The following subroutine calculates the parameters of orientation of the XYZ system to the plane of projection:
how to find the angles of rotation, we completed the search of the necessary parameters. In order to obtain a perspective view of an object we would need the coordinates of the point of view (which we impose a zero) angles defining the position of the optical axis, and the focal length or magnification of the projected image.
limited to what happens in the plant (Fig. 5), we can claim to know the HL image of a point object and the coordinates on the plate can be considered spatially, adding y as the focal distance d. So, it will coordinate HL XL, d, ZL.
perform a coordinate transformation and refer the point to a system rotated amount of alpha. So we will get the coordinates X2 and Y2. Now consider the similar triangles, which have the hypotenuse formed by the visual ray passing through the actual point of the object and the eye, among them we can impose the ratio between the sides:
X2 Y2 Z2
------ = -------- = -------
If XYZ we arbitrarily fix one of the unknowns, we can find the other two, for example, by setting the X and Y are
Y = X Y2 X2 -----------
Similarly, we find Z, always relying on the same Y
Y Z Y2 = Z2 -----------
In this way we found the spatial coordinates of a point object. Now, to return all the other points, you need to make some points. Arbitrarily imposing a coordinate all we did have to choose one of countless similar objects that may give rise to the same image, then, we have found an object that has the same elements in a certain proportion, directly dependent on the coordinated tax. If we return to another point which we note is the distance from the first, we can calculate the reduced or enlarged scale of the model we have found that, compared to the real.
Point G in Fig. 5 differs only from the point H on the x-axis, lying on a line parallel to the axis X. Then, repeating the above calculations, "borrowing" the Y coordinate of point H, we find other two coordinates of the point G.
In a similar way we can cross the edges of the object of fig.2. The point differs from G only for the Y point and differs from L only for Z, and so on. Hook, that is, one of the coordinates are known constants, we can find other points of the object, this is equivalent to moving along a straight line or along a plane.
Returning to what we said on the photograph of the facade of a building, so we built a method that allows us to give a statement, requiring constant as the coordinate that identifies the plane on which lies the façade.
