What follows is an unpublished writings, dating back to the now distant year of 1987 on a program for processing of the calculations by computer for the refund of perspective, today also called inverse perspective or "reverse perspective". The computer in question was an Apple Macintosh, one of them a phone, the display is small and gray, and the programming language was Basic 2.0 Microsoft (!).
Let's go back in time (23 years) and read as "a return perspective" by the method of "vanishing points".
"Returning Perspective" - \u200b\u200bRoberto Angeletti
March 26, 1987 The return of perspective could be seen as the inverse of the perspective. In essence, it is assumed that, by reproducing a picture in central projection of any object, whether it is a perspective drawing or photograph, you can extrapolate from this in some way the real distances or and proportions of the three-dimensional reality of the object. But what seems obvious, is not to be a more accurate analysis, in fact, is a mere hypothesis that a single image contains the information necessary and sufficient to reproduce the object represented in its space. This
imagine that our brains as a real object, and the shape that gives it, is only the result of a series of comparisons with models, or "shape", stored in memory by looking at the picture in Fig. 1, we compare it with the millions of visual information that we have in mind, and found that more similar, we decided that the series of signs that we see "are similar" to a box that casts a shadow over two areas next to it. This becomes key to sustained a conviction so strong that even reversing the design, many still see as a volume that is on the left, even if the information of the shadow should suggest otherwise.
The now famous experiment Ames Distorted Room and the illustrations of MC Escher shows us beyond any doubt, if there ever was one, that from an image perspective can also return the object that is not, or even can not understand shape of the object. It is fitting, therefore, decompose the problem in an analytical way.
An "image" can be defined as the locus of the intersections between the projective plane and the lines passing through the eye and the elements of the object.
For further reflects a single image objects of infinite forms. Choosing a form, are always infinite objects, this time all similar to each other, with that, the same proportions but different sizes. The object represented may in fact be small and close, or enormously large and distant. So to get back with a chart or an analytic method, an image from the spatial coordinates of the object, it is absolutely necessary to know some "conditions", we might call "quality" of the object. To be more explicit, we have approximated the object to a box or a series of boxes, of which we know, if not the true measure of the edges, at least the attitude of each other's faces.
Returning to the example of Fig. 1, assume that things are true of the object:
1) it is a box that casts a shadow on two portions arranged pano L-shaped.
2) the box and the element formed by two straight portions of the plan are common.
willing and able, at this point, you know the size of the object. Since un'assonometria, immediate guess is a system that allows us to "measure" the object image, just a ruler to realize that the vertical face disposed toward us along the horizontal side has 1 / 3 of the other side. By comparison, we realize immediately that the L-shaped vertical element is identical to the front of the box. As for the face that has its shadow, things could be more complex, but assuming that it is an isometric projection isometric, we find that the face is identical to the other side, although the isometric deformation. A similar thing happens to the sides, we discover to be two squares.
So far everything is clear. But what if, instead of an isometric projection, we had a square-angled perspective? In this case we could not take it for the attitude implicit in the projection plane to the object, but it should somehow rise.
We see fig. 2: the object is represented here in a vanishing point perspective in the context inclined, with three vanishing points. And 'well-known that the vanishing point is defined as the locus where all the converging lines passing through the object edges parallel. Essentially, we care about the signers turned to the right, forwards and upwards, and thus refer to a left-handed Cartesian system, we use the words "leaks x, y, z".
An analytical method to find the vanishing points may be to develop a system of equations of the lines they belong to two of the signers who compete for the same flight, using the coordinates of the points of beginning and end of segments.
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