Quadrilateral Perspective


In his treatise on painting, dated 1435, Alberti developed the perspective explaining that the light rays reflecting from the object to the eye form a cone. If we intercept this cone using a transparent square at a certain distance from our eyes, we will be able to outline the image of the object observed in it. This central linear perspective studied by Alberti and by the 15th century renaissance painters has a vanishing point to where all the drawing lines referring to the depth converge.

This mechanically performed type of perspective lacks mathematical precision and has not experienced any innovation; therefore, it has not improved throughout the past centuries.

The oblique perspective was a consequence of the architectonic development that occurred in the 20th century. It presents an image seen from a sharp corner, resulting in two opposed lateral vanishing points. It is a conic projection inside a system – Theory of Projections, which is mathematically precise. This type of perspective adapts itself almost totally to architectonic projects, but does not apply to other types of drawings that require a simpler making of but can not do without the mathematical precision. For example, decorators, landscape architects, scenographers, plastic artists, advertising professionals, etc.

The projection of a ground plan, with which the architects work, besides demanding a hard work is almost totally adaptable to building and house façades works (exterior projects).

Sometimes, the difficulties we face in our practice hinder the complete fulfillment of our performance. The documents left by our predecessors and that served as basis for our studies are not always exempt from doubts or questions. When we acquire our knowledge at school, reading books or through professionals, who perform the task right before us, we have to be inquisitive, otherwise there will be no possibility of improving the knowledge relayed.

We will stagnate and so will our professional work.

Every human being has the right to express his ideas and opinions, even under the risk of having them not accepted after being proved and examined.

This fact should not concern learned people, they should be concerned with the alienation and disregard for the novelties introduced by people who believe they are learned.

It is interesting to notice that sometimes, the creative and innovative solution for a problem lies in a new association of already existing elements.

The new perspective treatise introduced hereby is revolutionary and has a worldwide impact because it was developed based on a NEW BASIC CONCEPT which I had the privilege of finding out by making a new combination of the already existing elements.

This knowledge was “hidden” in books that I randomly bought in the city bookstores. With this knowledge plus the knowledge acquired in the routine skills of the work I managed to give life to imagination and get at the creation of a new exact perspective measured in millimeters.

The fundamental idea occurred to me as a result of my exhaustive search for a way to represent the plane on shortening scale (scorcio), without using the conic projection system to draw the oblique perspective.

The new system of remaking the vertical plane in three dimensions that I discovered has completely solved the perspective problems. The system frees the perspective, therefore, one can draw with mathematical precision in any type of perspective: parallel, oblique and aerial with 1, 2 and 3 vanishing points respectively. It has also allowed the creation of other types of perspective which I called aerial parallel perspective (2 vanishing points) and integrated perspective (5 vanishing points).

I created geometric structures for the perspective types, according to which one can draw anything in millimeters, at any height of the horizon line and with mathematical precision. Without calculations or mathematical formulas, the work is mechanically performed using only lines and several points as inherent to the perspective work.

All drawings, including those of the aerial views are made on open angles, presenting an ample and complete view, as our eyes are used to have in real world.

This new perspective system allows not only to make architectonic drawings but also any other type of drawing. The aspect of the system in millimeters dominates the three measurements relative to the three-dimensional space completely: height, width and length or depth. The latter has always been the perspective great incognito in the current systems.


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