Projection Modeling Technique

Modeling technique

Written with the participation of Igor Katrichek [email protected]

Projections of the surface in 3-D space on three projection planes allow the engineer to represent the simulated object, whether it be a part or a structure. To do this, correlate the points in the drawing with the points in space. This skill is taught in descriptive geometry lessons. But the idea of ​​the surface obtained as a result of this does not tell the engineer anything about what the object is made of, nor about its properties. To represent the detail, the surface must be interpreted (interpreted). To do this, you need to know the standards developed in special areas of activity. Only if the drawing is made in accordance with these standards, it can be read and unequivocally interpreted by other specialists. These standards do not apply to the subject of descriptive geometry; they relate to such fields of knowledge as architecture, mechanical engineering, material processing technology. Therefore, the first thing to learn to do is to separate the projection and interpretation of the projected object.

Exactly the same can be said about projection modeling. Projections of 4-D volume on space and time allow us to present a simulated 4-D volume. But the interpretation of this volume requires knowledge in special fields.

There is another important detail that is often forgotten. Suppose that there is a task: to build a drawing of the aircraft. To perform it correctly, it is necessary to clarify: do you need a model of an airplane as a whole object, or an airplane as a structure? Different 3-D volumes will be projected depending on the answer. For example, in an airplane as a whole, the air inside is part of the airplane, and if you consider the design, this volume will disappear from the model.

I will venture to suggest the following connection: the 3-D volume, interpreted as the design of the aircraft, is the design of the 3-D volume, interpreted as the aircraft-object. Continuing the analogy, we can say that the 3-D volume, treated as a substance, is the substance of the 3-D volume, treated as an object. For example, a heap of sand includes air between grains of sand, while a heap of sand as a substance consisting of grains of sand does not include this air. If we want to add the volume occupied by grains of sand to the volume occupied by the heap, we need to add the volume occupied by air. Perhaps this will not be enough, because the sum of the parts of the structure is not the result of the synthesis of these parts into a single whole.

We have identified the relationship between the 3-D volume treated as an object and the 3-D volume treated as a substance and as a structure. But what is the relationship between the 3-D volume treated as a construction and the 3-D volume treated as a substance? In my opinion, only after a 3-D volume, treated as an object. Not because such a connection cannot be invented, but because it cannot be imagined. And, since we agreed to consider only those representations that are created by man, we exclude such a connection from the model.

So the task to be solved is:

1. It is necessary to learn how to link the 4-D volume, its projection and its interpretation so that there is consistency between them.

   
   
2. It is necessary to learn how to connect 4-D volumes with bonds that are similar to bonds of the construction and substance type when modeling 3-D volumes.

How these tasks will be solved, I will tell in the following articles.