Simulation technique

Written with participation of Igor Katrychek katrichek@gmail.com

Projections of the surface in 3-D space onto three projection planes allow the engineer to represent the object being modeled, be it a part or a structure. For this it is necessary to correlate the points on the drawing with points in space. This ability is taught in descriptive geometry lessons. But the resulting idea of ​​the surface tells the engineer nothing about what the object is made of, or about its properties. To represent the part, the surface must be interpreted (interpreted). For this you need to know the standards developed in special areas of activity. Only if the drawing is made in accordance with these standards will other specialists be able to read and interpret it unambiguously. These standards do not relate to the subject of descriptive geometry, they relate to such areas of knowledge as architecture, engineering, material processing technology. Therefore, the first thing to learn is to separate the projections and the interpretation of the projected object.

Exactly the same can be said about projection modeling. The projections of 4-D volume on space and for time allow us to represent a simulated 4-D volume. But for the interpretation of this volume requires knowledge in special areas.

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

I would venture to suggest such a connection: 3-D volume, interpreted as an aircraft structure, is a 3-D volume structure, interpreted as an object plane. Continuing the analogy, we can say that the 3-D volume, treated as a substance, is the substance of a 3-D volume, treated as an object. For example, a heap of sand includes air between the 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 supplement 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 defined the relationship between 3-D volume, treated as an object and 3-D volumes, treated as a substance and as a structure. But what is the relationship between the 3-D volume, treated as a design and the 3-D volume, treated as a substance? In my opinion, only through 3-D volume, treated as an object. Not because such a relationship 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 to link among themselves the 4-D volume, its projections and its interpretations 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 those of the type construction and substance when modeling 3-D volumes.

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