The descriptive geometry It is one of the fundamental disciplines of engineering education, where spatial figures are studied for their projection images.
Descriptive geometry methods allow solve mathematical problems graphically With a high degree of precision. In art, architecture and construction, the projection method allows you to obtain visual images of the created objects.
The problems of descriptive geometry are solved graphically. Knowing the basic rules and theorems allows you to solve complex problems by dividing the process of solving them into a series of elementary operations of the same type.
The fundamental operation that must be performed in the resolution process is to determine the point of intersection of two lines.
The descriptive geometry It is one of the best means to develop a person’s spatial imagination, logical thinking, without which it is difficult to imagine any engineering work.
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What are the principles of descriptive geometry?
In descriptive geometry, there are basic problems, without mastering that it is impossible to study the subject further. This is the construction of orthogonal projections of points and surfaces, the definition of traces of lines and planes.
The metric problems they are those in which it is required to determine the real values of the values of flat figures, angles, segments, distances or construct geometric objects of a given size.
In the general case, the geometric figures they are located arbitrarily with respect to the projection planes and are projected onto these planes with distortion of their linear and angular values.
To determine the natural size of any flat figure, you must move to a position where it is parallel to one of the projection planes.
Positional problems are those in which it is required to determine the relative position of geometric objects: draw a line from its intersection or determine if a point belongs to a certain figure.
Several auxiliary surfaces are usually used to solve positional problems. They are chosen in such a way that they intersect with the figures given along lines that are easy to construct, for example, along straight lines and circles.
Possession of projection transformation methods It allows you to analyze independently and greatly simplify the solution of many problems.
Who established the principles of descriptive geometry?
Science originated at the end of the 18th century thanks to French mathematician Gaspard Monge in 1760-1770, when as a teacher at the Mezieres School of Engineering he was given the difficult task of calculating the relief of fortifications.
It is closely related to the theory of shadows and the method of axonometric projections.
The topic of descriptive geometry is the presentation and justification of the methods of image and construction of three-dimensional objects in the two-dimensional plane of the drawing and the methods to solve geometric nature problems (drawing) with these images.
Images constructed according to the descriptive geometry rules allow you to:
- Imagine the shape of the objects.
- Determine precisely their relative position and conjugation in space.
- Determine its true size.
- Explore the geometric properties of objects.
Descriptive geometry is the theoretical basis for implementation practice of technical drawings, ensuring its expressiveness and precision. And, consequently, the possibility of adequate manufacturing according to the drawings of real parts and structures.
What is the purpose of descriptive geometry?
The descriptive geometry it’s called science which is the theoretical basis of the drawing. In this science, the methods of image in the plane of several bodies and their elements are studied.
These images allow you to uniquely determine the shape and size of the product and do it. When working with drawings, two types of work are done: preparation of drawings and their reading.
To read a drawing is to reproduce in the mind the real form of the object and some of its parts using the drawing. Descriptive geometry is based on the projection method.
The main objective of this discipline is the development of methods to represent geometric shapes on one plane or another surface and its subsequent problem solving application.
The basic purpose of descriptive geometry is the unequivocal reproduction of spatial figures in a plane.
This process and its effects are called projection. Unlike theoretical geometry, it has been used in many fields of technology. A technical drawing, both freehand and machine, uses its achievements.
It is currently being replaced by computer images (computer-aided design and ray tracing systems).
Many universities are withdrawing the descriptive geometry of the curriculum in most fields, except those closely related to design (architecture, construction, geodesy).
However, subject teachers believe that descriptive geometry is useful because it develops the imagination.
Why is descriptive geometry studied in graphic design?
The purpose of studying descriptive geometry is to develop the spatial representation of students, geometric thinking, the ability to analyze the shapes, sizes and relative positions of space objects based on their projection models.
Descriptive geometry studies methods for map space objects three-dimensional in a plane and methods to graphically solve positional and metric problems associated with these objects using their flat mappings (models).
The simplest object (element) in space is a point. The points can be proper and improper (infinitely remote). In the model, the arrow will indicate the direction to an incorrect point.
All other geometric objects (line, plane, surface) can imagine so many points. To model three-dimensional space objects, we will use the projection operation.
It is an engineering discipline that represents a two-dimensional geometric apparatus and a set of algorithms to study the properties of geometric objects.
The geometry almost descriptive it is limited to the study of three-dimensional Euclidean space objects. The source data must be presented in the form of two independent projections.
Most tasks and algorithms use two orthogonal projections in planes perpendicular to each other.
Nowadays, discipline has no practical value due to the development of computer technology and the linear algebra apparatus.
But it is probably indispensable as a component of general engineering education in engineering and construction specialties.
The descriptive geometry is a science which studies spatial figures through the projection (placement) of perpendicular to about three planes, which are then considered combined with each other.