Technical Drawing and Geometric Representation Systems

Geometric Transformations and Symmetry

Translation consists of moving all vertices in a straight direction at the same distance. Rotation consists of turning all vertices in a circular sense with the same amplitude around any center point O. Triangulation consists of decomposing a surface into triangles and tracing them back. This is possible because the triangle is the simplest polygon and can be copied in a simple manner.

Types of Symmetry

Symmetry is the relationship between two figures where each point in the first corresponds to another in the second. There are several types:

• Axial symmetry: Establishes two points on an axis perpendicular to the symmetry of the first.
• Central symmetry: Two points on the first are symmetrical when they pass through a center point and are in opposite positions.
• Bilateral symmetry: Two symmetrical points are on each side of a plane and are equidistant from the axis of symmetry.

Similarity and Scaling

Similarity is the relationship between figures where the corresponding angles are equal and the sides are proportional. Vertex radiation is a procedure where two figures share a common vertex. Exterior from a point changes the situation from the same point to build the vertices of the similar figure.

Scale is the relationship between the length of a segment and its natural length in reality. There are reduction and enlargement scales.

Modular Structures and Grids

Modular structures are geometric grids that allow relating equal or similar figures called modules.

• Simple modular grids: These are formed by the repetition of a single figure (square, triangular, rectangular, or irregular shapes).
• Composite modular grids: These are formed by the juxtaposition of several regular geometric figures or the superposition of two.

Representation Systems

The Dihedric System

The Dihedric System is a representation system using orthogonal cylindrical projection, where the projecting lines are rays perpendicular to the screening plane. It uses two planes of projection: vertical and horizontal.

The ground line is the intersection of both planes and is represented with two small segments. The vertical distance from a point to the horizontal plane is called elevation, and the horizontal distance to the vertical plane is called depth.

Dimensioning Standards

The principal dimensioning standards are: UNE (Spain), DIN (Germany), ASA (USA), and the ISO (International).

Axonometric System and Perspective

The Axonometric System is an orthogonal cylindrical representation system. It is classified as:

• Isometric: All three angles are equal.
• Dimetric: Two angles are equal and one is unequal.
• Trimetric: All three angles are unequal.

Isometric perspective is used to represent a figure from its views. In Cavalier perspective, the X and Z axes are at 90°, and the Y axis is at a free angle of 135°. Measurements on the Y axis are subject to a reduction coefficient to imitate perspective.