Isometry
Introduction
An isometric projection is a method of graphic representation, more specifically an axonometric[1] cylindrical[2] orthogonal one.[3] It constitutes a visual representation of a three-dimensional object that is reduced in two dimensions, in which the three main orthogonal axes, when projected, form angles of 120°, and the dimensions parallel to said axes are measured on the same scale.
The term isometric comes from the Greek language: "equal to time", and from Spanish "equal measurement" since the measurement scale is the same in the three main axes (x, y, z).
Isometry is one of the forms of projection used in technical drawing that has the advantage of allowing representation to scale, and the disadvantage of not reflecting the apparent decrease in size - proportional to the distance - perceived by the human eye.
History
First formalized in 1822 by Professor William Farish "William Farish (chemist)") (1759-1837), the concept of isometry had existed in more or less approximate empirical form for centuries before.[5][6]From the middle of the century, isometry became an 'invaluable tool for engineers, and soon after axonometry and isometry were incorporated into the curriculum of training courses of architecture in Europe and the USA."[7] According to Jan Krikke (2000),[8] however, "axonometry originated in China. Its function in Chinese art was similar to that of linear perspective in European art. Axonometry, and the pictorial grammar that goes with it, has taken on new significance with the advent of visual computing.
Like all types of parallel projection, objects drawn with isometric projection do not appear larger or smaller as they move farther or closer to the viewer. While it is advantageous for architectural drawings, in which measurements must be taken directly, the result is a distortion of perception, since unlike perspective projection, it is not how human vision or photography normally works. It can also easily lead to situations where depth and height are difficult to measure, as shown in the image to the right. This may seem paradoxical or create impossible shapes, such as the Penrose staircase.
Display
Isometry determines a viewing direction in which the projection of the coordinate axes , , make up the same angle, that is, 120° relative to each other. Objects are displayed with a 30° viewpoint rotation in the three main directions (x, y, z).