It can be said that isometry is a type of projection.
The Royal Spanish Academy ( RAE ) recognizes three meanings of the term isometry . The first of them refers to the equivalence or correspondence of measurements .
In the field of geometry , the idea of isometry refers to the link established by two figures that preserve the distances between the corresponding points . Isometry can be obtained through reflection, rotation or translation.
A figure registers an isometric transformation in a plane when it maintains equality of measurements: that is, the change only implies a modification of position, and not of size or shape. The initial figure and the final figure, therefore, are geometrically congruent and similar.
Isometric transformation requires working with a coordinate system. This type of system allows the movement of a point in any direction, always remaining in the plane in question.
Isometry as a form of projection
Isometry, in this framework, is a form of projection that is usually used in technical drawing to represent to scale. Isometric projection helps to represent a three-dimensional object in two dimensions.
Video games have had a very close relationship with isometry, especially in the era of transition between two-dimensional and three-dimensional graphics. To explain the reasons and the techniques used we must go back to the first titles. Although there are examples of interactive applications from the 1960s that could be considered video games , the largest number of commercial and mass-reaching products came in the 1980s, with a slow start a decade earlier. At that time, characters and objects were drawn with pixels, that is, in two dimensions and in an absolutely static way.
Isometry is used in technical drawing.
Its importance in video games
A graphic made with pixels cannot be deformed infinitely without a loss of quality and definition: that is why when we enlarge or shrink it the result is not very satisfactory. To combat this limitation, vector graphics emerged, which depend on mathematical calculations to join pairs of points and form drawings of varying complexity. The main disadvantage they had was the absence of padding; basically, it was about contours. However, as a benefit it offered the developers of yesteryear to take their first steps in the world of three dimensions.
The vectors led to the creation of basic shapes in three dimensions, calculating their position in three axes, but the lack of textures made the result not so attractive after the initial impact. Let us not forget that the video game industry is largely made up of artists, both writers, illustrators and musicians, and such a hollow and poorly detailed finish was not suitable for giving life to their creations. That's when isometry came into action.
When it was still too early to calculate the deformation of complex, textured three-dimensional objects in real time, some video game developers began creating three-dimensional-looking worlds with two-dimensional resources, that is, with graphics made from pixels. How did they get it? Well, basically there were two ways: create the scenes in three dimensions and "photograph" them, to obtain the drawings in two dimensions; create scenes directly in pixels taking into account this false perspective.
Isometry as muscle contraction
Isometry, on the other hand, is a concept that is used in the field of medicine and physical education to name a muscle contraction that does not cause the muscle to shorten. Isometric contraction , in this way, implies that muscle shortening does not occur: its effect is an increase in tone.
Isometric exercises , in this framework, consist of tensing a muscle and making it remain in the same position, maintaining the tension . These exercises are recommended for those recovering from an injury that had limited range of motion.