isometric

Isometric is an adjective from Greek iso ('equal') and metron ('measure'). In mathematics, an isometry is a transformation that preserves distances between points. A map f between metric spaces X and Y is an isometry if d_Y(f(x), f(y)) = d_X(x, y) for all x, y. In Euclidean space common isometries include translations, rotations, reflections, and glide reflections. The composition of isometries is an isometry, and every isometry is a symmetry of space; the set of all isometries forms the Euclidean group.

Isometric projection is a method for drawing three-dimensional objects on a two-dimensional plane in which the three principal axes are equally foreshortened and separated by 120 degrees. Unlike perspective projection, it preserves scale along each axis, so lengths and angles appear consistent along the axes. It is used in technical drawings, computer graphics, and some video games to convey a 3D appearance without vanishing points.

In video games, the term isometric often refers to games that render a 2D grid with an isometric projection to imitate 3D. Classic titles use 2D sprites on a 2D isometric grid; modern engines can render true 3D while maintaining an isometric view. Dimetric and trimetric projections describe variants with unequal foreshortening.

In physiology, isometric (static) exercise describes muscle contractions with constant length, producing force without joint movement. Examples include planks and wall sits. Isometric contractions are distinguished from isotonic or isokinetic training.