Translation (geometry) of the object. The translation vector formula_8 common to all points of the object describes a particular type of displacement of the object, usually called a "linear" displacement to distinguish it from displacements involving rotation, called "angular" displacements. When considering spacetime, a change of time coordinate is considered to be a translation. For example, the Galilean group and the Poincaré group include translations with respect to time. Translation (geometry) In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction. In Euclidean geometry a
Glossary of Riemannian and metric geometry each simplex with induced metric is isometric to a simplex in Euclidean space. Principal curvature is the maximum and minimum normal curvatures at a point on a surface. Principal direction is the direction of the principal curvatures. Path isometry Proper metric space is a metric space in which every closed ball is compact. Every proper metric space is complete. Quasigeodesic has two meanings; here we give the most common. A map formula_29 (where formula_30 is a subsegment) is called a "quasigeodesic" if there are constants formula_31 and formula_32 such that for every formula_33 Note that a quasigeodesic is not necessarily