⊿ Point. {R} Glossary. ◢ Keyword: C. ◥ University. {q} PhD. {tr} Training. ⚫ UK. ↂ EndNote. ☝️ Weerakkody. Curvilinear coordinates. Coordinate system whose directions vary in space In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved. Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space (R3) are cylindrical and spherical coordinates.
A curvilinear coordinate system may be simpler to use than the Cartesian coordinate system for some applications. Orthogonal curvilinear coordinates in 3 dimensions[edit] Coordinates, basis, and vectors[edit] For now, consider 3-D space. Wherein . .