curvilinear

Curvilinear is an adjective describing something formed from or bounded by curved lines rather than straight ones. Etymologically, it combines Latin curvus “bent” with linea “line.”

In geometry and related fields, a curvilinear path or line follows a curve. Curvilinear coordinates are coordinate systems in which the coordinate lines are curves; they are used to describe complex shapes and motions where Cartesian coordinates are inconvenient. Classic examples include polar coordinates in two dimensions (r, theta) and their three-dimensional counterparts like cylindrical (rho, phi, z) and spherical (r, theta, phi) coordinates.

In statistics, a curvilinear relationship is a non-linear association between variables that cannot be adequately captured by a straight line; modeling often involves polynomial, spline, or other nonparametric methods under the umbrella of nonlinear or curvilinear regression.

In design and applied fields, curvilinear forms are common in art, architecture, and biology to describe objects with smooth, curved outlines. The term also appears in technical contexts, such as curvilinear ultrasound transducer arrays, which use a curved surface to expand the field of view. Overall, curvilinear conveys the presence of curves as opposed to linearity.