curvecurve

Curvecurve is not a standard term with a single, agreed definition in mathematics or computer science. In informal usage, it may refer to either a two-parameter family of curves or a curve that lies in the space of curves. In both cases the word emphasizes a layered or higher-order object built from ordinary curves. Context typically clarifies which sense is intended.

In differential geometry and related fields, a two-parameter family of curves can be described by a map F from a parameter domain S × I into a manifold M, where for each s in S the slice t ↦ F(s, t) is a curve in M. Such objects are sometimes discussed in connection with foliations or webs, where a family of curves covers a region in a structured way. The study may involve questions of smoothness, intersection patterns, and integrability.

In computer graphics and geometric modeling, a curvecurve may refer to a data structure or abstraction representing a parametric curve whose defining parameters themselves may vary, such as a curve whose control points are functions of time or another parameter. Operations often include evaluation, derivatives, curvature computation, arc-length parameterization, and rendering. This usage emphasizes practical manipulation and animation of curves within a scene.

Example interpretations include: a two-parameter family F(s, t) of points yielding a surface when t varies; or a parameterized curve γ(s) in the space of curves, where each s selects a distinct curve. The intended meaning is typically determined by the surrounding mathematical or computational context.

See also: curve, parametric curve, space of curves, foliation, web, Bézier curves, B-splines.