spinshaped

Spinshaped is a term used in some mathematical art and differential geometry contexts to describe a class of shapes generated by applying a spin transformation to a base curve or surface. The core idea is to produce forms whose geometry arises from rotating or twisting a starting shape as one moves along a second parameter, often with additional radial scaling or modulation. The result is a family of curves and surfaces that commonly exhibit spiral, rosette, or petal-like features.

Construction and basic idea can be described in simple terms. Start with a base curve or surface in three-dimensional space. A spin transformation then rotates each point around a chosen axis by an angle that may vary along the curve or with another parameter. In planar variants, the spin can be viewed as modulating the angular component while allowing the radial component to change through a function, producing patterns such as spirals and flower-like outlines. In 3D, applying a rotating frame along a second parameter yields surfaces that twist around an axis, often creating toroidal, helical, or coiled geometries depending on the modulation.

Properties and applications. Spinshaped objects typically inherit symmetries from the spin function and axis of rotation; they can form self-intersecting figures or smooth, embedded shapes depending on how the spin is defined. They appear in generative art, algorithmic design, and educational demonstrations of rotation groups and polar or cylindrical coordinates. Because the term is used informally in various communities, definitions and specifics can vary between contexts.