krümft

Krümft is a term used in differential geometry and computer graphics to describe a class of surfaces characterized by recurring folds or wrinkles that balance regions of positive and negative curvature. The word is derived from a Germanic root likened to crumpling, reflecting its association with creased, crinkled forms.

In geometric terms, a krümft surface exhibits a curvature distribution in which convex and concave regions appear in a patterned arrangement, and the magnitude and location of curvature changes are regulated by a small set of parameters.

A practical way to quantify krümft is through the krümft index, a scalar describing the average discrepancy between the principal curvatures over the surface, or via a curvature map that reveals alternating signs at multiple scales.

Construction methods rely on procedural rules or patch-based tiling that place folds with controlled angles and spacings, enabling stylized surfaces for rendering, terrain generation, or material simulations.

Krümft has appeared in academic discussions and software documentation as a niche concept within geometry and graphics. It remains less standardized than related ideas such as wrinkling or crumpling, with definitions varying by context.

See also: curvature, Gaussian curvature, wrinkling, crumpling, mesh generation.