figuren8

Figuren8 is a term used in mathematics and digital media to denote a family of figure-eight shaped curves and the software framework that manipulates them. The name combines "figure eight" with the stylized numeral eight, signaling both the geometric form and its typical use in animation and geometry tools.

In mathematics, figuren8 refers to parametric curves that trace a self-intersecting, looping path reminiscent of an eight. Common realizations include the lemniscate of Bernoulli, the Lemniscate of Gerono, and generalized eight-figure curves produced by combining circular or elliptic components. These curves are studied for properties such as arc length, curvature, and smooth traversal.

Figuren8 also denotes a software toolkit designed to generate, render, and animate figure-eight trajectories in two or three dimensions. It provides libraries of parametric equations, a rendering backend, and animation utilities for speed control, interpolation, and export to common formats. The framework is used by graphic designers, educators, and researchers to create looping motion patterns and simulations.

Since its initial release in the late 2000s, figuren8 has seen use across motion design, classroom demonstrations of curve theory, and robotics path planning where eight-shaped patterns offer coverage or sensing advantages.

See also: figure-eight knot, lemniscate, parametric curve, eight-figure.