Intrinsic equation

In geometry, an intrinsic equation of a curve is an equation that defines the curve using a relation between the curve's intrinsic properties, that is, properties that do not depend on the location and possibly the orientation of the curve. Therefore an intrinsic equation defines the shape of the curve without specifying its position relative to an arbitrarily defined coordinate system.

The intrinsic quantities used most often are arc length ${\displaystyle s}$, tangential angle ${\displaystyle \theta }$, curvature ${\displaystyle \kappa }$ or radius of curvature, and, for 3-dimensional curves, torsion ${\displaystyle \tau }$. Specifically:

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