eng

### curvature vector <differential geometry>

second derivative of a curve parameterized by arc length, at a point

Note to entry: If `c(s) = (x(s), y(s), z(s))` is a curve in a 3D Cartesian space (`bbb"E"^3`), and `s` is the arc length along `c(s)`, then the unit tangent vector is `dot c(s) = (dot x(s), dot y(s), dot z(s))`, i.e. the derivative of the coordinate values of `c` with respect to `s`. The curvature vector is `ddot c(s) = (ddot x(s), ddot y(s), ddot z(s))`. The curvature vector can be approximated by the inverse of the radius of a circle through any 3 nearby points on the curve (pointed from the curve to towards the centre of the circle)

ORIGIN: ISO/TC 211 Glossary of Terms - English (last updated: 2020-06-02)