ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note to entry: If ${\displaystyle c\left(s\right)=(x\left(s\right),y\left(s\right),z\left(s\right))}$ is a curve in a 3D Cartesian space (${\displaystyle {\text{E}}^3}$ ), and ${\displaystyle s}$ is the arc length along ${\displaystyle c\left(s\right)}$ , then the unit tangent vector is ${\displaystyle \stackrel{.}{c}\left(s\right)=(\stackrel{.}{x}\left(s\right),\stackrel{.}{y}\left(s\right),\stackrel{.}{z}\left(s\right))}$ , i.e. the derivative of the coordinate values of ${\displaystyle c}$ with respect to ${\displaystyle s}$ . The curvature vector is ${\displaystyle \stackrel{..}{c}\left(s\right)=(\stackrel{..}{x}\left(s\right),\stackrel{..}{y}\left(s\right),\stackrel{..}{z}\left(s\right))}$ . 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)