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 arc length along ${\displaystyle c}$ , then the tangent is ${\displaystyle \overrightarrow{\tau }\left(s\right)=\stackrel{.}{c}\left(s\right)=(\stackrel{.}{x}\left(s\right),\stackrel{.}{y}\left(s\right),\stackrel{.}{z}\left(s\right))}$ , i.e. the derivative of the coordinate values of ${\displaystyle c}$ with respect to ${\displaystyle s}$ . The curvature vector is ${\displaystyle \kappa \left(s\right)=\stackrel{..}{c}\left(s\right)=(\stackrel{..}{x}\left(s\right),\stackrel{..}{y}\left(s\right),\stackrel{..}{z}\left(s\right))}$ .