Normal Section

Let $M\subset\Bbb{R}^3$ be a Regular Surface and ${\bf u}_{\bf p}$ a unit Tangent Vector to $M$, and let $\Pi({\bf u}_{\bf p},{\bf N}({\bf p}))$ be the Plane determined by ${\bf u}_{\bf p}$ and the normal to the surface ${\bf N}({\bf p})$. Then the normal section of $M$ is defined as the intersection of $\Pi({\bf u}_{\bf p},{\bf N}({\bf p}))$ and $M$.

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 271, 1993.