In the geometry of planar
curves, a
vertex is a point of where the first derivative of
curvature is zero. This is typically a local
maximum or minimum of curvature, and some authors define a vertex to be more specifically a local extreme point of curvature. However, other special cases may occur, for instance when the second derivative is also zero, or when the curvature is constant. For space curves, on the other hand, a
vertex is a point where the
torsion vanishes.