Vertex (curve)

In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero.^[1] This is typically a local maximum or minimum of curvature,^[2] and some authors define a vertex to be more specifically a local extremum of curvature.^[3] 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.