For Planar Curves, any Point at which the Value of the First Derivative of Curvature with respect to Arc Length is 0 is called the Vertex of the Curve.
For Non-Planar Curves or Space Curves, any Point at which the Value of Torsion is 0 is called the Vertex of the Curve.
The Curve Traced by the Center of Curvatures of all Points of a Curve is called the Evolute of the Curve.