A curve in the plane is determined, up to orientation-preserving Euclidean motions, by its curvature function, $\kappa(s)$. Here is one of my favorite examples, from Alfred Gray's book, Modern
CS 15-458/858: Discrete Differential Geometry – CARNEGIE MELLON
Principal curvature - Wikipedia
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry
dg.differential geometry - Sectional curvature and Gauss curvature
Curvature and normal curvature at a point on a curve on a surface
Curves and Surfaces: Second Edition
Geodesics, geodesic curvature, geodesic parallels, geodesic
Visual Differential Geometry & Forms
Differential Geometry: Lecture 21 part 2: total Gaussian curvature