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Take a point  ξ  on the boundary of a convex body  F  in, near which the boundary is given by an implicit equation. We present some notes on the formula, proposed in Pereira [A directional curvature formula for convex bodies in. J Math Anal Appl. 2022;506(1):125656.], for calculating the curvature of  F  at  ξ  in the direction of its any tangent vector. Namely, we see that our formula is equivalent to the existing one for the curvature of a certain curve given by the intersection of  n −1 implicit equations, but it is easier to apply. Furthermore, we show that when the directional curvature of  F  is positive, there is the directional derivative of the Minkowski functional of the polar set, and we propose a formula to calculate it.

Some notes on directional curvature of a convex body in ℝ n