Hey! I discovered a type of problems where we have for example n points and we want to discover the convex hull (the border) using some of those points, but after that calculate the area of the smallest rectangle in which that convex hull can lie inside. I saw that we can rotate the convex hull with some degrees, but I didn't understand it very well. Can anybody give me more details about how to rotate a convex hull with sin and cos, some links eventually. Thanks!

Maybe this should work: For each edge of the convex hull, rotate it so that the edge becomes parallel to x-axis, then draw rectangle with leftmost, rightmost, topmost point and the edge. For the rotation see this: https://vlecomte.github.io/cp-geo.pdf#subsection.2.2.3

Why rectangle with the smallest area will always have an edge parallel to an edge of convex hull?

problem on wiki (see references)

another proof

paper with algorithm

Thank you! This helped me

Hi. Could you please post some problems related to this from online judges?