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How to find an arbitrarily oriented minimum bounding box in c++

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How do you find bounding box area?

Same way you compute the area of any other rectangle, by multiplying the width by the height.

What are the types of bounding boxes available?

... are five types of bounding boxes, i.e., a surrounding sphere (SS), an axis-aligned bounding box (AABB), an oriented bounding box (OBB), a fixed-direction hull (FDH), and a convex hull (CH) [26].

What is minimum bounding geometry?

In geometry, the minimum or smallest bounding or enclosing box for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie.

What is minimum bounding rectangle in GIS?

The minimum bounding rectangle (MBR), also known as bounding box or envelope, is an expression of the maximum extents of a 2-dimensional object (e.g. point, line, polygon) within its 2-D (x, y) coordinate system, in other words min(x), max(x), min(y), max(y).


So let's say I have a list of N pairs of positive long coordinates (points).
How do I find the smallest rectangle containing all of them?
The rectangle can also have floating coordinates and be rotated in any angle and further shrunk... Not just X, Y, Width and Height!

Just an image I found on the web...

I already know how to find the smallest polygon or not rotated rectangle, but it's not what I need...I wish to know how to find the arbitrarily oriented minimum bounding box.