I have an arc with three known points B(Xb,Yb), C(Xc,Yc), and D(Xd,Yd).B and C are the two endpoints of the arc, and D is a random control point on the arc. Now I need to get the minimum bounding box of this arc.

Please ignore the coordinates and grid points in the chart，arcs may be of any shape.

I am currently writing a C++ geometry library about arc polygons. Obtaining the bounding box of arc polygons is a relatively basic part of it. However, I have little experience in geometry and I was stumped in the first step. Is there any good calculation method? Thanks for your discussion and help.