Python: Calculate the 2D area of an object from a 3D projection

Question

Context
I have a object in 3D for which I have the co-ordinates for. I then rotate the object n number of times and I want calculate the 2D area (in nano meteres) of the object, when the object is projected onto a grid.

For example ,
I have an image below which describes my problem. I have the same object but in three different orientations. If i were to project that object onto the grid how would I calculate the area the object occupies in 2D?

My question is
How can I project the object onto a grid (if necessary) and measure the area of the object at that particular orientation? I'm not necessarily looking for code but maybe libraries people can point me to.

Answer 1

If I understand correctly, if your 3d object is convex, then you only need to project it's vertices and take the convex hull of those. The area of the convex hull polygon will be your area.