Python: calculate a 2D area of ​​an object from a 3D projection

Question

Context
I have an object in 3D for which I have coordinates. Then I rotate the object n times, and I want to calculate the 2D area (in nanometers) of the object when the object is projected onto the grid.

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

My question
How can I project an object onto a grid (if necessary) and measure the area of ​​an object in this particular orientation? I'm not necessarily looking for code, but maybe people that people can do with me.

Answer 1

If I understand correctly, if your 3D object is convex, you only need to design its vertices and take the convex hull from them. The convex hull polygon area will be your area.