If I have a 2D shape on a plane embedded in 3D cartesian space and I know the area of that shape. I would like to calculate the area of the projection of that shape when viewed with an orthogonal camera at a certain angle (angle 0 meaning viewing right from the direction of the surface normal, so the projected area equals the actual area).
Intuitively I'd guess it will be actual area * cos(angle), but I'm not sure whether that's correct
You are correct. Assume that you have the plane of the shape and the plane of the camera. If they are parallel, then the projection will be the same size as the original. If they are not parallel, it means that the two planes intersect along a line. Lines in the plane of the shape that are parallel to the direction of the intersection have the same length in the projection on the camera plane. Lines that are perpendicular are scaled by $\cos\theta$, where $\theta$ is the angle between normals to the two planes. You can divide your original shape into rectangles with one side parallel to the intersection, the other perpendicular to it. Then you scale only one side by $\cos\theta$, so the area scales by that factor.
