This should be a simple matter, but for some reason I can't grasp it.
I have a parallelogram, defined as four points (in anti-clockwise order, but apart from that I do not know which corner is which). I also have the center point of the parallelogram, and it's orientation (the angle it if "facing"). What I want to get is the midpoint of the line at the "front" of the parallelogram.
To do this, I imagine I would have to trace a ray from the midpoint, at the angle the parallelogram is facing, and check which of the four lines it intersects and where. This is where I'm stuck. I can't figure out a formula to achieve this goal. Any ideas?
I am coding in C#, but this is a math problem more than anything, so I'll accept a formula or psuedocode.
EDIT: It seems there has been a bit if confusion in my problem; apologies for that. I should have specified that I'm working with two dimensions, and the "front" is defined as the line on the parallelogram that intersects the ray generated by casting from the midpoint, at the angle provided (to the origin). As suggested in the comments, here is a diagram:
The orange points represent the corners of the parallelogram, the blue point is the centroid, and the yellow curve is the angle I am given. The purple line is simply parallel to the X-axis to help represent the angle. The grey line extending from the blue point is (a subsection of) the ray I mentioned previously, and thus the green point is the point I wish to calculate. Please also note that this diagram is just a sketch to help visualize the problem, and not generated by my program.
Hopefully this helps clear up any confusion.