But at least I would consider trigonometry in this case the easiest solution although I am usually not a big fan of excessive trigonometry usage, e.g., constructing rotation matrices by hand and so on.

Cheers,
Ferdinand

I cannot help you more with the math, as such topics are out of scope of support. There is nothing special about how to construct the vector in our APIs.

You can either rotate a unit vector scaled to length, here assuming that up is the y-axis and alpha the z-axis.

v: c4d.Vector = c4d.Vector(0, length, 0) * c4d.utils.MatrixRotZ(alpha)

Or you can just scale the axis component of the global/local transform of your rectangle which is parallel with your v. I am again assuming that the local up is along y for your rectangle. This only works when the respective axis component is really parallel to v, but I assume that is the case here.

# I operate here in global space, you could also do this locally.
mg: c4d.Matrix = rectangle.GetMg() #The global transform of the rectangle.
j: c4d.Vector = mg.v2.GetNormalized() # Its normalized v2/j/y component, its "y-axis"  
v: c4d.Vector = j * length

# Or in one go
v: c4d.Vector = rectangle.GetMg().v2.GetNormalized() * length

Cheers,
Ferdinand

@ferdinand How would I construct this vector in c4d in python?

Thank you for reaching out to us. This topic is out of scope of support because it is just a math question. I will answer here once, but for follow-up questions you would have to rely on the community.

About your Question

Your question is ambiguous since you tell us what you want, v, but not what you know/have. Your image is also a bit confusing with the red and black rectangle being slightly offset on their local horizontal axis, but I assume that has been done to make the image more readable.

I am going assume that you know the angle of your black rectangle in relation to the ground line and that you know the side length of the black rectangle.

This is then just a simple trigonometric identity. We have a point O which lies on a line ground and the line segment/vector opp originating from it, which is half the side length of your rectangle long. ground and opp form a right triangle with an angle alpha between them. We can therefore use the tangent relation to compute the adjacent adj in this triangle whose length is identical to v.

v is a vector with the length opp/tan(alpha) and the orientation alpha in relation to the ground line.

Cheers,
Ferdinand