Turn x,y angles into vector

Question

I have a direction defined by two angles alpha and beta which I need to convert to a vector of length 1.

alpha and beta define the angle between the z-axis and the projection of the desired vector on the x,z-plane (or y,z-plane respectively). Please see the below image for illustration.

Note the difference to ordinary spherical coordinates, where alpha is the angle between the desired vector and the z-axis and beta describes the rotation of the vector around the z-axis.

My python implementation below is pretty close to the solution posted here, but it does not quite return the expected results:

from math import sin,cos,sqrt

def get_vector(alpha,beta):
    alpha=alpha/180*pi
    beta=beta/180*pi
    x=sin(alpha)*cos(beta)
    z=cos(alpha)*cos(beta)
    y=sin(beta)
    l=sqrt(x**2+y**2+z**2)
    target_vector=[round(x/l,3),round(y/l,3),round(z/l,3)]
    return target_vector

print((90,0)," -> ",get_vector(90,0))
print((-90,0)," -> ",get_vector(-90,0))
print((0,90)," -> ",get_vector(0,90))
print((0,-90)," -> ",get_vector(0,-90))
print((0,0)," -> ",get_vector(0,0))
print((180,180)," -> ",get_vector(180,180))
print((90,90)," -> ",get_vector(90,90))
print((45,0)," -> ",get_vector(45,0))

Here are the expected results for some angles:

- alpha=90, beta=0 (pointing to x): (1,0,0)
- alpha=-90, beta=0 (pointing to -x): (-1,0,0)
- alpha=0, beta=90 (pointing to y): (0,1,0)
- alpha=0, beta=-90 (pointing to -y): (0,-1,0)
- alpha=0, beta=0 (pointing upwards): (0,0,1)
- alpha=180, beta=180 (pointing downwards): (0,0,-1)
- alpha=90, beta=90 (pointing diagonal on x,y-plane): (0.707,0.707,0)
- alpha=45, beta=0 (pointing diagonal on x,z-plane): (0.707,0,0.707)

What my solution returns:

- alpha=90, beta=0 (pointing to x): (1,0,0)
- alpha=-90, beta=0 (pointing to -x): (-1,0,0)
- alpha=0, beta=90 (pointing to y): (0,1,0)
- alpha=0, beta=-90 (pointing to -y): (0,-1,0)
- alpha=0, beta=0 (pointing upwards): (0,0,1)
- alpha=180, beta=180 (pointing downwards): (0,0,1) -> WRONG
- alpha=90, beta=90 (pointing diagonal on x,y-plane): (0,1,0) -> WRONG
- alpha=45, beta=0 (pointing diagonal on x,z-plane): (0.707,0,0.707)

This is as close I could get until now, but the result is still wrong for certain angles.

Turn x,y angles into vector

0 Answers