Issue with hemisphere part with textures

Code:
def signed_angle(a, b, normal):

    # See https://stackoverflow.com/a/33920320

    s = a.cross(b).dot(normal)

    c = a.dot(b)

    return math.degrees(math.atan2(s, c))







pt1 = mathutils.Vector( (textureMap.x1, textureMap.y1, textureMap.z1) )

pt2 = mathutils.Vector( (textureMap.x2, textureMap.y2, textureMap.z2) )

pt3 = mathutils.Vector( (textureMap.x3, textureMap.y3, textureMap.z3) )



# Pre-calculate useful values

len_p1p2 = (pt2 - pt1).length

len_p1p3 = (pt3 - pt1).length



if textureMap.projType == 'PLANAR':

    n1 = (pt2 - pt1).normalized()

    n2 = (pt3 - pt1).normalized()

elif textureMap.projType == 'CYLINDRICAL':

    n1 = (pt2 - pt1).normalized()

elif textureMap.projType == 'SPHERICAL':

    # take the cross product of the two vectors extending from pt2 to get a third vector n3 at right angles to those.

    n3 = (pt1 - pt2).cross(pt3 - pt2).normalized()

    n2 = (pt1 - pt2).cross(n3).normalized()



for i in range(len(newPoints)):

    # Get the point in question (scaling the point back to original ldraw size, just for the purposes of UV coordinate calculation)

    pt = mathutils.Vector( newPoints[i] / globalScaleFactor )



    if textureMap.projType == 'PLANAR':

        # Calculate U

        if len_p1p2 > 1e-8:

            u = math.fabs((pt1 - pt).dot(n1)) / len_p1p2

        else:

            u = 0.0



        # Calculate V

        if len_p1p3 > 1e-8:

            v = math.fabs((pt1 - pt).dot(n2)) / len_p1p3

        else:

            v = 0.0



    elif textureMap.projType == 'CYLINDRICAL':

        # Calculate U

        distanceToPlane = (pt1 - pt).dot(n1)

        ptOnPlane       = pt - distanceToPlane * n1

        u  = LDrawGeometry.signed_angle(ptOnPlane - pt1, pt3 - pt1, -n1)

        u /= textureMap.a   # U is normalised

        u += 0.5            # U is centred



        # Calculate V

        if len_p1p2 > 1e-8:

            v = distanceToPlane / len_p1p2

        else:

            v = 0.0



    elif textureMap.projType == 'SPHERICAL':

        # Calculate U

        distanceToPlane = (pt - pt1).dot(n3)

        ptOnPlane       = pt - distanceToPlane * n3



        u  = LDrawGeometry.signed_angle(ptOnPlane - pt1, pt2 - pt1, n3)

        u /= textureMap.a   # U is normalised

        u += 0.5            # U is centred



        # Calculate V

        distanceToPlane = (pt - pt1).dot(n2)

        ptOnPlane       = pt - distanceToPlane * n2



        v  = LDrawGeometry.signed_angle(ptOnPlane - pt1, pt2 - pt1, n2)

        v /= textureMap.b   # V is normalised

        v += 0.5            # V is centred



    else:

        # Unknown UV projection type

        u = 0.0

        v = 0.0

    <store uv for point>