How to consistently create arcs of ellipses for rotated normals

[bernhard-42]

I currently use OCC version (7, 4, 0, '-rc1') and tried to create arcs of an ellipse for three normals:

• (0,0,1) rotated by 30° around x-yaxis
• (0,0,1) rotated by 45° around x-yaxis
• (0,0,1) rotated by 46° around x-yaxis

from OCC.Core.gp import gp_Elips, gp_Ax2, gp_Pnt, gp_Dir
from OCC.Core.GC import GC_MakeArcOfEllipse
from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeEdge

from math import pi, sin, cos
import numpy as np

def rad(deg):
    return deg /180.0 * pi

def Rx(angle, t):
    angle = rad(angle)
    mat = np.array([
        [1, 0,           0         ], 
        [0, cos(angle), -sin(angle)], 
        [0, sin(angle),  cos(angle)]
    ])
    return tuple(np.matmul(mat, t))

def sample(d):
    pnt = gp_Pnt(0.0, 0.0, 0.0)
    dir_ = gp_Dir(*d)

    ellipse_gp = gp_Elips(gp_Ax2(pnt, dir_), 20, 10)
    ellipse = BRepBuilderAPI_MakeEdge(ellipse_gp).Edge()

    ellipse_geom = GC_MakeArcOfEllipse(ellipse_gp, 0.0, pi/2, True).Value()
    return BRepBuilderAPI_MakeEdge(ellipse_geom).Edge()

sample(Rx(30, (0,0,1)))
sample(Rx(45, (0,0,1)))
sample(Rx(46, (0,0,1)))

The result is surprising (magenta=30°. black=45°, cyan=46°):

Why does the arc flip to the other side when I move from 45° to 46°?

[bernhard-42]

After digging deeper into opencascade it looks like gp_Ax2(pnt, dir) calculates x direction and y direction automatically and this seems to flip when going from 45° to 46° (and again from 135° to 136°).

I guess I need to use gp_Ax2(pnt, dir, dir) to control the x direction and hence the orientation of the ellipse arc on the plane:

def sample(d, v):
    pnt = gp_Pnt(0.0, 0.0, 0.0)
    dir_ = gp_Dir(*d)
    v = gp_Dir(*v)

    ellipse_gp = gp_Elips(gp_Ax2(pnt, dir_, v), 20, 10)
    ellipse = BRepBuilderAPI_MakeEdge(ellipse_gp).Edge()

    ellipse_geom = GC_MakeArcOfEllipse(ellipse_gp, 0.0, pi/2, True).Value()
    return BRepBuilderAPI_MakeEdge(ellipse_geom).Edge()

This seems to work well, when d is the normal of the plane in which the ellipse is to be created and v is a vector on the plane denoting the x direction.

Is this correct from an OCC persepctive?

For the choice of v: I use cadquery where each plane has a xDir, yDir and zDir. So I would use d=zDir and v=xDir of the plane on which the ellipse should be drawn.
@adam-urbanczyk Does this choice make sense for cadquery?

[bernhard-42]

The above approach proved to be ok