openCV solvePnP returns wrong results

Question

With cv2.solvePnP I try to do pose a estimation in pyvista, which is a python wrapper for vtk. The results of solvePnP seem wrong to me, i.e. the resulting translation and rotation. For simplicity I try to "undo" a translation of the camera. I expect the inverse of the translation to be the result of solvePnP.

The translation is just

Translation = np.array([[  1.,   0.,   0., 1000.],
                        [  0.,   1.,   0.,   0.],
                        [  0.,   0.,   1.,   0.],
                        [  0.,   0.,   0.,   1.]])

i.e. a shift along one axis. But the resulting rvec,tvec are

 rvec = array([ 0., 0., -3.142]),
 tvec = array([ 707.107, 408.248, 8882.736])

The resulting translation and rotation seem nonsensical to me. Since the translation does no rotation, I expect that only tvec has non zero entries to undo the translation in the opposite direction. Concretely, I expect tvec= [-1000,0,0] and rvec=[0,0,0]. If I then apply this (wrong) result to the camera, all points disappear completely.

Here is What I do:

import cv2
import pyvista as pv
from pyvista import examples
import pyvistaqt
from vtk import vtkMatrix4x4, vtkMatrix3x3, vtkTransform
from vtk.util.numpy_support import vtk_to_numpy  
import numpy as np

np.set_printoptions(suppress=True,precision=3)

def getCamMatrix():
    
    narray = np.eye(4)
    vmatrix = plotter.camera.GetModelViewTransformMatrix()
    vmatrix.DeepCopy(narray.ravel(), vmatrix)
    return narray    

def toVTK(m,n =4):
    if n == 4:
        newMatrixVTK = vtkMatrix4x4()
    else:
        newMatrixVTK = vtkMatrix3x3()    
    for i in range(n):
        for j in range(n):
            newMatrixVTK.SetElement(i,j, m[i,j])            
    return newMatrixVTK

def applyMatrixToCam(newMatrix):
    global plotter
    newMatrixVTK = toVTK(newMatrix)    
    transform = vtkTransform()
    transform.SetMatrix(newMatrixVTK)
    transform.Update()
    plotter.camera.ApplyTransform(transform)
    pass

print("Setting up points in world coordinates")
Points =  np.array([[ 2918.972,  -887.573,   416.331,1],
        [ 2338.002,  -702.07 ,  1039.864,1],
        [ 1458.473,  -707.246,  1005.19,1 ],
        [ 1219.4  ,  -890.161,   377.004,1],
        [ 1318.727, -1017.829,  -156.537,1],
        [ 2529.132, -1026.888,  -169.222,1]])


pMesh = pv.PolyData(Points[:,:3]) # vtk object to hold the six points


plotter = pyvistaqt.BackgroundPlotter() # setting up the plotting function
plotter.enable_trackball_style()
plotter.add_mesh(pMesh)



print("Transforming from World to Image Coordinates")
# Rotating the points towards a camera at the origin, i.e. applying the default camera transform
projected = (getCamMatrix() @ Points.T)[:3,:].T 

print("store original image points")
image_points = projected.copy()[:,:2]
print("Applying the perspective transform, i.e. division by the Z-coordinate")
image_points /= projected[:,-1].reshape(-1,1) 


print("Setting up a simple translation of the camera position")
Translation = np.array([[  1.,   0.,   0., 1000.],
                        [  0.,   1.,   0.,   0.],
                        [  0.,   0.,   1.,   0.],
                        [  0.,   0.,   0.,   1.]])

applyMatrixToCam(Translation)


print("Apply the new Camera Matrix to the six points")
projected_shift = (getCamMatrix() @ Points.T)[:3,:].T

retval, rvec, tvec = cv2.solvePnP(projected_shift, np.array(image_points), np.eye(3), None, None, None, False, cv2.SOLVEPNP_EPNP)

R = cv2.Rodrigues(rvec)[0]
extrinsicReal = np.vstack([np.hstack([R.T, -R.T@tvec]), [0,0,0,1]])
applyMatrixToCam(extrinsicReal)