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Rotation_matrix_T = cv.Rodrigues(rvec)[0]
Rotation_matrix = Rotation_matrix_T.T
Translate_vector = - np.dot(Rotation_matrix , tvec)

Transformation_matrix = np.eye(4)
Transformation_matrix[:3, :3] = Rotation_matrix
Transformation_matrix[:3,  3] = Translate_vector

## method 1 ##
proj_matrix = np.hstack((Rotation_matrix_T, - np.dot(Rotation_matrix_T, Translate_vector)))

## method 2 ##
proj_matrix = np.zeros(3, 4)
Transformation_matrix_inv = np.linalg.inv(Transformation_matrix)
proj_matrix = Transformation_matrix_inv[:3, :4]

# # # # # # # # # # # # # # # # # #
# #     R | s*t                 # # 
# # T = -------                 # # 
# #     0 0 0 1                 # #     
# #                             # #
# #           R.T | -R.T*s*t    # # 
# # inv(T) =  --------------    # # 
# #            0  0  0  1       # # 
# #                             # #
# # P = R.T| -R.T*s*t           # # 
# # P = inv(T)[:3, :4]          # # 
# # # # # # # # # # # # # # # # # #

This projection Matrix don't contain Camera Matrix

proj_matrix_Final_Camera1 = np.dot(cameraMatrix, np.eye(4)[:3, :4])
proj_matrix_Final_Camera2 = np.dot(cameraMatrix, proj_matrix)

Rotation_matrix_T = cv.Rodrigues(rvec)[0] Rotation_matrix = Rotation_matrix_T.T Translate_vector = - np.dot(Rotation_matrix , tvec) tvec) Transformation_matrix = np.eye(4) Transformation_matrix[:3, :3] = Rotation_matrix Transformation_matrix[:3, 3] = Translate_vector ## method 1 ## proj_matrix = np.hstack((Rotation_matrix_T, - np.dot(Rotation_matrix_T, Translate_vector))) ## method 2 ## proj_matrix = np.zeros(3, 4) Transformation_matrix_inv = np.linalg.inv(Transformation_matrix) proj_matrix = Transformation_matrix_inv[:3, :4] # # # # # # # # # # # # # # # # # # # # R | s*t # # # # T = ------- # # # # 0 0 0 1 # # # # # # # # R.T | -R.T*s*t # # # # inv(T) = -------------- # # # # 0 0 0 1 # # # # # # # # P = R.T| -R.T*s*t # # # # P = inv(T)[:3, :4] # # # # # # # # # # # # # # # # # # # # # s = Scale You don't need it now # # # # # # # # # # # # # # # # # # # This projection Matrix don't contain Camera Matrix proj_matrix_Final_Camera1 = np.dot(cameraMatrix, np.eye(4)[:3, :4]) proj_matrix_Final_Camera2 = np.dot(cameraMatrix, proj_matrix)

          3    No.3 Revision 
      updated 
        2020-10-08 20:57:57 -0600
     
    supra56  
 943  ●9 ●6  
 
 
 
  
 
 
 
  Code:
 Rotation_matrix_T = cv.Rodrigues(rvec)[0]
 Rotation_matrix = Rotation_matrix_T.T
 Translate_vector = - np.dot(Rotation_matrix , tvec)
 tvec)

Transformation_matrix = np.eye(4)
Transformation_matrix[:3, :3] = Rotation_matrix
Transformation_matrix[:3,  3] = Translate_vector

## method 1 ##
proj_matrix = np.hstack((Rotation_matrix_T, - np.dot(Rotation_matrix_T, Translate_vector)))

## method 2 ##
proj_matrix = np.zeros(3, 4)
Transformation_matrix_inv = np.linalg.inv(Transformation_matrix)
proj_matrix = Transformation_matrix_inv[:3, :4]

# # # # # # # # # # # # # # # # # #
# #     R | s*t                 # # 
# # T = -------                 # # 
# #     0 0 0 1                 # #     
# #                             # #
# #           R.T | -R.T*s*t    # # 
# # inv(T) =  --------------    # # 
# #            0  0  0  1       # # 
# #                             # #
# # P = R.T| -R.T*s*t           # # 
# # P = inv(T)[:3, :4]          # # 
# # # # # # # # # # # # # # # # # #
# s = Scale You don't need it now #
# # # # # # # # # # # # # # # # # #
 This projection Matrix don't contain Camera Matrix
 proj_matrix_Final_Camera1 = np.dot(cameraMatrix, np.eye(4)[:3, :4])
proj_matrix_Final_Camera2 = np.dot(cameraMatrix, proj_matrix)
 
 
          4    No.4 Revision 
      updated 
        2020-10-09 02:45:32 -0600
     
 
 
  
 
 
 
  Code:
 Rotation_matrix_T = cv.Rodrigues(rvec)[0]
Rotation_matrix = Rotation_matrix_T.T
Translate_vector = - np.dot(Rotation_matrix , tvec)

Transformation_matrix = np.eye(4)
Transformation_matrix[:3, :3] = Rotation_matrix
Transformation_matrix[:3,  3] = Translate_vector

## method 1 ##
proj_matrix = np.hstack((Rotation_matrix_T, - np.dot(Rotation_matrix_T, Translate_vector)))

## method 2 ##
proj_matrix = np.zeros(3, 4)
Transformation_matrix_inv = np.linalg.inv(Transformation_matrix)
proj_matrix = Transformation_matrix_inv[:3, :4]

# # # # # # # # # # # # # # # # # #
# #     R | s*t                 # # 
# # T = -------                 # # 
# #     0 0 0 1                 # #     
# #                             # #
# #           R.T | -R.T*s*t    # # 
# # inv(T) =  --------------    # # 
# #            0  0  0  1       # # 
# #                             # #
# # P = R.T| -R.T*s*t           # # 
# # P = inv(T)[:3, :4]          # # 
# # # # # # # # # # # # # # # # # #
# s = Scale You don't need it now #
# # # # # # # # # # # # # # # # # #
 This projection Matrix don't contain Camera Matrix
 proj_matrix_Final_Camera1 = np.dot(cameraMatrix, np.eye(4)[:3, :4])
proj_matrix_Final_Camera2 = np.dot(cameraMatrix, proj_matrix)
  To answer your question:
The rvec and tvec returned by solvepnp don't include the values of the camera matrix.
The rotation and translation are recovered in this way
 Rotation = cv.rodriges (rvec) [0] .T
Traslation = - np.dot (Rotation.T, tvec)