Let say I have a image that represent a 3D scene. I did not have the 3D camera orientation of that scene (left, up and forward vectors) and i'd like to calculate it.
On that picture, I draw the following segments : A1, A2 and B1, B2.
A1 and A2 are vanishing lines for the plane defined by left and up axis.
B1 and B2 are vanishing lines for the plane defined by forward and up axis.
As input, I only have 2D coordinates of segments (in screen space), so eight coordinates in total. This is the "handles "of the segments on the picture. I also have P0, a 2D position (in screen space) of the origin of the up / left / forward axis (not sure if this information is needed).
Is there a way, from that information, to retrieve the 3D orientation (in world space) of the 3D scene (so the left, up and forward vectors) ?
Once the forward and left vector are calculated getting the up one is trivial : cross product would do.
EDIT : As Peethor stated, there was some missing information to get what I wanted. I have update question and picture to add more details and make it more clear.