Oystein
Penultimate Amazing
- Joined
- Dec 9, 2009
- Messages
- 18,903
Oystein post 703: "This is true, for reasons.
For the same reasons it is also true that it is impossible to reproduce motion in the viewer axis coordinate system by using the Sauret video."
But if you use 2 or more viewpoints, 3-D vector reconstruction is possible. WHen we do that, viewer coordinate systems will be useful.
2 or more viewpoints means 2 or more viewer cs. The 3D reconstruction will have to take place in 1 cs only; is any viewer cs preferable to any other, or indeed preferable to a planet-earth-cs?
Recall:
Basically, any vector can be expressed in terms of 2 components, the part parallel with the line of sight and the part perpendicular to it, as shown:
[qimg]http://www.sharpprintinginc.com/911/images/photoalbum/13/perp_and_parallel.png[/qimg]
The line of sight is the vector p. The blue lines are projection lines, or projection planes in 3-D. The viewer actually sees the vector as it projects onto a blue plane.
The parallel component is the portion of D that is invisible to the viewer. The perpendicular component is the portion of the vector D that is completely visible to the viewer. The viewer sees all of the perpendicular component and none of the parallel component.
3-D vector reconstruction from knowledge of 2 or more vector projections is the effort to rebuild these invisible parallel components of the vector D from knowledge of the visible perpendicular parts from each viewpoint.
This becomes a simple procedure with viewer coordinates. That is why I use them.
The perpendicular part of D is totally visible to the viewer and lies totally within a y, z projection plane in the viewer coordinate system. You can know the y and z components of vector D in the viewer coordinate system. You cannot know the x component because it points directly iway from the viewer. If you do that from 2 viewpoints, you can reconstruct the whole vector.
The choice of viewer coordinates means that for each projection, 2 of the 3 vector components in the viewer system are totally visible and measurable. The third component is totally invisible. It allows us to measure 2 of the 3 vector components directly from the video from the viewpoint.
Concerning my use of cartesian coordinates, it is justified if the object viewed is sufficiently small relative to the distance of the viewer. If not, spherical coordinates seem to be best for the viewer coordinate system.
Yes, we are justified in using cartesian coords for Sauret and the NE viewpoints. If you want to see, I'll show you why over the weekend. I won't have sufficient time until then.
Could you check whether you think that Myriad's post 815 applies to the situation you are analysing? I think it does, and it refutes your entire post.