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Is there any algorithm for determining the 3d position in this case? (images below)

So, first of all, I have such an image (and, of course, I have the coordinates of all the points in 2d so that I can restore the lines and check where they intersect)

alt text
(source: narod.ru )

But, hey, I have another image with the same lines (I know that they are the same) and the new coordinates of my points, as in this image (source: narod.ru )alt text

So ... now having the points (coordinates) in the first image, how can I determine the rotation of the plane and the depth Z in the second image (assuming that the first center was at the point (0,0,0) without rotation)?

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: . , . , . , , .

, 2D- /. , , ( , , , ). (a_i, b_i), ,

P = [ px  0  0  0 ]
    [ 0   py 0  0 ]
    [ 0   0  pz pw]
    [ 0   0  s  0 ], s = +/-1

​​. , ,

a_i = px x_i / (s z_i)
b_i = py y_i / (s z_i)

(x_i, y_i, z_i) - 3D- .

, ( ), (x0_i, y0_i, z0_i). C. - . V.

V = R C + v 1^T             (*)

1^T - , R , V .

V : { s a_1 z_1 / px, s b_1 z_1 / py, z_1 } ..

(*) z_i, R V.

  • , R z_i
  • , , 2D- ( , ).
  • , ; , , (*); .
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, , . , , , . .

, .

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() . Google.

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( , ..), :

Ma, Soatto, Kosecka, Sastry, , Springer 2004.

Beware: this is an advanced engineering text and uses many methods that are mathematical in nature. Browse the samples presented on the book’s web page to get an idea.

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