POV-Ray : Newsgroups : povray.pov4.discussion.general : A false projection matrix!!!! : A false projection matrix!!!! Server Time
8 Dec 2021 07:51:42 EST (-0500)
  A false projection matrix!!!!  
From: StudentPHD
Date: 18 Mar 2013 02:40:01
Message: <web.5146b5e68dc236d254c63d880@news.povray.org>
Hello,

I am developping an 3D reconstruction application. So I am generating some
testing images using pov ray. To achieve the 3D reconstruction, I have to
calculate the matrix projection.
I am developping all necessary functions and I calculate the matrix project p=
K*[R,-R*C] where R is the rotation matrix and C is the camera center and K is
the internal matrix of the camera.
my camera setting is like this:

camera {
                        location<0, 0, 0>
                        rotate<20,-45,0>
                        translate<300, 250, -300>
                        up <0,2,0>
                        right <2,0,0>
                        direction <0, 0, 1>
                        look_at <0,0,1>  }


The focal f=1, (norm[direction]), the angle =90 and the image is rendered as
600*800 pixels, so the matrix K=
(400 0 400.
0 -300  300.
0 0 1 ).


I calculate the rotation matrix like this:

Rx=RotationMatrix[20,{1,0,0}];
Ry=RotationMatrix[-45,{0,1,0}];
Rz=RotationMatrix[0,{0,0,1}];

R=Transpose[Rx,Ry,Rz].

C=[300,250,-300];

To check if my Matrix P is true or not.
1)  I photograph a cube using the camera above. I obtain its image 2D.
Therefore, I extract the coordinates of  3D corner of the cube and the
coordinate of its projection in the image 2D. for example corner 1= (100,0,-180)
its projection is (123,439).
2) I construct the same cube on matlab and I project it on 2D using the
projection matrix p and I get the coordinate 2D of the corners. I obtain the
results:

if I cancel the rotation and the translation (R=matrix identity and C=(0,0,0))
the coordinate of corners are maching very well, so P is correct

If I translate the camera, The corner are matching very well, so P is correct.

If I make a translation and rotation, the corners does not match, so P is not
correct. So where is the error in my code and  is the  camera setting is correct
(I mean that I rotate the camera then I translate it or the inverse, regarding
the calculation of the matrix P=K*[R,-R*C]) ?

Is the calculation of the R is false or what????!! thanks to help me


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