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I'm trying to compute the extrinsic matrix from the pose (position and orientation) of the camera given in world coordinates. I used the following to compute the extrinsic matrix,

T = [R -Rt; 0 1] 3x4 Matrix

The rotation(theta2) of the camera is about the Y-axes of the camera i.e. yaw about the camera axis. The translation vector is [x, y, z] in meters.

My Setup

theta1 = deg2rad(theta1); 
RW1 = [[cos(theta1), 0, sin(theta1)];
    [0,1, 0];
    [-sin(theta1), 0, cos(theta1)]];
tW1 = [0; 0; 0];
TW1 = [RW1 tW1; 0 0 0 1];

theta2 = deg2rad(theta2);
R12 = [[cos(theta2), 0, sin(theta2)];
    [0,1, 0];
    [-sin(theta2), 0, cos(theta2)]];
t12 = [x; y; z];
T12 = [R12 t12; 0 0 0 1];

P1 = K * TW1;
P2 = K * T12;
K - Camera Intrinsic Matrix

Is this the right way to calculate the extrinsic matrix? Am I missing any transformations between the world and the camera frame?

I'm trying to implement this https://www.cs.cmu.edu/~16385/s17/Slides/11.4_Triangulation.pdf and for the camera matrix, I followed this https://www.cs.cmu.edu/~16385/s17/Slides/11.1_Camera_matrix.pdf.

Stark
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  • work with 4x4 matrices. I'm only reading things that are based on 4x4 matrices. `R[I|-t]` is probably even wrong. that encodes translation followed by rotation. it's supposed to be rotation, followed by translation. please find teaching material you can point to if you have any questions not answered by the teaching material. – Christoph Rackwitz Sep 27 '22 at 13:29
  • @ChristophRackwitz With 4x4 do you mean [R t; 0 1]? I have camera locations in the world coordinate system, both translation, and rotation. I should use them to build an extrinsic matrix. This extrinsic matrix should be used to build a camera projection matrix. I'm trying to implement this cs.cmu.edu/~16385/s17/Slides/11.4_Triangulation.pdf. – Stark Sep 27 '22 at 16:49

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