# Laser scanner and the math behind

Hi, I need to confess I'm lost( or stupid:) I'm not able to understand the math I need for my laser scanner project. I will try to highlight my greatest problem.

The first is the setup. It is let say common. Camera + line laser 10 cm apart from the camera, closing 85deg angle with the camera. Let say I'm able to somehow get intrinsic matrix by chessboard calibration.

I will put some thing before the camera and the camera will see the curve on in created by the line laser. Now I need to calculate the Z-index of points this curve contains. But how???

1)Extrinsic matrix can be calculated according to chess board position. So if I will put the chessboard in to the laser plane(chessboard will have the same direction like the laser plane) can I use the extrinsic matrix to calculate the Z-index( I will measure the distance to the corner of the chessboard that I will consider to be the coordinates center)

or

2) Can I just calibrate as usually and let the laser shine. Find out the lines created on the chessboard and let openCV to calculate homography from image plane to the plane created by the laser lines on the chessboards? I can again measure the distance from the first chessboard to settle correctly the scale, to see the real word dimensions.

or

3) or none above works and I should change my project:)

I will appreciate any hint, link whatever.

Regards

Martin