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For projecting 3d point to the image plane you should use the equations:

I assume that there is no distortion (or you already have called undistort() function) For back projection you also can use these equations. Let you have pixel with coordinates (u,v) and you want to find 3d points that can be projected to this point (it is a ray in 3d space).

These points: z = any value >= 0 x = (u-cx)z/fx y = (v-cy)z/fy

Image plane is the plane z = 0.

For projecting 3d point to the image plane you should use the equations:

I assume that there is no distortion (or you already have called undistort() function) For back projection you also can use these equations. Let you have pixel with coordinates (u,v) and you want to find 3d points that can be projected to this point (it is a ray in 3d space).

These points: z = any value >= 0 x = (u-cx)z/fx y = (v-cy)z/fy

For projecting 3d point to the image plane you should use the equations:

I assume that there is no distortion (or you already have called undistort() function) For back projection you also can use these equations. Let you have pixel with coordinates (u,v) and you want to find 3d points that can be projected to this point (it is a ray in 3d space).

These points: z = any some value >= = 0 x = (u-cx)z/fx y = (v-cy)z/fy

For projecting 3d point to the image plane you should use the equations:

I assume that there is no distortion (or you already have called undistort() function) For back projection you also can use these equations. Let you have pixel with coordinates (u,v) and you want to find 3d points that can be projected to this point (it is a ray in 3d space).

These points: z = some value = > 0 x = (u-cx)z/fx y = (v-cy)z/fy

For projecting 3d point to the image plane you should use the equations:

I assume that there is no distortion (or you already have called undistort() function) For back projection you also can use these equations. Let you have pixel with coordinates (u,v) and you want to find 3d points that can be projected to this point (it is a ray in 3d space).

These points: points:

z = some value > 0
x = (u-cx)z/fx
(u-cx)*z/fx
y = (v-cy)z/fy
(v-cy)*z/fy