They are the same direction according to the camera coordinate system, correct?
mpotoole
Yes. The vector going in the direction $x$ and the vector going in the direction $PX$ are parallel to one another.
the
Thanks!
ml2
Could you explain again why they are parallel?
mpotoole
The 2D (homogeneous) image point $x$ and the 3D point $PX$ (transformed into the camera's coordinate system) both point in the same direction. Here, the origin of the camera is at $(0,0,0)$. If we were to cast out a ray towards the 3D point $PX$, the ray would intersect the image plane at $x$. The vectors pointing towards points $PX$ and $x$ are therefore parallel.
Because of this, the cross product between $x$ and $PX$ must be zero.
They are the same direction according to the camera coordinate system, correct?
Yes. The vector going in the direction $x$ and the vector going in the direction $PX$ are parallel to one another.
Thanks!
Could you explain again why they are parallel?
The 2D (homogeneous) image point $x$ and the 3D point $PX$ (transformed into the camera's coordinate system) both point in the same direction. Here, the origin of the camera is at $(0,0,0)$. If we were to cast out a ray towards the 3D point $PX$, the ray would intersect the image plane at $x$. The vectors pointing towards points $PX$ and $x$ are therefore parallel.
Because of this, the cross product between $x$ and $PX$ must be zero.