I have a question about figure on the right. We can find more than one point in 3 dimension space whose projections to 2 dimension space is a same point, right? but f(x) is a function, which means each input is related to exactly one output. then why ?

connorzl

The function that maps multiple 3D points to the same 2D point can be described as f(x) = Px, where P is the projection matrix that takes you from 3D to 2D. However, the inverse of P (which projects from 2D to 3D) does not necessarily exist. In fact, I believe the only invertible projection matrix is the identity matrix I itself. We'll cover projection matrices in further detail later in the course.

I have a question about figure on the right. We can find more than one point in 3 dimension space whose projections to 2 dimension space is a same point, right? but f(x) is a function, which means each input is related to exactly one output. then why ?

The function that maps multiple 3D points to the same 2D point can be described as f(x) = Px, where P is the projection matrix that takes you from 3D to 2D. However, the inverse of P (which projects from 2D to 3D) does not necessarily exist. In fact, I believe the only invertible projection matrix is the identity matrix I itself. We'll cover projection matrices in further detail later in the course.