Scientific progress goes 'boink'
Ph.D. Candidate
Princeton University
Department of Computer Science
We often want to know how to project 3D objects onto a 2D plane (e.g., display an image on a screen).
Orthographic Drop the $z$ component of any three-dimensional point $p$ to obtain the two-dimensional point $x$. We can write this transform as:
If we use homogenous, or projective coordinates $\tilde{x}$ and $\tilde{p}$:
Orthographic projections are fixed-depth.
Perspective The perspective projection divides the $x$ and $y$ components by the $z$ component, weighting them by distance to the camera. We can write this transform using homogenous coordinates as:
where we drop the $w$ coordinate. Note that we do not divide by $z$ because homogenous coordinates are equivalent by a multiple.