积木世界与平行投影

What a vision system must do

A world of paper blocks

Parallel projection

The projection equations

Choosing a goal small enough to reach

A photographer photographs the same building facade twice. Photo A is taken from 200 meters away with a long lens, photo B from 5 meters away with a wide lens, and both frames show the facade at the same apparent size. Which photo is better approximated by parallel projection, and which observation decides it?

Under the projection model of this lesson, $x = X$ and $y = \cos(\theta)Y - \sin(\theta)Z$ with a fixed tilt angle $\theta$. A block face moves 2 units in the world direction parallel to the $X$-axis. What happens in the image?

A camera in the blocks world has square pixels with unit scale and a tilt angle $\theta$ such that $\cos(\theta) = 3/5$ and $\sin(\theta) = 4/5$. A world point sits at $(X, Y, Z) = (3, 10, 5)$. Compute its image coordinate $y$ from $y = \cos(\theta)Y - \sin(\theta)Z$, and write the number.