I was given this image, seen below, as a study guide,I color coded it for ease of reading, for the homework (which is to setup 3 perspectives that map $(a,b,c,d) \to (c,d,a,b)$). I am having trouble seeing the projectives.
$\color{red}{Q}\left(a,\color{red}{b^{\prime}},\color{red}{c^{\prime}},\color{red}{d^{\prime}}\right)\overset{d}{\doublebarwedge}\color{blue}{B}\left(b,\color{red}{b^{\prime}},\color{green}{c^{\prime\prime}},\color{yellow}{p}\right)\overset{\color{red}{c^{\prime}}}{\doublebarwedge}P\left(b,a,d,c\right)$
The ones that I don't understand are:
- How come $\color{red}{c^{\prime}} \to \color{green}{c^{\prime\prime}}$
- How does $\color{red}{b^{\prime}} \to a$
- How does $\color{green}{c^{\prime\prime}} \to d$
- How does $p \to c$
Please, (Yes, I understand that this was given to help with a homework problem) explain the projections.
Mistake on graph, point $E$ should be $C^{\prime}$
I'll demonstrate this in a single example.
You are performing a perspectivity between four lines through $Q$ and four lines trough $B$. You are using the points of intersection with line $d$ as the glue to identify them.
So $c'$ passes through $Q$, and it intersects $d$ in $E$. The line joining $E$ to $B$ is $c''$. This is why $c'$ gets mapped to $c''$.
The others should be the same.