Artist here.

Okay. Working out perspective by hand is hard. It's a lot of work, that takes a lot of arcane knowledge.

So's doing a photorealistic painting of a thing. You have to look at the thing, consider a bunch of relationships of the particular feature you're interested in at this very moment, and transfer those relationships to your canvas. That's a pretty complicated set of habits and brain circuitry you have to build up over a period of years.

Tracing an image is immensely easier. There's all the perspective, there's all the proportion relationships. There's all the colors. Right there in front of you. You can spend an hour or two essentially doing manual edge-detection, and then start filling in areas.

There's still stuff to learn - how to mix the paint to get the colors you want, how to apply it to the canvas, stuff like that. And if you trace organic stuff too closely, it starts to look stiff and dead. But compared to the amount of skill you have to learn to draw this kind of stuff out of your head? It's nothing.

I mean, hell. Take a photo, print it out. Tape it to a sunny window, tape another piece of paper over it, and trace it. Then take that same photo and try to draw a copy of it, without tracing. There will be a huge difference between the two drawings you just made. The one made without tracing will probably have taken a lot longer, and have many more bits erased and redrawn.

A lot of modern artists have this weird thing going on with respect to tracing. It's the worst thing ever, they'll say. Tracing another person's work to learn from, or tracing off of a photo, they're different kinds of art crimes, but they're still art crimes. Leaping around learning to break a scene down in your head and reconstruct it from scratch - essentially building a wetware 3D modeller in your brain, really - is considered CHEATING by some people.

So Hockney's book on Vermeer's work is essentially saying "dude Vermeer was totally a tracer". Which in many artist's eyes is like calling him Not An Artist. Artists get weird about what is Art and what is Not Art, it's this whole thing that's about as inexplicable to a layperson as a programmer's choice of text editor.

By using mirrors and lenses to project an image onto his camera to trace, Vermeer only had to learn the basic painting technique stuff. If he did, if he traced all this stuff, then some people will start saying that his work is no longer Art. It's just Illustration. Which, in the eyes of people who care about this, means that it is a lower, less respectable thing. Now it's just a filter applied to an image, albiet manually instead of via Photoshop or whatever.

The truth of the matter (IMHO) is that a lot of the people who will scream bloody murder when someone is tracing are amateurs. Real pros can and will project images and work over them, build reference models in the real world or in 3D programs, and do any damn thing they can to make the hard parts of their work easier, to get all those little details they'd never make up out of whole cloth.

I am pretty sure I've repeated myself a couple times here, thanks to the tiny window HN allows to type in. But hopefully this helps.

tl;dr: If Vermeer used these techniques then he's a dirty cheating TRACER and is thus not a REAL ARTIST in some people's eyes.