One e-mail question I received awhile back hit on a problem that confuses lots of people. Including me, at times. The question is a tricky one, because the answer seems counter-intuitive. My answer covers a number of different solutions for the practical problem. Hopefully everything gets laid out with some clarity here:
Dear Jason Cheeseman-Meyer,
I liked Vanishing Point a lot and appreciated how focused it is on things I actually need as an illustrator. I came across something that puzzled me in one of your diagrams, so I recreated part of that diagram in three stages to help clarify some questions I have. This is the perspective diagram that eventually becomes a scene of a cyborg King Kong demolishing an overpass, and I’m sure you’ll recognize the similarity. What I found was so strange I decided to ask.
While studying the diagram I tried to imagine how I would accurately place a car along the red line I’ve drawn in pic number one. The only way I could think of to do this was two create two new vanishing points to the right of the center axis, and this, it seems, creates a second center axis. (In the pics, I didn’t work out the exact placement of the second center axis, but I’m assuming it would be between the two new vanishing points.)
I’ve also tried rotating the grid to the red axis but I get the same result: two new vanishing points to the right of the first center of vision. I would like to be able to draw the car along the red axis from the perspective of the first cone so I can handle similar problems in the future.
Did I screw up? Am I missing something? Or is it impossible to draw a car along the red axis from the perspective of the first cone and center of vision? The latter doesn’t seem likely. Would you be willing to give me some tips?
Okay Alex, here we go:
You’ve got a technical question here, and I’m going to give you a technical answer. But keep in mind that “correct” and “right” aren’t the same thing in art. Sliding the centerline over is a legit solution, if it looks right in the end. If you were drawing a giant tile floor and trying to draw the one tile that was out of angle because the workers hadn’t put it in yet, it probably wouldn’t work. But a car on a blank road surface probably wouldn’t look wrong to anybody. So take all my answers below with a grain of salt — they’re about technical correctness, but technical correctness isn’t the end goal of art, just a tool you sometimes use to get to your end goal.-
What you’ve got here is essentially a cone of vision problem — you’re drawing things too far away from the center of vision and are running into some serious distortion. Remember that the centerline is the center of your canvas/image area/picture plane/ however you want to call it.
If you check out illustration A, the green circle is your 90 degree cone of vision (as determined by your magic spot and your centerline), the purple circle is your 60 degree cone of vision, which your traditionalists usually put the limit of a perspective drawing (Personally I stretch that a bit — distortion problems are worth the extra excitement). So the dark purple box is the picture plane for a distortion-free drawing of this scene, where even the corners of the picture fall within the distortion-free 60 degree cone of vision. And your red-line care falls well outside that distortion-free zone.
So given this setup, where would the second vp for the line you’ve drawn go? It’s actually way over to the LEFT of the centerline. We put our first VP where your red line hits the horizon. Extend a line from that VP to the magic spot, and then take a 90 degree angle off of that. 90 degrees off to the right would never hit the horizon, it’s moving further from it, not towards it. 90 degrees to the left intersects the horizon at our second VP. See illustration B. Illustration C shows the car drawn from these VP’s. Pretty distorted — especially if it’s anywhere in your picture other than the very very corner.
So what do we do? We can fake it and slide the centerline, as you suggested. We can pick a different angle for the car (like illustration D, which moves your first VP just left of the centerline, and kicks that second VP WAAAY over to the right.)
But perhaps the best solution is to start over, moving anything that isn’t working for us. We’ll keep the placement of the objects and the first two VP’s, and lay in our image area (the purple box) and take a centerline from that.
Since we’ve had some trouble, let’s go ahead and set in our 90 degree cone of vision (red). It should go outside the image area. The closer the image area gets to that circle, the more distortion we’re going to get. But the more drama, too. Let’s push it a bit and keep it fairly close. We’re outside the 60 degree distortion free cone of vision, but we’re going to run with it. It’s a crazy image – the perspective can add to that.
The intersection of the horizon and the centerline is the center of the cone of vision in 2-pt perspective (with wiggle room if needed). The intersection of the centerline and the 90 degree cone of vision is the magic spot.
So we put the corner of the t-square on the magic spot and find we’ve got to move the second VP and the diagonal VP a bit. So we redraw the car’s footprints to match the new VP’s. Even though we haven’t moved the 2nd VP very far, the change in the diagonal VP is quite significant, and the cars don’t look anywhere near as stretched out.
Then we pop in the new VP’s and DVP for the car at an angle, eyeballing the relative size of the cars, and lay in that third car. (2C) Which should look just fine once it’s drawn up. It IS weird — it’s drawn to the left of BOTH of it’s VP’s. All by itself, it’s distorted, but as part of the scene, it works. It may not seem right highlighted like this, but it is really how the world works.
Now, if this car was going to be a center of attention (the hero’s car heading to the giant monkey or something) then we might look at our earlier tricks (sliding the centerline just for that car, changing the angle of the car) or making the image area smaller relative to the cone of vision to get it distortion-free as befits a center of interest.
Hope this is helpful!