One of the first things you learn when you start studying perspective is that identical objects – like fence posts, telephone poles, or the trees in Van Gogh’s Avenue of Poplars - appear smaller and closer together as they get farther away. But how much smaller, and how much closer together? Sometimes an “eyeballed” estimate is close enough, but if you want accurate spacing you need to understand perspective centre.
You probably remember from your high school geometry that the centre of any rectangle is the point where its diagonals cross. Well, the same thing applies to a rectangle drawn in perspective; the point where its diagonals cross is its perspective centre:
Let’s change that rectangle-in-perspective into the side of a house, and add a door in the middle of it. (Again, eyeballing it might be fine most of the time, but I’m going to be super-accurate here just for the practice.)
Here’s our little house, with the orthogonals, or perspective lines, converging on a vanishing point on the horizon. I’ve added a blue line, receding to the same vanishing point, to show where the top of the door will be.
Next, I’ve drawn the diagonals of the side of the house (in red), to find its perspective centre. (Notice that the half of the rectangle that’s closer to us appears a bit bigger than the half that’s farther away.) Drop a vertical line (green) through the perspective centre to mark the centre of the door.
Here I’ve added a vertical line to indicate one side of the door. There’s nothing special about its placement – it just depends on how wide you want the door to be. I’ve also added a dot on the green centre line to indicate the middle of the door’s height (measured with a ruler). That point will be the perspective centre of the door. Then I drew a diagonal (orange) through that point to find the nearer top corner of the door.- Now drop a vertical line from that top corner, and there it is – a door in perfect perspective centre!
We can use a similar method to determine the spacing of fence posts, etc.
Draw the first post. Extend the orthogonals to the vanishing point, and add the second post between the orthogonal lines. The distance between the first two posts is arbitrary – just put it wherever it looks right!
Find the perspective centre of the rectangle created by the first two posts, by drawing the diagonals. Connect the perspective centre to the vanishing point. This line (blue) will cross the middle of each post we will draw.
Now draw a line from the top of post #1 through the middle of post #2. The point at which this line intersects the bottom orthogonal is where the third post will go. Draw the vertical line for post #3 between the two orthogonal lines. (Notice that the the space between posts #2 & #3 appears less than between #1 and #2.)- Repeat step 3 as many times as necessary to complete the row of posts:
You can use this method for any equal-sized rectangles in perpective, such as a tiled floor.
