Perspective: X Marks the Center

Perspective is merely a trick to help create realistic-looking three dimensional space on a two dimensional surface.  One, two and three point perspectives are very good tools for creating this sense of depth.  However, within the basic rules of perspective there are little tricks to help you calculate distance of specific objects that can’t be measured by using a vanishing point.  Little things like these can turn a good drawing into a realistic drawing. 

Edgar Degas, The Dance Foyer at the Opera on the Rue le Peletier, 1872

Today we’ll take a look how to find the center of a rectangle in perspective.  Though this doesn’t sound like an overly helpful tool, once we get to the practical applications you’ll see a world of possibilities.

Begin with a simple square.  Draw a line from the top right corner to the bottom left corner and visa versa.  The spot where these two lines cross marks the exact center of the square.  Simple enough.

Now let’s put this same square into one and two point perspectives (fig. 2).

Draw the same lines from corner to opposite corner (fig. 3).  Even though these lines are not of equal length, where they cross will mark the precise center of the square. 

Before dismissing this little trick as insignificant, take a look at some of its practical applications (fig. 4).  Finding the center of a rectangle can help with the placement of elements in a perspective drawing.

Not only can we find the center of the square or rectangle, but by extending a line vertically from the middle of the X, we can also find the center of the top and bottom lines of the shape.  This becomes particularly handy when working with things like buildings and windows. 

As you can see in the house on the right in figure 4, the X can be used to subdivide space as well.  By finding the center of the side of the house with an X, we can split it into two equal rectangles.  We can then find their centers by placing an X within both rectangles.  This is the only way to properly place the windows.

The archway of the door in the Degas painting from above is a good example of this perspective trick.  By outlining the rectangle in which it sits, we can make an X and extend a line upward from its center.  The point where this line meets the top of the rectangle will be the center (and thus the apex) of the arch.

The use of an X to find the center of a rectangle has many more applications than those shown here.  So the knowledge of this simple trick will prove to be very helpful any time you are trying to create an accurate illusion of perspective.

-Ray Radigan