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This lesson stretches your brain into space and gets it exact. You will learn how to measure away or toward the viewer. We will start with the simplest trick to divide things in half in perspective.

X Finds the Center

Drawing an X from corner to corner of a rectangular plane finds the exact center. This cuts the plane perfectly in half.

The angle of your tapering lines changes the position of that central point. A highly foreshortened rectangle with a close camera pushes that halfway division far back. You get some leeway for how much you taper the edges and how far back you place the center.

You can use this to find halfway points on the floor, the walls, and the ceiling. You can do it again to divide the space into fourths. You can keep dividing from fourths into eighths.

Notice that when there is already a halfway line on one axis, you do not need a full X. Just one diagonal will find the center of that rectangle to create the halfway line on the other axis.

A grid of halves stays in place when you put it in space. This works in any kind of perspective. It works close up or far away. It works in 1, 2, or 3-point perspective on any rectangular plane. It is simple, fast, and precise.

The Limit of X Finds the Center This method only gives even divisions. It cuts things in twos, halves, and their halves.

Diagonal Transfers

If you want odd divisions like thirds, fifths, or sevenths, you need a different approach. We call this the checkerboard method. It uses a diagonal line to transfer divisions. The advantage over finding the center with an X is that this works for both even and odd divisions.

Here is how to divide equal segments on a foreshortened plane:

• Find a line that is not foreshortened, like the front edge of your plane.
• Divide this unforeshortened line into your desired equal parts.
• Run those dividing points back to the vanishing point to create converging lines.
• Run a diagonal line from corner to corner of the plane.

Every point where the diagonal touches the converging lines transfers those divisions into perspective. It perfectly calculates how much smaller to make each partition as it goes back in space.

Dividing the Front Line

Dividing a straight line is easy for halves. Dividing an odd number is not always that simple.

Measuring the distance in millimeters and dividing it by your chosen odd number is slow. The fast way is to find a stretch on your ruler that nicely divides with your chosen number. Angle the ruler until that divisible length fits between your boundaries. Mark your divisions and use those points.

Transferring Uneven Divisions

The segments do not have to be all the same length. You can have a short one, a long one, and a medium one. They will all transfer front to back from one line in draft view to one in perspective.

When the sections recede in a particular order, place them on the non-foreshortened line in the order you want them to go away. Start your diagonal in that particular corner to send them front to back.

The Guiding Principle Get anything out of perspective, divide it, and transfer the divisions with a diagonal line. This takes care of the whole room.

These methods work on a floor, a ceiling, or a wall. They just require a back boundary to work.

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