Drawing a grid or tile floor in perspective

1. How long do you want the viewing distance d to be?

Realistically, it should be at least 8" (20.5cm), and even that is small. But for the purposes of this diagram I will use something smaller so it fits into a compact space.

2. Place your primary vanishing point V wherever you choose.
3. If you are drawing a tile floor, draw the horizon line through V. Place the secondary vanishing point V' on the horizon line d units away from V

For the sake of compactness, I put the primary vanishing point at the one edge of the page and the secondary vanishing point at the other edge. You may want to center the grid or tile floor with respect to the vanishing point, in which case you may want a big piece of paper.

4. Draw the "front" or "near" edge of the grid parallel to the horizon line. Decide how wide you want the front squares to be; make marks that width evenly along this front edge.

You can locate it left/right anyway you like, and make it however long you like, but be sure to put it far enough away from the horizon line so that successive grid lines can move closer and closer to it.
5. Connect each mark to the vanishing point.

The orthogonal grid line segments will lie along these lines.

6. Draw a diagonal from (in this case) the left end of the front edge across the orthogonals to V'

Mark where this new line crosses the orthogonals - this will tell you how far back to put the next several horizontal lines of the grid.

7. Add horizontal lines through each of these points.

This forms a square grid -- each piece is a square, and we have the same number of squares across as we do back, so the whole thing is a square.

(The reason each piece is a square is because we have learned that diagonals of squares vanish at the secondary vanishing point V' which is located d units away from V along the horizon line.)

If this is what you wanted to draw, go to Step 9.
8. To extend the grid farther back, repeat Steps 6 and 7, using the farthest "back" edge as your starting point.

Continue until your grid goes as far back into the distance as you want it to.

9. Finish up the edges, and erase all bits we only added to help us draw the grid.

Voila! We have created the perspective image of a grid parallel to the floor. (Or, if you turn the page sideways, to the side wall).

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