To draw grids using linear perspective, it is best to start with a square. The diagram above shows a perspective view of a room drawn in one-point perspective. After you have established a horizon line and a vanishing point follow this step by step procedure to create a gridded floor pattern:

1. Begin by creating a square plane in perspective. Remember that when drawing objects in perspective one must trust observed forms as models. You will find that when you look at a square in perspective it appears to be a very flat form in space.
2. Make marks at equal increments across the back edge of the square. You can use a ruler to mark off 1" increments or any regular measurement that you choose (my diagram uses 40 points for each segment, which is approximately 40/100ths of an inch).
3. Draw a line from the vanishing point through each point until it reaches the back of the square. Notice that the points where the lines meet the front edge of the square are further apart than the points at the back edge.
4. Draw a horizontal line across these lines indicating a row of tiles along the back edge of the square space that we are subdividing. Double check to be sure that you compare this placement to observed square spaces in perspective, the way we did in step 1.
5. Using the top left corner of the space as a staring point, draw a line from the top left corner through the bottom right corner of the small square in that corner of the drawing and continue out until it reaches the side of the square. This line will meet at the front right corner of the large square if it is a perfect square.
6. Draw a horizontal line at each point that the diagonal crosses the radiating lines that subdivide the large square. This will create a grid pattern.

This grid system can be carried into walls and ceiling areas to create grids on all planes. This may make it possible to systematically place objects in a space by using the grid on all planes.

An example of a gridded floor that is done in this manner is Botticelli's The Annunciation of 1489. By clicking on the smaller image you can inspect this floor in greater detail.