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Constructing the floor grid for a picture

We can put all the theory together to create a foreshortened floor grid from a plan grid to support any picture, those of an artistic temperament may prefer to mould the plan by eye:

1 Create two horizontal guides to represent your horizon (eyeball height), ground line and a vertical one for central line of sight. These in turn define the station point and primary vanishing point by their intersections. Now for the clever bit, a superimposed plan view. From the station point construct a regular three sided polygon with one apex at the station point such that all sides equal the width of your picture. This marks the angle of vision with the picture plane marked along the top. Don't worry that it seems in an odd position.

2 Now construct a square plan grid above it as indicated by blending two horizontal lines the width of the picture and the same distance apart, cloning the blend and turning it 90 degrees to form a square grid. Now we need to translate the grid into a foreshortened one to fit into the picture, by constructing its foreshortened outline and moulding it into place.

3 Run two vertical guides to mark the edges of the plan grid. The intersections of these with the ground line will pinpoint the front corners of the foreshortened grid since they are also on the picture plane. Since we are dealing with single point perspective the sides of the foreshortened grid will lie on lines joining these to the central vanishing point, shown left in green.

4 Now in plan mode, add the lines of sight joining the station point to the back corners of the grid and 5 where they intersect with the picture plane (bottom of grid) insert two vertical guides. 6 Where these intersect with the green lines are the rear corners of the foreshortened grid. The shape of the grid is indicated in orange, all we have to do is to fit a copy of the grid using the mould tool. Save a copy of the file at this point as a template for future use. It's worth noting that you can add other markings to the grid before compressing.

For now just Clone (Ctrl k) the grid and use the arrow keys to nudge it down into the base of the picture. Select the Mould Tool and click the floor perspective. With the selector tool nudge and squash the grid, using the vertical handles, to fit between the horizontal lines of the orange shape. Make sure the edit points button is pressed and drag the perspectives vanishing point to line up with that of the drawing. You might need to repeat the operation for fine tuning, until the mould fits exactly into the shape.

The plan grid, floor grid and picture plane are shown in their true relationship in 3D below. The original plan grid should be retained to measure the dimensions of objects you wish to place in the picture.

Adding a side grid.

Take the plan grid, clone it, rotate it 90 degrees. Using the arrow keys on your computer's keyboard, nudge it to the side so that its bottom corner coincides with the front corner of the plan grid, then stretch, with the width handles only, until the smaller side coincides with the vertical guide. Now drag the vanishing point to align with the floor plan's vanishing point, and the back corners will touch. Because we didn't change the height of the grid, the squares will represent the same distance as do those of the plan and floor grids.

You could go on to construct a tunnel in the same way.

Fitting objects into grids.

You can fit any plans for your picture into this grid quite simply by placing them into a square and moulding that to fit the corresponding squares on the floor grid. Whatever the vanishing points of your plan, the square around it will have a single point perspective which lines up with that of the floor grid. Any objects within it will realign correctly when the single point is manipulated. 1 Put the plans into a square, place it on the plan grid and count the squares. 2 Apply the floor perspective. 3 Bring the front edge down and locate it where required on the grid (in this case sized 9 grid squares). Adjust width if necessary to get the front edge to the correct number of squares. 4 Compress the plan with the selector tool so that it fits within the same number of squares deep. 5 Drag the vanishing point up to align with the grid's vanishing point. Make fine adjustments if required. You could extend each line to the horizon to locate its own vanishing point.

Now we are ready to build upwards.