5
GEOMETRIC TOOLS: DIAGONALS, SQUARES, AND CUBES
DIAGONALS
In addition to their use in constructing perspective grids, diagonals serve several useful functions in the drawing of perspective views.
One basic rule is that diagonals of any rectangle will cross at the center of that rectangle; this is also true of rectangles viewed in perspective.
Finding the center automatically means that rectangles can be subdivided and multiplied geometrically in the perspective system, as detailed in the following two exercises.
Dividing a Rectangle with Diagonals
1. Cross two diagonal lines to find the center.
2. Pass a line, parallel to the axis to be divided, through the center.
3. Pass a line through the center perpendicular to the first center line, to quarter the rectangle.
4. Repeat the procedure in the newly divided axis to continue the subdivisions.
Adding Rectangles with Diagonals
1. Divide the rectangle in half, using diagonals.
2. Draw a diagonal from one corner through the halfway ...
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