## Below Are Several Examples Of This Method Study The Various Applications   Suppose we wanted to divide face A of this object into two equal spaces, face B into four equal spaces, and the top into eight equal spaces.

BELOW is the solution when each face is viewed head-on.

AT RIGHT is the same solution in perspective.  STEP 2: Connect point 7 to opposite lower corner and continue to horizon line. This gives us a special vanishing point for all guide lines parallel to this one.

STEP 1: From lowest corner of face to be divided draw horizontal line and tick off the number of equal spaces desired (7 in this case).

STEP 3: Connect other six points to special vanishing point. These guide lines will intersect base line of object, creating seven equal spaces in perspective.

Note: The equal spaces ticked off in step 1 could be at any scale. Those shown are each spaces, but could be V4", etc. Naturally every spacing will shift the special vanishing point, but the resulting perspective spacing will always be the same.

Why this is so is explained in this top view. Let's divide the same face in two, using different spacings. From the lowest corner tick off two units of 1/2" each, two of 1" and two of 2". Now, connect each second tick to the far corner (3 lines shown dotted). Then, from the first ticks, draw lines parallel to these. Note that the second lines all intersect at the midpoint of the face. Therefore any of these spacings would work even though each resulting set of parallel-horizontal lines would have it own (special) vanishing point (see across page).

Suppose we wanted to divide face A of this object into two equal spaces, face B into four equal spaces, and the top into eight equal spaces.

BELOW is the solution when each face is viewed head-on.

AT RIGHT is the same solution in perspective.

Dividing A Surface Into Equal Spaces By Using A Measuring Line And A Special Vanishing Point

Naturally, this method works only when the number of spaces is 2, 4, 8, 16, 32, 64, etc. Suppose we wished to divide a face into 7 or 10 spaces. Then the following method should be used, for it works for any number of equal spaces.

img point for object*

STEP 2: Connect point 7 to opposite lower corner and continue to horizon line. This gives us a special vanishing point for all guide lines parallel to this one.

measuring line measuring line

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### Responses

• kiros
How to divide a space into eight equal spaces?
8 years ago