1. The depth locations of the mullions (and screens) are found as before (see pp. 70, 71) — by ticking off three equal spaces on a measuring line and drawing converging lines to a special vanishing point.
2. The left to right locations of the screens are then found by means of another measuring line ten units long (2 + 2 + 4 + 2). (Units may be at any scale. Here, each unit= V&"«)
3. The location of this measuring line is determined by sliding a ruler back and forth until the desired number of units fits exactly between projections of the floor lines.
In this top view, the elements receding from observer are unequally spaced. But, as we have seen on the previous page, the same method can be used.
In this top view, the elements receding from observer are unequally spaced. But, as we have seen on the previous page, the same method can be used.
Again the depth locations are found by ticking off the appropriate spaces along the measuring line, connecting the last tick with room corner, and then all other ticks to the special vanishing point. This locates spacing along the left wall base, from which it is carried across the room. The left to right locations are the same as in the case above and are found as above.
Another Way Of Getting Depths: The Sliding Ruler And Diagonals Method [73]
Suppose we wanted 5 equal vertical divisions in this rectangle (to draw, for instance, 5 equally-thick books).
STEP 1: Simply tick off the required spacing on some vertical line by sliding a ruler (as on the previous page) to find a position where 5 equal units fit. (Note that either 5 @ 1/2" or 5 @ 3/g" would be o.k.)
STEP 2: Converge each tick to vanishing point at right.
STEP 3: Draw diagonal as shown.
STEP 4: Draw vertical lines at each point of intersection. These will correctly demarcate 5 equal divisions in perspective.
Why this is so is explained by these front views of various rectangles. The diagonals always divide the adjacent sides proportionately. In other words, by means of the diagonal the spacing along a vertical edge is transferred proportionately to a horizontal edge.
Suppose, instead of being divided into equal spaces, the rectangle were to be divided unequally. For example, on the same 5-unit-long wall let's draw a 2-unit door located 1 unit away from the front end. The drawings at right show that the same method can be used for unequal spacing.
(Note: always start vertical spacing ticks from the same top or bottom edge as diagonal. E.g., at far right the diagonal starts at bottom, therefore the 1-unit tick also starts there.)
This method is also applicable to horizontal planes such as a floor. Again, equal or unequal spacing can be determined.
For instance, let's divide both the depth and width of this plane into 5 equal spaces.
STEP 1: 5 spaces @ fit here and so can be used to divide the width. (Or use 5 units @ below.)
STEP 2: Draw guide lines to vanishing point, then draw diagonal.
STEP 3: Draw horizontal lines at intersection points. These are the required 5 equal spaces in depth.
Another Way Of Getting Depths: The Sliding Ruler And Diagonals Method [73]
Suppose we drew one shape, such as rectangle A, and wished to repeat it (for instance, in order to draw a line of cars on a road). If the rectangles were touching, the method of diagonals shown on page 69 could be used, but since they are not, another method is needed.
diagonals vanishing point
STEP 3: Draw front line of next shape (shown dark). Then from point 1 draw line to diagonals' vanishing point. Intersection at point 2 locates the back line and thereby creates a second rectangle equal to the first.
STEP 1 : Draw the diagonal of the first rectangle and extend it to the horizon line. This locates the vanishing point for this and all other lines parallel to it.
STEP 2: Extend the sides of rectangle A to their vanishing point. These are the "width guide lines" for all rectangles in line with the first.
STEP 4: For other rectangles, follow the same procedure. Identical diagonals will produce identical rectangles.
This method will also work for vertical planes, such as a row of building facades, sides of trucks, etc.
The procedure is exactly as above and the diagram is identical. (Revolve this book 90 degrees and see.)
Note that the horizon line of the first case now becomes a vertical line. But like the horizon line, this vertical receives all lines on, or parallel to, the wall plane. The diagonals, therefore, converge to a point on this line as shown. (If the other set of diagonals (shown dotted) were used, their vanishing point would be above eye level but on the same vertical line.)
diagonals vanishing potnt
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