Receding spaces and divisions in parallel lines
Using foreshortening perspective to map out equally spaced divisions on a flat surface or plane.
All Tutorial Text & Images - Copyright © 2011 KHI, Inc.
In perspective drawing, creating equal divisions or "receding spaces" between parallel lines within a flat surface or plane is referred to as "foreshortening perspective," and is a simple matter when using a series of diagonal lines to calculate the spacing between objects. Giving the illusion of depth, this type of drawing technique is also referred to as "foreshortened perspective." This method of calculating equally spaced divisions is useful in drawing windows on a building, fence posts, telephone poles, floor tiles or anything else that resides on a vertical of horizontal plane and requires lines or objects to be equally spaced as they recede into the distance.
When drawing an object in perspective, that object appears to get smaller as it recedes towards a given Vanishing Point (infinity). This phenomenon is due to the fact that the "viewer" is at a steeper angle of view when looking an object that is in close proximity as opposed to an object of the same size that is farther away and therefor, viewed at a shallower angle.
Division Layout in 1 Point Perspective
As with all Perspective drawing techniques, we will start out with the ubiquitous perspective grid Fig. 1. In this case, we are using 1 point perspective. Only one vanishing point will be used and our flat vertical plane will emanate from that point forward. Our horizon line will be dead center of our POV (point of view). For additional information on creating a perspective grid go to the 2 Point Perspective tutorial.
We start by drawing our first vertical line (A). The placement of our second dashed line (B) is arbitrary, but the distance between lines A and B will be maintained and repeated throughout the entire plane.
Now we will start the process of duplicating the exact spacing of our first two lines (Fig. 2) creating the foreshortening perspective as the lines recede into the distance. Starting from the top of line (A) we will draw a diagonal line downward until it intersects with the horizon line and continues to point C.
From point C we will draw our third vertical line upward to point D (Fig. 3). We now have established our divisional spacing that could continue to infinity which is our right vanishing point along the horizon line.
From this point forward it is simply a matter of repeating the process for the total number of divisions required in our foreshortened receding space. In (Fig. 4) we are drawing our diagonal line from the top of line B through the centerline of line C and continuing until it intersects with our "ground" or "baseline." In Fig. 5 we are drawing our 4th division line.
Our last example (Fig. 6) shows a multitude of foreshortened divisions all of which are equally spaced along our vertical plane receding towards infinity.
Receding Spaces in 2 Point Perspective
In this section we will use the same technique of projecting diagonal lines but first we will need to fine a center point for our first division shown in Fig. 4. To locate the center point of our foreshortened vertical lines you will draw two diagonal lines (dashed) connecting all four corners of the divided space.
Next you will project a straight line from the vanishing point towards the intersecting diagonal dashed lines (Fig. 8). This will serve the same purpose as the horizon line did in the last segment.
Just as before we will project a series of diagonal lines to find the position of each new segment (Fig. 9). As you can see from the lines that recede towards the left vanishing point (L VP) this method works equally well on a horizontal flat plane.
Calculating The Depth of Multiple Squares
This same technique of foreshortened perspective can be used to determine the width and depth of multiple squares that are in randomized locations on a surface plane. In Fig. 10 or first square in the center foreground will determine the exact width and depth of every other square on our flat plane.
For this demonstration we will assume that all of the squares are of equal dimension (x). We start by will projecting a diagonal line from the lower left corner of the square through the upper right corner and beyond until it intersects with the horizon line (R VP). Next we will project the sides of the square to the horizon center point (C VP). Using (x) as our constant, we can locate our new square in any random location and by projecting parallel lines to both vanishing points we can determine the width and depth of our second "matching" square.
Calculating Equally-Spaced Divisions
In this next example we will create a series of equally-spaced, or equally-sized divisions on a perspective plane that is receding from the foreground to the background. To accomplish this you will need to create a ruler with equally-sized spaces, marks or divisions. In our example below, "X" represents a single division which is infinitely variable, and in this example, totally arbitrary. The ruler can be placed horizontally or vertically as long as it is either parallel to the horizon line, or perpendicular to the horizon line.
Our receding plane will be traveling rearward towards the right vanishing point. To determine the exact location of each division along the ground line (lower line) of our receding vertical plane we will draw a line from the left vanishing point to the first mark on the ruler (dashed line to the left). The we will create our first vertical division at the point where this line intersects with the ground line from the right vanishing point. Then, it is a simple matter of repeating these steps for each mark on the ruler until you have created the necessary number of divisions (darker line with green dots).
Technical Note: The following hardware and software was used in this tutorial: Apple Mac Pro, a Wacom Intuos 6x8 drawing tablet and Adobe Illustrator CS-CS5 or CorelDRAW vector drawing software.
All of the principles covered in this perspective foreshortening tutorial were utilized to create the floor and ceiling tiles seen in this line drawing of a hospital MRI room (screenshot above). By learning and following this basic set of drawing fundamentals you can create perspective illustrations of any subject, regardless of the level of complexity.
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