Drawing objects of the same size equal distances apart

From Earnest Norling’s book “Perspective made easy” page 113, he has a brilliant illustration depicting the idea of equal distance.

This illustrates the idea of intersecting diagonals to help find equal distances when two points are known.  By drawing a line through the mid-point of the fence post and continuing out until it intersects with the baseline (or top line) then you can just draw a new vertical and all of the posts will be at the same distance from one another. This same procedure can be extrapolated to use in other perspectives as well.

Figure 1

This is a setting below the horizon, but it could just as easily be done above the horizon.

Step 1: After you have drawn your Horizon and have the Vanishing Point established, make a  dark blue “baseline and second line towards the horizon which fits parallel with the first line (in this case the line is Light Blue). You set the distance. There are ways to figure it out, but that is beyond the scope of this tutorial. Usually in art, you would observe the distance between the two parts an make that distance correct in the drawing.

Step 2: Make an X  (not shown) by starting at the top of the first object to the base of the second, then from the top of the second object to the base of the first. This line will bisect the widths of the first and second objects.

Step 3:Draw a line from the Vanishing point through the middle of the X. This is the mid-line. This will give you a line which bisects (divides into two equal halves) the dark blue “baseline”  and the Light Blue second line.

Step 4: Draw a diagonal from one end of the dark blue line through the mid-point of the second blue line… in this case the line is light green. This gives you the third distance just as it did in the diagram of the fence posts.

Step 4: A new horizontal line at that level will give you the pink third line.

Note if this process is continued by drawing a diagonal from the Light blue line (not shown), through the mid-point of the pink line, you get the purple line and on and on through the drawing.

It is important to notice if you extend all of the diagonals they are terminating at the same vanishing point .

Also note the distance doubles every time you draw a new diagonal. We’ll arbitrarily call the distance from the Dark Blue Baseline to the Light Blue Line (labeled 1) to be 10 feet. The next distance to the Pink Line is 20 Feet, and the next distance to the purple line is 40 feet, and to the Yellow Line is 80 feet. In this scale the 8th line would be about a mile away.  If  you changed the scale to each distance only equaled 1 foot, by the 12th line you would be a mile away!

Figure 2

The basic process is the same for the Vertical as it is for the horizontal.

• Draw the height of the first object, then set the vanishing point on the horizon. Draw a line from the top and base of the first object to the Vanishing Point on the horizon. This will give you the height of all the other objects. This vanishing point can be anywhere on the horizon, if it is a line which should relate to something already in your picture, you probably already have a vanishing point.
• Set your First distance – this is an arbitrary distance in most cases. There are methods to figure this out exactly, but it is more complicated than needed for this class.
• Make an X by starting at the top of the first object to the base of the second, then from the top of the second object to the base of the first. This line will bisect the heights of the first and second objects.
• Draw a line from the Vanishing point through the middle of the X. This is the mid-line.
• From the top of the first object, draw a line through where the mid-line crosses the second object to the base line. This is the base of the 3rd object.
• Draw a vertical line from the base of the 3rd object to the top vanishing point line.

Note: all of the diagonals will terminate at the same Vanishing Point. Also note the orange lines… the line drawn from the base of the line 1 through the mid-point of line 2 gives you the distance of line 3. A line drawn from the base of line 2 to the Vanishing Point will give you Line 4 and so on… in this case it is labeled 3 because it is the “third unit”.

When would this be useful?  How about if somewhere there were columns or arches and you wish to make them at the correct distance?  Let’s look at an example done in 1636 by the 17th-century Flemish artist Pieter Neefs the ElderAn Interior of a Gothic Church.  The same technique was used to draw the columns. All the distances are correct all the way back into the distance.  If someone nearly 400 years ago knew how to handle this perspective, there isn’t any reason you shouldn’t.
The text passage describes a method for drawing objects of the same size at equal distances apart using perspective techniques. It includes a step-by-step guide and an example of how this technique can be applied in art.
no_question

the passage does not contain any mathematical questions or provide answers to such questions. it is purely instructional and descriptive.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Drawing objects of the same size equal distances apart

From Earnest Norling’s book “Perspective made easy” page 113, he has a brilliant illustration depicting the idea of equal distance.

This illustrates the idea of intersecting diagonals to help find equal distances when two points are known.  By drawing a line through the mid-point of the fence post and continuing out until it intersects with the baseline (or top line) then you can just draw a new vertical and all of the posts will be at the same distance from one another. This same procedure can be extrapolated to use in other perspectives as well.

Figure 1

This is a setting below the horizon, but it could just as easily be done above the horizon.

Step 1: After you have drawn your Horizon and have the Vanishing Point established, make a  dark blue “baseline and second line towards the horizon which fits parallel with the first line (in this case the line is Light Blue). You set the distance. There are ways to figure it out, but that is beyond the scope of this tutorial. Usually in art, you would observe the distance between the two parts an make that distance correct in the drawing.

Step 2: Make an X  (not shown) by starting at the top of the first object to the base of the second, then from the top of the second object to the base of the first. This line will bisect the widths of the first and second objects.

Step 3:Draw a line from the Vanishing point through the middle of the X. This is the mid-line. This will give you a line which bisects (divides into two equal halves) the dark blue “baseline”  and the Light Blue second line.

Step 4: Draw a diagonal from one end of the dark blue line through the mid-point of the second blue line… in this case the line is light green. This gives you the third distance just as it did in the diagram of the fence posts.

Step 4: A new horizontal line at that level will give you the pink third line.

Note if this process is continued by drawing a diagonal from the Light blue line (not shown), through the mid-point of the pink line, you get the purple line and on and on through the drawing.

It is important to notice if you extend all of the diagonals they are terminating at the same vanishing point .

Also note the distance doubles every time you draw a new diagonal. We’ll arbitrarily call the distance from the Dark Blue Baseline to the Light Blue Line (labeled 1) to be 10 feet. The next distance to the Pink Line is 20 Feet, and the next distance to the purple line is 40 feet, and to the Yellow Line is 80 feet. In this scale the 8th line would be about a mile away.  If  you changed the scale to each distance only equaled 1 foot, by the 12th line you would be a mile away!

Figure 2

The basic process is the same for the Vertical as it is for the horizontal.

• Draw the height of the first object, then set the vanishing point on the horizon. Draw a line from the top and base of the first object to the Vanishing Point on the horizon. This will give you the height of all the other objects. This vanishing point can be anywhere on the horizon, if it is a line which should relate to something already in your picture, you probably already have a vanishing point.
• Set your First distance – this is an arbitrary distance in most cases. There are methods to figure this out exactly, but it is more complicated than needed for this class.
• Make an X by starting at the top of the first object to the base of the second, then from the top of the second object to the base of the first. This line will bisect the heights of the first and second objects.
• Draw a line from the Vanishing point through the middle of the X. This is the mid-line.
• From the top of the first object, draw a line through where the mid-line crosses the second object to the base line. This is the base of the 3rd object.
• Draw a vertical line from the base of the 3rd object to the top vanishing point line.

Note: all of the diagonals will terminate at the same Vanishing Point. Also note the orange lines… the line drawn from the base of the line 1 through the mid-point of line 2 gives you the distance of line 3. A line drawn from the base of line 2 to the Vanishing Point will give you Line 4 and so on… in this case it is labeled 3 because it is the “third unit”.

When would this be useful?  How about if somewhere there were columns or arches and you wish to make them at the correct distance?  Let’s look at an example done in 1636 by the 17th-century Flemish artist Pieter Neefs the ElderAn Interior of a Gothic Church.  The same technique was used to draw the columns. All the distances are correct all the way back into the distance.  If someone nearly 400 years ago knew how to handle this perspective, there isn’t any reason you shouldn’t.
user
The text passage describes a method for drawing objects of the same size at equal distances apart using perspective techniques. It includes a step-by-step guide and an example of how this technique can be applied in art.

TYPE: NO_QUESTION

The passage does not contain any mathematical questions or provide answers to such questions. It is purely instructional and descriptive.