Activity Sheet: Perspective Drawing
The following instructions will take you through the process of using The Geometer's
Sketchpad® to make a two-point perspective drawing of a rectangular prism (a simple box) and
ask you to transform the result, observing the results of the transformation. Commands, tools,
and toolbar menus are all in bold.
A two-point perspective drawing is based upon a single, horizontal line that is referred to as the
"horizon line." Two points, called the vanishing points, are chosen on the horizon line, and give
two-point perspective drawings their name. All vertical lines in such drawings are constructed
perpendicular to the horizon line. All horizontal-appearing lines in such drawings intersect the
horizon line at one of the vanishing points.
First, activate the Line Tool and make a horizontal line (line AB) to act as the horizon line. (If
the Line Tool is not showing click and hold on the Ray or Segment Tool and select the Line
Tool from the horizontal menu that appears.)
Figure 1
Second, construct a vanishing point (C) on this horizon line by using the Arrow Tool to select
the line, opening the Construct menu, and choosing the Point On Object option. Repeat to
construct the second vanishing point (D). Move these points apart, so that one is near the left
edge of the screen and the other is near the right edge of the screen.
Charles A. Dana Center
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Figure 2
Third, construct the first vertical line. To do this, construct another point (E) on the horizon line
to be the point of intersection with this vertical line. Then select both this point and the horizon
line. Remember to shift-click to select more than one object at a time. Finally, open the
Construct menu and select Perpendicular Line. Move this vertical line near the center of the
screen. This line represents the edge of the box that is closest to the viewer. Since there will be at
most three vertical lines of the box visible to the viewer, repeat the steps (constructing points F
and G on the horizon line) to construct two more lines perpendicular to the horizon line.
Charles A. Dana Center
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Figure 3
Now you are ready to make the lines that are horizontal in the object. Remember that these lines
must intersect the horizon line at one of the vanishing points. To make the upper edges of the
box, construct a point (H) on the central vertical line. Then use the Line Tool to draw lines from
this point to each of the vanishing points (C and D). To identify the intersection points (J and K)
of this line with the other two vertical lines, use shift-click to select a pair of intersecting lines,
open the Construct menu, and choose the Point at Intersection option.
Charles A. Dana Center
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Figure 4
Repeat these steps (constructing point L and identifying points M and N) to form the lines that
contain the bottom edges of the box.
Figure 5
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It is a good idea now to make all of our lines dotted and hide all the point labels. Activate the
Line Tool, open the Edit menu, and choose the Select All Lines option. Then open the Display
menu, choose the Line Weight page, and select the Dashed option. To hide the point labels,
activiate the Point Tool, open the Edit menu, and choose the Select All Points option. Then
open the Display menu and choose the Hide Labels option.
Figure 6
At this point, go to the Display menu, open the Line Weight page, and select the Thick option.
Then change the Line Tool so that it draws segments instead of lines. You are now ready to
draw the "front" edges of the box.
Charles A. Dana Center
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Figure 7
To complete the rectangular prism, construct four dotted lines, one with each endpoint of the outside
vertical lines and the vanishing point it is not already connected to. Identify the points of intersection
(Q and R) of the pairs of lines. Points Q and R are the other two vertices of the rectangular prism.
Figure 8
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Construct thin segments joining points Q and R to the appropriate vertices of the rectangular
prism to represent the "back" edges of the prism. Hide the labels for points Q and R.
Figure 9
After drawing all the segments, the box is completed and the entire drawing can now be
manipulated in a variety of ways. Write a short sentence stating the effect that each of the
following transformations has on the drawing.
1.
Select the central vertical line and move it to the left and to the right. (For an example,
see Figure 10.)
2.
Select the edge of the prism that appears closest to you and move it up and down (in
order to change the relationship of the horizon line to the object). Make sure you have
selected only the segment, and not the entire line. (For an example, see Figure 11.) As
you move it higher and lower, you can see if you have not outlined the entire top or
bottom yet!
3.
Select one of the vanishing points and move it left and right. (For an example, see Figure
12.)
4.
Select one of the other vertical lines and move it.
5.
Select the horizon line and move it.
6.
Select any point, any line, or any segment and move it.
Charles A. Dana Center
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Figure 10
Figure 11
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Figure 12
Charles A. Dana Center
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