In the Middle Ages, much of the art was commissioned by the Roman Catholic Church. An interesting thing about art of this time was that the people were often sized by their importance. But, check out the perspective in the drawing to the left. You can almost guess where the vanishing point is.

As art moved into the Renaissance period, many artists were also architects and engineers. Geometry was a tool for them to make objects look realistic even though they were painted on a flat surface. They began to pay attention to the viewer’s perspective. They knew from geometry that objects closer to them should be bigger than similar objects that were farther behind. Check the archways in the picture to the left.

Drawing parallel lines directly in front of us seem to meet at a point called the vanishing point as we look farther away. Check out the walkway under the arches and the drawing of the box.

One of the simplest objects to draw with perspective is a solid box. Follow the steps below, using geometer’s sketchpad to draw a box.

Step 1: In one-point perspective drawing, you’ll be using solid lines for lines you can actually see and dotted lines to represent the parts of the box that you could not actually see from the front. Horizontal lines are all parallel and the lengths of the vertical lines are determined by the heights between the vanishing lines.

Draw a horizon line. Hold down the shift key while drawing the line and you can get a nice horizontal line. Put a point on your line. – the vanishing point.
Draw a rectangle for the front face of your box. To do this, draw a horizontal SEGMENT. Change the line width to thick (DISPLAY – Line width – thick). Select the segment and one endpoint. CONSTRUCT a perpendicular line. Select the other endpoint and the first line and CONSTRUCT another perpendicular line. Pick a point on one of the perpendicular lines and the original line and construct a parallel line. Make a point at the intersection of all of the lines. Select and hide the lines (DISPLAY – hide lines) and then draw segments to create the rectangle.

figure 1

Step 2: Create the edges of your box so that they appear to be farther from the view point, draw lines called vanishing lines. To do this,

Select a corner of the rectangle and the vanishing point.
CONSTRUCT segment.
Change the solid lines to dotted lines (DISPLAY – line width – dotted).
Connect the rest of the corners of the rectangle to the vanishing point with dotted lines.

figure 2

Step 3: Create the back of the box. The labels/colors are for reference only. You do NOT have to label or color your diagram!

Put a POINT E on the top left dotted line that connects the top of the rectangle to the vanishing point – the red dotted line in figure 3 (yours is blue!).
Select segment AB and point E and CONSTRUCT – parallel. Change the line width to thin (DISPLAY – Line width – thin).
Select line EF and the right top red dotted line and CONSTRUCT intersection to create point F.
Hide the parallel line EF and create a segment from point E to point F.
Select segment EF and point E. CONSTRUCT perpendicular.
Change the line width to thin (DISPLAY – Line width – dotted).
Select segment EF and point F. CONSTRUCT perpendicular.
Select line EH and the bottom (blue) dotted line and CONSTRUCT intersection (point H).
Select line FG and the bottom (blue) dotted line and CONSTRUCT intersection (point G).
Select the perpendicular lines (EH and FG) and DISPLAY – hide lines.
CONSTRUCT segment EH.
Change EH to a dotted line (DISPLAY – line width – dotted)
Construct segments HG and FG.
Select point A and point E and CONSTRUCT segment AE.
Change AE to a thin line (DISPLAY – line width – thin)
CONSTRUCT segment FB.

figure 3

Step 4: Finish the box.

Select point A and point E and CONSTRUCT segment AE.
Change AE to a thin line (DISPLAY – line width – thin)
CONSTRUCT segment FB.
To get a different perspective, select the vanishing point and drag it around to change your point of view!
Show the teacher so that it can be checked and points can be given.
You can hid the extra lines if you’d like….
Select the dotted lines that are connected to the vanishing point.
Hide lines (DISPLAY – Hide lines)
Your box is done.

figure 4

Now, try to draw this one using one-point perspective. (Start by drawing the horizon line with a vanishing point.
OR
Draw a picture of your own design using one-point or two-point perspective.

Show the teacher so that it can be checked and points can be given.

Remember you can pull on the vanishing point and change your point of view….try different viewpoints!