# 3-D Drawing and Geometry

### by Cathi Sanders

#### A Math Forum Summer Institute Project

1998 Summer Institute || Participant Projects || List of Participants || Sum98 Staff || Agenda

## One-Point Perspective Drawing

This photograph of a New York City street in the early 1900s comes from Dale Abalos' site, Architecture on the Web. It represents a type of perspective called One-Point Perspective. One-point perspective and two-point perspective drawings are shown below. Compare their appearances and features:

Two-point perspective gets its name because there are two vanishing points: one on the left and one on the right. This is the most common type of perspective used in architectural drawings and in artwork. It is what we usually see in the real world or in a photograph. There are two sets of "vanishing lines," one to the left vanishing point (VPL) and the other to the right vanishing point (VPR). Lines that are vertical on the real object appear as vertical lines on the drawing.

In one-point perspective, however, there is only one vanishing point (labelled just VP) and therefore only one set of vanishing lines. In the place of the second set of vanishing lines we have a set of parallel horizontal lines. Lines that are vertical on the real object appear as vertical lines on the drawing, as they did in the two-point perspective drawing.

In the photo below of the Eurostar, the first direct passenger train to connect Brussels and Paris with London via the Channel Tunnel, we see a train and railroad track disappearing into the distance, an example of one-point perspective:

Read all the technical details on Clem Tillier's excellent Eurostar pages. One-point perspective is also often used for Interior Design, to draw the interiors of homes or offices.

To illustrate two-point perspective as seen in a photograph, the Vanishing Lines have been drawn to the Vanishing Point in the picture of the New York city street:

To draw a box in one-point perspective, first draw the front of the box as a rectangle, using horizontal and vertical lines. Then choose a point to be the vanishing point. Draw lines radiating out from the vanishing point and passing through each of the four corners of the front of the box, as shown in step 1 below. The dotted line would actually not be seen if the box were solid, so we normally don't draw that edge. Then draw a horizontal line to represent the back top edge of the box, and a vertical line for the back right edge as shown in step 2 below. The dimensions of the box can, of course, be anything you like.

You can draw many different things in perspective, using the techniques described above for a simple box. A castle, for example, would be made up of different shaped "boxes": prisms, pyramids, cones and cylinders.

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