Foreshortening in cube drawings by children and adults

The lengths of lines and the sizes of angles were measured in freehand drawings of cubes produced by 190 children and 158 adults. The lengths of oblique lines depicting receding cube edges were foreshortened relative to horizontal lines showing nonreceding edges. In the drawings from children aged 9 and 10 years the obliques were foreshortened by about 40%, compared with 30% in adults' drawings. The amount of foreshortening was not correlated with the angle at which the obliques were drawn. Line lengths were also foreshortened in "transparent" drawings, which are often said to show "what is known" about cube structure. One explanation of the results is that line lengths are foreshortened by children and adults to create the visual impression of equal-length cube edges, even in transparent drawings. This foreshortening fits with how the receding edges of a square face of a cube project to a vantage point. Children and adults who use foreshortening are not depicting the structure of cubes by matching features such as equal-length edges with similar features in the physical lines on the page, as has been suggested in some recent approaches to drawing development.