What can drawing tell us about our mental representation of shape?

When we draw or sketch a three-dimensional object, what aspects of its geometric structure do we usually choose to depict and how are these depictions executed? More importantly, what can these renderings tell us about our mental representation of these shapes? Art instruction literature and practice is replete with techniques for depicting objects. Not surprisingly, in such a large variety of sources there is a large amount of contradictory advice. Despite this, it is obvious that even the simplest and most naïve drawing can convey information about shape. Willats et al. have investigated a wide variety of spatially representational drawing techniques and have developed a broad taxonomy based around them. We are interested in furthering our understanding of the mental representation of objects via direct comparison of drawing production with the depicted objects. We performed a series of experiments designed to correlate the markings made when depicting an object with the object's underlying differential structure. In one scenario, subjects were shown two-dimensional renderings of random, smooth, three-dimensional objects from a dynamically changing view point. As there was no fixed viewpoint the subject couldn't depict the object by simply replicating image information. (Many classical drawing techniques suggest this sort of ‘drawing from the image’.) The resulting drawings are, therefore, likely to be based on a three-dimensional mental representation derived during the viewing period. In other conditions, subjects were shown static boundary contours, static shaded images, dynamic images with subject-controlled viewpoint, and physically realized three-dimensional models. Each of these conditions provides a different variety and quantity of image information to the illustrator. Results from each are compared to contrast the information derived and depicted directly from the optical image with the information available in some higher-level representation.