Where do people draw lines?: technical perspective
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o n c e u P o n a time, computer graphics focused exclusively on realism and the generation of synthetic images that follow the laws of optics. The field eventually realized that other pictorial styles, such as line drawing, offer compelling depictions that can be more visually economical, better at focusing attention and abstracting out unimportant areas, and be more aesthetically pleasing. After all, a significant amount of the pictures generated by artists and designers are not photore-alistic; indeed, a great many of them are line drawings. For example, educational diagrams and user manuals often use such simplified style to better eliminate superfluous detail and focus attention. The breadth of situations in which line drawings are used makes it important to develop algorithms to generate them either automatically or in a user-assisted manner. Inspired by artists' work, a new sub-field called non-photorealistic rendering has emerged that seeks to imitate traditional media such as pencil drawing or oil painting. Whereas this new area has contributed exciting algorithms and vastly broadened the variety of visual styles that can be created with computers, the establishment of clear problem statements and evaluation metrics has proven challenging. In contrast to photorealistic computer graphics, which can be formulated as the solution of the light propagation equation, non-photorealistic styles are elusive. Consider line drawing. What is a set of line strokes that can convey a 3D shape from a given viewpoint? This issue touches upon art and perception, but these two fields offer few answers. The effectiveness of line drawing has been demonstrated with perceptual studies, but the question of what lines should be drawn was ignored and such studies relied on hand-drawn pictures for which the mathematical link between lines and shape cannot be easily investigated. Computer graphics researchers have had to base line drawing algorithms on hypotheses and intuitions about the relationship between local properties of a shape and the location of appropriate lines. Before computer graphics became interested in the issue , the great mathematician David Hilbert hypothesized that differential geometry holds the answer and that lines should be drawn at so-called par-abolic curves. However, once computers enabled the automatic extraction of such curves from 3D models, it became clear they do not lead to compelling drawings. New definitions of lines based on a variety of differential geometry properties were proposed and the quality of computer-generated drawings improved. We now have many available …