*** Problems on the use of perspective in art *** (For detailed citations of sources of illustrations, see: http://graphics.stanford.edu/courses/cs99d-01/bibliography.html) 1. How many vanishing points can there be in a perspective drawing? 2. Does a pair of lines parallel to the picture plane converge? -> Leonardo's On Painting, p. 63 3. How to avoid distortion of objects in wide-angle perspectives? o Leonardo's paradox - in wide-angle linear perspective views, objects near the edges of the canvas look distorted. Switching to a curved (cylindrical or spherical) perspective fixes this, but straight lines now appear curved. -> Dubery and Willats, row of columns o linear perspective, p. 84 o curvilinear perspective, p. 85 o Explanation: objects look distorted only if you move away from the proper eyepoint. But in large paintings, people do this. o Similarly, a perspective view displayed on a CRT is only correct from a single viewpoint. The same is true of movies in a theater. o Solution #0: enforce the eyepoint, e.g. using a peephole, as Brunelleschi did for the Baptistery panel o Solution #1: narrower angle of view, scaled up to canvas o Leonardo suggests standing 10-20x from object -> Caravaggio's The Supper at Emmaus, Gombrich's Shadows, p. 24 o limit of this is a parallel projection o Solution #2: shallow range of depths (except near edges) -> Canaletto's Venice: The Feast of St. Roch (1727), Dubery and Willats, p. 81 (B&W) o Solution #3: multi-viewpoint perspective -> Raphael's The School of Athens, Gardner, p. 742 o background architecture is wide-angle one-point o groups of philosphers in their own local perspective o notice sphere held aloft at right is not ellipsoidal