------------------------------------------------------------------------------- CS 99D - Perspective lecture #2, January 16, 2001 Marc Levoy Stanford University (c) 2001 (with corrections, March 14, 2003) ------------------------------------------------------------------------------- ==> Give modern constructions for 1,2,3-point perspective. ------------------------------------------------------------------------------- *** Early perspective masterpieces *** 1428 Masaccio's Holy Trinity, Santa Maria Novella, Florence -> Gardner, fig. 21-25, p. 698, or --> Cole, p. 14-15, with reconstructed 3D model "assertion of the intellectual and visual power of perspective" - Kemp, p. 17 o perspective is a player in the artistic programme: o virtual wall, which continues the plane of the real wall, separates the mortal from the spiritual world o some errors - deliberate adjustments? o antique architecture - collaboration with Brunelleschi? 1425-52 Ghiberti's Gates of Paradise, Baptistery, Florence -> Gardner, fig. 21-8, p. 686 -> Closeup and analysis sketch, panel of Jacob and Esau, in Kemp, p. 25 or much better overview and closeup (same panel) in Field, p. 19 o won a competition for first set of doors against Donatello, Brunelleschi, and others o second set (this set) took 25 years o Michelangelo said they could be the "Gates of Paradise" o again, perspective is a player in the programme: o allows Ghiberti to place subscenes at various depths Renaissance treatises on art: o inspired by Vitruvius's Ten Books of Architecture: o only surviving ancient treatise on art -> Read table of contents from Vitruvius's Ten Books o casts a broad net: o moral conduct -> artistic taste -> construction details o breadth became a matter of pride in the Renaissance o Ghiberti ties science to art in two ways: o called on artists to become learned in *all* arts, 3rd section, Commentaries is anthology of writings on optics o appealed to "rational considerations" (-Ghiberti) o Italian (or German) for locals, Latin for international audience 1474 Piero della Francesca's De prospectiva pingendi ("on perspective for painting") o in Latin and "Tuscan" o first book was pure math - "On the Five Regular Solids" (tetrahedron, octahedron, icosahedron, cube, dodecahedron) -> Field, p. 69 o hard shapes like angles, circles, column capitals -> column capital, Field, p. 105 o very hard shapes like the human body -> tilted face, Field, Field, p. 111, used in -> Resurrection of Christ, Gardner, p. 702 or face and picture together (B&W) in Kemp, p. 34 o supposed self-portrait of Piero, according to Cumming's Annotated Art Masterpieces (continued): 1455 Piero della Francesca's Flagellation of Christ ->Cole, p. 18-19, with partially reconstructed 3D model o compare to column capital in Field o again, perspective is a player in the programme: o allows Piero to place a local light on Christ alone 1474 Andrea Mantegna's ceiling, Palazzo Ducale, Mantua -> Gardner, p. 726 o first trompe l'oeil painting o adjustments - feet too small o similar adjustments in Dead Christ (1501) in reading in Solso -> Gardner, p. 727 (B&W) ------------------------------------------------------------------------------- *** Problems on the use of perspective in art *** Problems of technique: o keeping all construction lines within the canvas o for wide-angle shots, can fold construction lines o for telephoto shots, no solution? Problems of style: o converging orthogonals must get thinner o need for multiple levels-of-detail Problems of correctness: 1. How many vanishing points can there be in a perspective drawing? 2. Does a pair of lines parallel to the picture plane converge? o Consider buildings seen from across the street in wide-angle. -> Leonardo's On Painting, p. 63 ==> Prove that spacing of projected mullions stays constant on a parallel picture plane using plan view and similar triangles. o In this case, faraway mullions do not shrink on the canvas, Q. Yet their visual angle does shrink. How does this occur? A: They shrink when the canvas is viewed. ==> Demonstrate using reconstruction of Durer's artist's glass o Review difference between projection onto plane: -> drawing from Piero (1474), Kemp, fig. 32, p. 28 and visual angle when viewed: -> drawing from Euclid (3c BC), in Kemp, fig 31, p. 27 o architect's camera used to eliminate third vanishing point Problems of application: 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, great figures 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 True, there is no distortion of mullions on a parallel picture plane. Distortion in wide-angle views is caused by parallax between objects at *different* depths, i.e. having orthogonals o Solution #0a: enforce the eyepoint, e.g. using a peephole, as Brunelleschi did for the Baptistery panel o Solution #0b: enjoy the distortions -> van Gogh's Vincent's Room (1888), Gombrich, SoA, fig. 357, p. 549 (or Dubery and Willats, fig. 88, p. 89 (B&W)) o drawing with a pencil at arms length -> cylindrical perspective! Willats, p. 90-91 o Solution #1: narrower angle of view, scaled up to canvas o Leonardo suggests standing 10-20x from object, p. 61 -> Caravaggio's The Supper at Emmaus, Gombrich's Shadows, p. 24, (or Dubery and Willats, p. 80 (B&W)) o limit of this is an oblique projection -> Mughal miniature, Indian (or Persian?) Dubery and Willats, p. 25 o vertical oblique 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, fig. 22-15, p. 742, or Annotated Art, p. 32-33 o background architecture is wide-angle one-point o groups of philosphers in their own local perspective o notice sphere held aloft (by Ptolemy) is not ellipsoidal o portraits of contemporaries o Plato = Leonardo o Euclid = Bramantes o Heraclitus = Michelangelo (as a stonemason) o Raphael himself at right, looking out -> Also Leonardo's Last Supper, Gombrich SoA, p. 299++ (fold-out) (or L'Ultima Cena, p. 99) -> Disney's Pinocchio, Disney book, p. 161 -> Salesin et al, Proc. Sig97, p. 243 ------------------------------------------------------------------------------- *** Sidelight: non-perspective projections *** Projections for curved surfaces: ~1507 projection onto a curved vault -> Leonardo's diagram, in Kemp, p. 50 Perspective-in-perspective (so-called anamorphic): 1533 Hans Holbein (the Younger)'s The Ambassadors -> Cole, pp. 32-33 Modern uses of unusual projections: o Mercator and other projections for mapmaking o cinorama movies using an anamorphic lens o computer graphics for IMAX screens -------------------------------------------------------------------------------