What is “Perspective?”• A mechanism for portraying 3D in 2D• “True Perspective” corresponds toprojection onto a plane• “True Perspective” corresponds to an idealcamera imageViewTransformations• 3D world– Determine 3D camera viewpoint andorientation– Project 3D to 2D– Map 2D representation to physical device– Go to notesViewTransformations• ViewportOrthographicEngineering DrawingAASection AAIsometric ProjectionIsometric ViewCavalier ProjectionCabinet ProjectionPositioning the Camera• Use gluLookAt to specify– Eye location– “Look-at” point– “up” vector• gluLookAt(10,10,10,1,2,3,0,0,1);– Eye is (10,10,10)– Look at point is (1,2,3)– Up is (0,0,1)• Usually done in GL_PROJECTION matrix and combinedwith perspective matrixFrustumPerspective ProjectionEye = eGaze = LookAt = gUp = yDistance to viewplane = dZ = distance to object on z axisysgeydzviewplanePerspectiveVanishing Points:One Point PerspectiveVanishing Points:Two Point PerspectivePerspective in ArtFirst ever painting (Trinity with the Virgin, St. John and Donors)done in perspective by Masaccio, in 1427.Perspective in ArtA painting (The Piazza of St. Mark, Venice) done byCanaletto in 1735-45 in one-point perspective.Perspective in ArtPainting in two point perspective by Edward HopperThe Mansard Roof 1923; Watercolor on paper, 13 3/4 x 19 inches; The Brooklyn Museum, New YorkPerspective in ArtA painting (City Night, 1926) by Georgia O'Keefe.Approximately in three-point perspective.Many Kinds ofPerspective Used• Mechanical Engineering• Cartography• ArtPerspective in Art• Naïve (wrong)• Egyptian• Cubist (unrealistic)• Esher• Miro• MatisseEgyptian Frontalism• Head profile• Body front• Eyes full• Rigid styleUccello's (1392-1475)handdrawing was thefirst extant complexgeometrical formrendered according tothe laws of linearperspective(Perspective Study ofa Chalice, Drawing,Gabinetto dei Disegni,Uffizi, Florence, ca1430 1440)23Perspective in Cubism Braque,GeorgesWomanwith aGuitarSorgues,autumn1913Perspective in CubismPablo Picaso,Madre con niñomuerto (1937)26Pablo PicasoCabeza de mujerllorando conpañuelo27Perspective (Mural) GamesM C Esher,AnotherWorld II(1947)PerspectiveM.C. Escher,AscendingandDescending(1960)M. C. EsherM.C. Escher,AscendingandDescending(1960)M. C. Esher• Perspective is “local”• Perspective consistency is not “transitive”• Nonplanar (hyperbolic) projectionNonplanar ProjectionM C Esher,Heaven andHellNonplanar ProjectionM C Esher,Heaven andHellDavid McAllisterThe March ofProgress,(1995)Joan MiroThe TilledFieldFlatPerspective:What cuesare missing?Henri Matisse,La Lecon deMusiqueFlatPerspective:What cues aremissing?36Henri Matisse, Danse II (1910)37Norway is at High LatitudeEngineeringDrawing:ExplodedViewUnderstanding3D Assembly in a2D Medium40Credits• Slides and text– Rich Riesenfeld’s Introduction to CG slides– SIGGRAPH Educators Hypercard slides•