Student Name Server Spring 2005Utah School of Computing1 What is “ Perspective ?” A mechanism for portraying 3D in 2D “ True Perspective ” corresponds to projection onto a plane “ True Perspective ” corresponds to an ideal camera image

Student Name Server Spring 2005Utah School of Computing2 Differert Perspectives Used Mechanical Engineering Cartography Art

Student Name Server Spring 2005Utah School of Computing3 Perspective in Art “Naïve” (wrong) Egyptian Cubist (unrealistic) Esher –Impossible (exploits local property) –Hyperpolic (non-planar) –etc

Student Name Server Spring 2005Utah School of Computing4 “ True ” Perspective in 2D (x,y) p h

Student Name Server Spring 2005Utah School of Computing5 “ True ” Perspective in 2D

Student Name Server Spring 2005Utah School of Computing6 “ True ” Perspective in 2D This is right answer for screen projection

Student Name Server Spring 2005Utah School of Computing7 “ True ” Perspective in 2D

Student Name Server Spring 2005Utah School of Computing8 What is “ Perspective ?” A mechanism for portraying 3D in 2D “ True Perspective ” corresponds to projection onto a plane “ True Perspective ” corresponds to an ideal camera image

Student Name Server Spring 2005Utah School of Computing9 Many Kinds of Perspective Used Mechanical Engineering Cartography Art

Student Name Server Spring 2005Utah School of Computing10 Perspective in Art Naïve (wrong) Egyptian Cubist (unrealistic) Esher Miro Matisse

Student Name Server Spring 2005Utah School of Computing11 Egyptian Frontalism Head profile Body front Eyes full Rigid style

Uccello's ( ) hand drawing was the first extant complex geometrical form rendered according to the laws of linear perspective Perspective Study of a Chalice, Drawing, Gabinetto dei Disegni, Uffizi, Florence, ca 1430) 12

Student Name Server Spring 2005Utah School of Computing13 Perspective in Cubism Woman with a Guitar (1913) Georges Braque

Madre con niño muerto (1937) 14 Pablo Picaso

Pablo Picaso, Cabeza de mujer llorando con pañuelo 15

Student Name Server Spring 2005Utah School of Computing16 Perspective (Mural) Games M C Esher, Another World II (1947)

Student Name Server Spring 2005Utah School of Computing17 Perspective Ascending and Descending (1960) M C Escher

Student Name Server Spring 2005Utah School of Computing18 M C Escher Perspective is “ local ” Perspective consistency is not “ transitive ” Nonplanar ( hyperbolic ) projection

Student Name Server Spring 2005Utah School of Computing19 Nonplanar ( Hyperbolic ) Projection M C Esher, Heaven and Hell

Student Name Server Spring 2005Utah School of Computing20 Nonplanar ( Hyperbolic ) Projection M C Esher, Heaven and Hell

Student Name Server Spring 2005Utah School of Computing21 David McAllister The March of Progress, (1995)

Student Name Server Spring 2005Utah School of Computing22 Joan Miro: Flat Perspective The Tilled Field What cues are missing?

Henri Matisse, La Lecon de Musique Flat Perspective: What cues are missing? 23

Student Name Server Spring 2005Utah School of Computing24 Atlas Projection

Student Name Server Spring 2005Utah School of Computing25 Norway is at High Latitude There is considerable size distortion

Student Name Server Spring 2005Utah School of Computing26 Isometric View

Student Name Server Spring 2005Utah School of Computing27 Engineering Drawing: 2 Planes AA Section AA

Student Name Server Spring 2005Utah School of Computing28 “ True” Perspective in 2D (x,y) p h

Student Name Server Spring 2005Utah School of Computing29 “ True” Perspective in 2D

Student Name Server Spring 2005Utah School of Computing30 “ True” Perspective in 2D

Student Name Server Spring 2005Utah School of Computing31 Geometry is Same for Eye at Origin (x,y) h Screen Plane

Student Name Server Spring 2005Utah School of Computing32 What Happens to Special Points? What is this point??

Student Name Server Spring 2005Utah School of Computing33 Let’s Look at Limit We see that Observe,

Student Name Server Spring 2005Utah School of Computing34 Where does Eye Point Go? It gets sent to on x-axis Where does on x-axis go?

Student Name Server Spring 2005Utah School of Computing35 What happens to ? It comes back to virtual eye point!

Student Name Server Spring 2005Utah School of Computing36 What Does This Mean?

Student Name Server Spring 2005Utah School of Computing37 What Does This Mean?

Student Name Server Spring 2005Utah School of Computing38 The “Pencil of Lines” Becomes Parallel

Student Name Server Spring 2005Utah School of Computing39 Parallel Lines Become “ Pencil of Lines ” !

Student Name Server Spring 2005Utah School of Computing40 Parallel Lines Become “ Pencil of Lines ” !

Student Name Server Spring 2005Utah School of Computing41 What Does This Mean?

Student Name Server Spring 2005Utah School of Computing42 “ True ” Perspective in 2D

Student Name Server Spring 2005Utah School of Computing43 “ True ” Perspective in 2D

Student Name Server Spring 2005Utah School of Computing44 Viewing Frustum

Student Name Server Spring 2005Utah School of Computing45 What happens for large p ?”

Student Name Server Spring 2005Utah School of Computing46 Projection Becomes Orthogonal: “Right Thing Happens” (x,y) h=y