Visual Imaging in the Electronic Age. Drawing Perspective Images

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1 Visual Imaging in the Electronic Age Lecture # 2 Drawing Perspective Images Brunelleschi s Experiment August 24, 2017 Prof. Donald P. Greenberg

2 User Name: art2907 Password: student17

3 O che dolce cosa e' questa prospettiva! - Paolo Uccello

4 The Miracle of the Profaned Host, Paolo Uccello. Tempera on wood. 33 x 55 cm. Urbino, Galleria Nazionale delle Marche.

5 The Flagellation of Christ, c Piero della Francesca. Tempera. 59 x 81.5 cm. Urbino, Galleria Nazionale delle Marche.

6 Albrecht Durer, Untitled (Two draughtsmen plotting points for the drawing of a lute in foreshortening) From Underweysung der Messung mit dem Zirkel und Riichtscheyt, 1 st Ed., Woodcut print.

7 Light as Rays

8 Light as Waves

9 Light as Photons

10 Planar Geometric Projections Planar Geometric Projections Parallel Perspective Orthographic Oblique One-point Two-point Three-point Multiview Orthographic Axonometric Cavalier Cabinet Isometric Dimetric Trimetric

11 Planar Geometric Projections Planar Geometric Projections Parallel Perspective Orthographic Oblique One-point Two-point Three-point Multiview Orthographic Axonometric Cavalier Cabinet Isometric Dimetric Trimetric

12 Orthographic Projections Projectors are perpendicular to the image plane Object faces are parallel to the image plane Diagram from Axonometric and Oblique Drawing: A 3-D Construction, Rendering, and Design Guide by M. Saleh Uddin. New York: McGraw-Hill P. 9.

13 Architecture Plan and Elevations

14 Planar Geometric Projections Planar Geometric Projections Parallel Perspective Orthographic Oblique One-point Two-point Three-point Multiview Orthographic Axonometric Cavalier Cabinet Isometric Dimetric Trimetric

15 Axonometric Projections Projectors are perpendicular to the image plane Object faces are not parallel to the image plane Diagram from

16 Comparison of Axonometric & Perspective Drawings What are the advantages of an axonometric drawing? Can measure distances on axonometric. Can t measure distances on perspective.

17 Planar Geometric Projections Planar Geometric Projections Parallel Perspective Orthographic Oblique One-point Two-point Three-point Multiview Orthographic Axonometric Cavalier Cabinet Isometric Dimetric Trimetric

18 Oblique Projections Projectors are parallel but not perpendicular to the image plane Object faces are parallel to the image plane Diagram from Axonometric and Oblique Drawing: A 3-D Construction, Rendering, and Design Guide by M. Saleh Uddin. New York: McGraw-Hill P. 9.

19 Planar Geometric Projections Planar Geometric Projections Parallel Perspective Orthographic Oblique One-point Two-point Three-point Multiview Orthographic Axonometric Cavalier Cabinet Isometric Dimetric Trimetric

20 Perspective Projection Projectors are not parallel but converge on a single focal point (eye, camera) Diagram from Axonometric and Oblique Drawing: A 3-D Construction, Rendering, and Design Guide by M. Saleh Uddin. New York: McGraw-Hill P. 9.

21 Picture Plane Looking Through a Window Note: all rays converge on our one cyclopean eye

22 One Point Perspective

23 Perspective Projection (2-point) Rays of light travel from the object, through the picture plane, and to the viewer's eye. This is the basis for graphical perspective.

24 Computer Graphics Perspective Image Generation

25 Model Standard Computer Graphics Pipeline Camera Perspective Transform Raster Operations Image Storage Display

26 Camera Definition Camera View direction Model The camera location, view direction, and frustum must be defined relative to the object.

27 Model Coordinate System Z The model is described in a right handed coordinate system. X Y

28 Eye Coordinate System Z Y e The model is described in a right handed coordinate system. Z e X e The eye coordinate system is a left handed coordinate system. X Y

29 Eye Coordinate System Y e Picture Plane Note the eye coordinate system is a left-handed coordinate system

30 Left Handed and Right Handed Coordinate Systems z Left Handed z Right Handed x y z y x z y x x y

31 DPG- Note that the picture plane is a left handed coordinate system, similar to the eye coordinate system. X is to the right, y is vertical and z increases with depth.

32 Simple Perspective Transformation Y e Picture Plane P (x s, y s ) Point On Object P(x e, y e, z e ) X e S Z e S Z e = 0 Z e = D

33 Simple Perspective Transformation Y e P(x e, y e, z e ) P (x s, y s ) O D Q S Q Z e z e = 0 display screen Elevation drawn in the Y e, Z e plane.

34 Simple Perspective Transformation xs D x = = x z e e Dx e s y s ze,, ys D = = y z e e Dy z To convert to a dimensionless fraction, can divide by the window size S. e e Dx y e x s =, s = Sze Dy Sz e e

35 Perspective Projection Picture Plane Object Eye coordinate system Plan or elevation view

36 Pinhole Camera Note that the entire image through the pinhole is totally in focus on a single image plane.

37 Ibn al-haitham (Al-Hazen) Credited with the having built the first camera obscura in the 10 th Century.

38 Camera Obscura

39 Solar Eclipse 8/21/17

40 Brunelleschi s Perspective Experiment How do you draw a perspective image? How do you know it is correct? Martin Kemp. THE SCIENCE OF ART, Chapter 1 (Linear perspective from Brunelleschi to Leonardo), pp AVAILABLE ON COURSE WEBSITE

41 Brunelleschi s Perspective Experiment

42 Brunelleschi

43 Brunelleschi

44 Ghiberti s Doors

45

46 Brunelleschi

47 Brunelleschi

48 Brunelleschi

49 Brunelleschi s Experiment

50 Brunelleschi s Experiment

51 Brunelleschi Video (render01_wmv)

52 Brunelleschi s Experiment

53 Brunelleschi s Experiment

54 Brunelleschi s Experiment

55 Assignment #1

56 Plan View (Not to scale)

57 Elevation View (Not to scale)

58 End...

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