Visual Imaging in the Electronic Age Lecture # 2
Drawing Perspective Images Brunelleschi’s Experiment August 28, 2014 Prof. Donald P. Greenberg
http://www.graphics.cornell.edu/academic/art2907/ User Name: art2907 Password:
The Flagellation of Christ, c. 1458-60. Piero della Francesca. Tempera. 59 x 81.5 cm. Urbino, Galleria Nazionale delle Marche.
Albrecht Durer. Untitled (Artist using a glass to take a portrait). From Underweysung der Messung mit dem Zirkel und Riichtscheyt, 1st Ed, 1525. Woodcut print.
Albrecht Durer, Untitled (Two draughtsmen plotting points for the drawing of a lute in foreshortening) From Underweysung der Messung mit dem Zirkel und Riichtscheyt, 1st Ed., 1525. Woodcut print.
Reference • Ingrid Carlbom , Joseph Paciorek. "Planar Geometric Projections and Viewing Transformation," Computing Surveys, vol. 10, no. 4, December 1978.
Planar Geometric Projections Planar Geometric Projections
Parallel
Oblique
Orthographic
Multiview Orthographic
Isometric
Axonometric
Dimetric
Perspective
Cavalier
Trimetric
Cabinet
One-point
Two-point
Three-point
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. © 1997. P. 9.
Axonometric Projections Projectors are perpendicular to the image plane Object faces are not parallel to the image plane Diagram from http://imeulia.blogspot.com/2011/07/axonometric-projection.html
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. © 1997. P. 9.
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. © 1997. P. 9.
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.
Computer Graphics Perspective Image Generation
Model
Standard Computer Graphics Pipeline
Camera Perspective Transform Raster Operations Image Storage
Display
Model
Standard Computer Graphics Pipeline
Camera Perspective Transform Raster Operations Image Storage
Display
Camera Definition Camera
View direction
Model
The camera location, view direction, and frustum must be defined relative to the object.
Eye Coordinate System Z
Ye
The model is described in a right handed coordinate system.
Xe Ze
Y
X
Eye Coordinate System Ye
Picture Plane
Note the eye coordinate system is a left-handed coordinate system
Left Handed and Right Handed Coordinate Systems z
z
Left Handed
x
Right Handed
y
y
x
z
z x
y
x
y
Simple Perspective Transformation Ye
Picture Plane P(xs, ys)
Point On Object P(xe, ye, ze)
S
Xe
Ze
S
Ze = 0 Ze = D
Simple Perspective Transformation Ye P(xe, ye, ze) P(xs, ys)
O Q
S
Q
Ze
D Ze = 0
display screen
Elevation drawn in the Ye, Ze plane.
Simple Perspective Transformation xs xe , D ze
y s ye D ze
Dxe xs , ze
Dye ys ze
To convert to a dimensionless fraction, can divide by the window size S.
Dxe xs , Sze
Dye ys Sze
Perspective Projection
Picture Plane
Object
Eye coordinate system Plan or elevation view
Pinhole Camera
Note that the entire image through the pinhole is totally in focus on a single image plane.
Ibn al-Haitham (Al-Hazen)
Credited with the having built the first camera obscura in the 10th Century.
Camera Obscura
Brunelleschi’s Perspective Experiment • How do you draw a perspective image? • How do you know it is correct?
Brunelleschi’s Perspective Experiment
Brunelleschi
Ghiberti’s Doors
Brunelleschi
Brunelleschi’s Experiment
Brunelleschi’s Experiment
Brunelleschi’s Experiment
Brunelleschi’s Experiment
Description of Homework Assignment #1
Assignment #1
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