Visual Imaging in the

Electronic Age

Lecture # 2

Drawing Perspective Images

Brunelleschi’s Experiment

August 27, 2015

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.

Planar Geometric Projections

Parallel

Oblique

Multiview

Orthographic

Isometric

Perspective

One-point Two-point Three-pointOrthographic

Axonometric Cavalier Cabinet

Dimetric Trimetric

Planar Geometric Projections

Reference

• Ingrid Carlbom , Joseph Paciorek. "Planar Geometric

Projections and Viewing Transformation," Computing

Surveys, vol. 10, no. 4, December 1978.

(This reference contains a matrix method for combining

all of the above types of projections)

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.

Projectors are

perpendicular to the

image plane

Object faces are

parallel to the image

plane

Orthographic

Projections

Diagram from http://imeulia.blogspot.com/2011/07/axonometric-projection.html

Projectors are

perpendicular to the

image plane

Object faces are not

parallel to the image

plane

Axonometric

Projections

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.

Projectors are parallel

but not perpendicular

to the image plane

Object faces are

parallel to the image

plane

Oblique

Projections

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)

• Can measure distances on axonometric.

• Can’t measure distances on

perspective.

What are the advantages of an

axonometric drawing?

Comparison of Axonometric &

Perspective Drawings

Rays of light travel from the object, through the picture plane, and

to the viewer's eye. This is the basis for graphical perspective.

Perspective

Projection

(2-point)

1, 2, 3 Point Perspective Animation (Perspective02_wmv)

Computer Graphics

Perspective Image Generation

Camera

RasterOperations

ImageStorage

Display

Standard Computer

Graphics PipelinePerspectiveTransform

Model

Camera Definition

Model

The camera location, view direction, and frustum must be defined relative to

the object.

View

direction

Camera

Y

Z

X

Ze

Xe

Ye

Eye Coordinate System

The model is described in a

right handed coordinate system.

Note the eye coordinate system is a left-handed coordinate system

Picture Plane

Eye Coordinate SystemYe

Left Handed and Right Handed

Coordinate Systems

Left Handed Right Handed

x

y

z

x

y

z

z

yx

z

yx

Picture Plane

Point On Object

Simple Perspective Transformation

Ze = D

ZeXe

Ye

Ze = 0

P(xe, ye, ze)

P(xs, ys)

S

S

S

display

screenze = 0

P(xe, ye, ze)

P(xs, ys)

D

O

QQ

Elevation drawn in the Ye, Ze plane.

Simple Perspective Transformation

Ye

Ze

Simple Perspective Transformation

e

e

e

e

e

es

e

es

z

Dy,

z

Dxx

z

y

D

y,

z

x

D

x

ss y

e

es

e

es

Sz

Dyy

Sz

Dxx ,

To convert to a dimensionless fraction,

can divide by the window size S.

Eye coordinate systemPlan or elevation view

Perspective Projection

Picture PlaneObject

Pinhole Camera

Note that the entire image through

the pinhole is totally in focus on a

single image plane.

Camera Obscura

Brunelleschi’s Perspective Experiment

Brunelleschi

Ghiberti’s Doors

Ghiberti’s Doors

Brunelleschi

Brunelleschi

Brunelleschi

Brunelleschi’s Experiment

Brunelleschi’s Experiment

Brunelleschi Video (render01_wmv)

Brunelleschi’s

Experiment

Brunelleschi’s Experiment

Description of Homework Assignment #1

Assignment #1

270

475

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