Notes on the project

1
Notes on the project

• Note that aid on the project is authorized from
  myself, students in the Writing Lab and
  Mathematics Tutoring Lab, and Magale librarians
  and no one else.
• For help on citing WWW sites, please visit
  www.mla.org

2
Overview

• 0 dimensions points
• 1 dimension lines and curves
• between 1 and 2 dimensions fractals
• 2 dimensions tilings and symmetry
• between 2 and 3 dimensions perspective

3
Our pictures from last Friday

• What is true of slanted lines?

4
Vanishing Points

• The picture plane is the plane containing the
  image.
• Lines that are parallel to each other and not
  parallel to the picture plane have images that
  converge to a vanishing point.

5
Examples

• A picture might have many vanishing points.
  (Print from Vredeman de Vries Perspective)

6
Examples

• Transition in the early Renaissance
• Giottos Slaughter of the Innocents (1305)
• Giottos Pentecost (1305)
• Leonardos Annuciation (1472-75)
• The canvas is an open window through which I
  see what I want to paint.' - Alberti

7
Terminology

• The object is projected upon the picture plane to
  form an image.

One of Albrecht Durers machines for creating a
perspective drawing.
8
The Mathematics

• The lines perpendicular to the picture plane
  converge to the principal vanishing point.
• Why does this happen?

9
The Mathematics