Viewing II: the mathematics of perspective

CS 248 - Introduction to Computer Graphics
Autumn Quarter, 2003
Marc Levoy
Lecture notes for Thursday, November 6 (finished on Nov. 11)

Table of contents:

• Specifying a perspective view
  • Problems on the use of perspective in art
  • The viewing frustum
  • An intuitive specification method
  • glFrustum specification method
  • Comparison of formulations
• OpenGL implementation of viewing:
  • Coordinate systems
  • Modeling and viewing transformations
  • Orthographic projection
  • Perspective projection: x' and y'
  • Perspective projection: z'
  • Perspective interpreted as a distortion of 3-space
  • Clipping before versus after homogenization
• Polygon clipping
  • Uses of polygon clipping
  • Sutherland-Hodgman polygon clipping

If you want to play with the program I used in class to demonstrate changing the field of view (zooming) versus changing the distance to the scene (dollying), then log on to a firebird or raptor and type:

/usr/class/cs248/support/bin/i386-linux/frustum.linux /usr/class/cs248/data/Inventor/spheres.iv