CS 285: SOLID MODELING
Lecture #5 -- We, Feb. 6, 2002.
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Review of the Symmetry Groups
The use of symmetry is an important design-aid when creating artificial objects.
Warm-up Exercise:
Compare the two collections of eight frieze patterns
and match corresponding numbers and alpha-characters.
Understanding the symmetries of 1D friezes is crucial to the understanding of the symmetries of
2D figures, 3D objects, and 2D and 3D tilings.
Examples of Friezes
Some fine books on symmetry and tilings:
- Hermann Weyl: "Symmetry", Birkhaeuser, 1955.
- Alan Holden: "Shapes, Space, and Symmetry", Dover, 1971.
- Alan Holden: "Orderly Tangles", Columbia, 1983.
- Robert Williams: "The Geometrical Foundation of Nature and Structure", Dover, 1972.
- Gruenbaum / Shephard: "Tilings and Patterns", Freeman, 1986.
(You could of course spend many hours studying symmetry from these books.
But it is far more efficient on your time to think along in class;
this way you can absorb the essentials in a couple of hours.)
Symmetry in 2D Space:
Symmetry in 3D Space:
Open your eyes to the symmetry of everyday objects...
- What are the symmetries of the objects you encounter in your daily life ?
- Brain teaser: -- Why does an ordinary wall mirror reverse left and right, but not up and down ??
Current Homework Assignment:
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