Wallpaper Symmetries CS 39 Carlo H. Séquin

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Presentation transcript:

Wallpaper Symmetries CS 39 Carlo H. Séquin Florida 1999 CS 39 Wallpaper Symmetries Carlo H. Séquin EECS Computer Science Division University of California, Berkeley Back to TWO dimensions! Adding translator symmetry on (infinitely large) 2D “wall papers”.

Wallpaper Symmetries Worksheet Some examples of wall paper patterns. Granada 2003 Wallpaper Symmetries Some examples of wall paper patterns. How do we analyze them and compare them to one another? Worksheet

Take One Pattern at a Time . . . Granada 2003 Take One Pattern at a Time . . . Find rotation centers, mirror lines, glide axes ! Find rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Pure Rotation: 3 Mirror Line Kaleidoscope Point: 3 >> Symm.: 3*3 Find all unique rotation centers, mirror lines, glide axes

Different Kaleidoscope Points Count different ones individually!

3 Different Kaleidoscope Points Symmetry: *442

Take One Pattern at a Time . . . Find rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Pure Rotation: 2 Pure Rotation: 2 Glide Axis >> Symm.: 22X Find all unique rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Find rotation centers, mirror lines, glide axes

Take One Pattern at a Time . . . Mirror Line Glide Axis >> Symm.: *X Find all unique rotation centers, mirror lines, glide axes

Different Glide Axes ? Find rotation centers, mirror lines, glide axes

Two Different Glide Axes Glide Axis Glide Axis >> Symm.: XX Find all unique rotation centers, mirror lines, glide axes