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1992-10-11
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You can use Kali to draw Escher-like tilings, infinite knots, and
other cool stuff. It lets you draw patterns in all of the 17 planar
symmetry groups. It was written by Nina Amenta at UC Berkeley. It
was later extended at the Geometry Center at the University of
Minnesota: the capability to move lines was added, and Tamara Munzner
added user interface panels using the public domain Forms Library by
Mark Overmars of the University of Utrecht, which is available via
anonymous ftp at archive.cs.ruu.nl.
Kali is available for free via anonymous ftp from the Geometry Center:
(geom.umn.edu or 128.101.25.31). It is copyrighted.
CHOOSING A SYMMETRY GROUP:
Select the symmetry group you wish to work in by clicking on one of
the icons on the control panel. Each icon shows some of the
symmetries which your pattern will contain. Each group is also
labeled in Conway notation and the traditional crystallographic
notation.
Re-selecting the current symmetry group clears the window and throws
away your pattern.
DRAWING:
Clicking the left mouse puts down points in your pattern. Once a
point is down, a new line "rubber-bands" from the point to the current
cursor position. Click the left mouse again to fix the second
endpoint of the current line and start the next one.
Clicking infrequently often gives nicer patterns.
Click the middle mouse to let go of the current rubber-banding line.
TRANSFORMATIONS:
You can scale your by clicking on "Zoom". Now holding down the left
mouse button and moving the mouse left and right makes your pattern
bigger or smaller. When editing (see the next section) it is often
useful make the pattern very big, edit, and then shrink it again.
Clicking "Rotate" lets you rotate the pattern within the window.
Again, hold down the left mouse and move it left and right. Some
symmetry groups have some additional degrees of freedom in the
symmetry lattice. If the "Angle" or "Ratio" button has black letters,
you can change the angle between the two vectors forming the lattice,
or the ratio between the lengths of the two vectors, respectively.
You can always resize the window to fit your pattern into a
differently shaped rectangle by picking up its lower righthand corner.
To get back to Draw mode after a transformation, click on the "Draw"
button.
EDITING:
Click on the "Delete" control panel button to get into Delete mode.
Now clicking the right mouse highlights the line closest to the
cursor. To delete the highlighted line, click the middle mouse. To
select another line, move the mouse and click right again. Clicking
on "Move" puts you in Move mode. Again, clicking the right mouse
highlights the closest line. To pick up the nearest endpoint of the
highlighted line, click the left mouse. To put the endpoint down
somewhere new, click the left mouse. This is handy for tidying up your
patterns.
To get back to Draw mode, click on "Draw".
SAVING A PATTERN:
Click "Save" on the control panel to save your pattern. It will prompt
you for a name under which to save it, and puts it in a file with that
name. You have to save your pattern before you can print it out.
To look at (or edit!) an old pattern, click "Load". It will ask you
for the name it was saved under. Some demonstration patterns to look at are
"weaving.kali", "turtles.kali", and "people.kali".
"Esc" clears the input panel in the popup window.
PRINTING A PATTERN:
There is a separate program for printing. From the Unix shell, type
"kaliprint filename | lpr", only replace the word "filename" with the
name of the file containing your pattern.
HOW IT WORKS:
Every symmetry group is defined by a lattice and a set of two
generators, which are either a rotation, reflections, or glide
reflections. A pattern is just a list of lines. Each line is first
reflected (if there are any reflection or glide reflection generators)
and then all reflections are rotated (if there is a rotation
generator). Finally the resulting figure is redrawn around every
lattice point. The list of lines, the lattice, and the symmetry group
are written into the file when you save your picture. Kaliprint turns
this information into a Postscript file. Postscript is a format which
you can print on a laser printer or mail to your friends.