* introduction

** definition

Pies are circular menus, 
the selection from which is based on the direction between two points,
indicated by 
mouse clicking, 
pen marking, 
screen touching, 
hand waving,
or whatever. 

A pie menu is centered on the first point, 
at the location of the cursor when the mouse button pressed down, 
the beginning of the pen stroke, 
or whatever location is appropriate for the input device. 
In the center of the pie, where the cursor starts out, 
is an inactive region that selects nothing. 
The wedge shaped slices of the pie, 
adjacent to the cursor but in different directions,
correspond to the menu selections.

The selection is based on the direction 
from the menu center to the second click, 
not the path of the cursor between clicks. 
So you can move around and click in any slice to select it, 
or click in the center to cancel.

Pies are fast, 
because pointing in the direction of a slice 
requires very little cursor motion, 
and can be done without even looking. 

They're reliable,
because of the large area and triangular shape of the slices,
whose active area extends to the edge of the screen.

** learning pie menus

For the novice, pie menus are easy 
because they're self revealing,  
popping up a window displaying the available selections 
and their associated directions. 

For the expert, they're efficient
because they're gestural,
utilizing muscle memory,
allowing you to "click ahead" and
selecting from a menu without looking.

To select from a pie menu,
you click to pop it up, 
look at the labels, 
move in the desired direction, 
then click to select.

They are very efficient, 
because you soon learn to make selections 
without waiting for the menu to display, by "clicking ahead".

By clicking ahead, you can select without looking at the menu.
When you click ahead in a smooth motion, 
using the same physical gesture as normal menu selection,
the menu does not display on the screen,
and you can select from familiar menus very swiftly. 

* explain why they are so defined

Pie menus may be implemented in many ways, 
but one essential design goal is
to facilitate smooth reliable gestural interaction.
In particular, this describes pie menus for the mouse.
Pie menus can be made to work with other input devices,
like pens and touch screens,
by adapting their display and tracking behavior 
to the constraints and features of the particular input device. 

When a mouse based pie menu pops up, it is ideally centered at the
location of the click that invoked it: where the mouse button was
pressed, the screen was touched, or whatever. The cursor might have
moved in the time it took to respond to the click, so simply centering
the menu on the current cursor position would interfere with click
ahead.  The center of the pie is inactive, and clicking again in the
center dismisses the menu without making a selection.

The slices of the pie are all adjacent to the cursor, each in a
different direction. This arrangement minimizes the motion required to
make a selection. As you move the cursor further into the wider area of
a slice, your directional control becomes more precise.  So the active
areas of the slices extend out to the edges of the screen, and you can
move the cursor as far as you want in any direction to select a slice.
The ability to increase the angular accuracy by moving the cursor as far
as you need is another property of pie menus that makes reliable click
ahead possible.

* disadvantages and solutions

One disadvantage of pie menus is that when they pop up, they take a
lot of screen space due to the circular layout.  Pie menus with long
labels can be very large, while those with short labels or small icons
tend to be more compact and take up less screen space.

The layout algorithm should minimize the menu size, prevent the labels
from overlapping, and clearly associate each label with its respective
direction. It is not necessary to confine each label to the interior of
its slice -- that could result in enormous menus. Rotated text is also
undesirable, since it's jagged, hard to read, and still results in
large menus. I have implemented a successful layout policy that
justifies the label edges against the center of the slice, at an inner
radius big enough that no two adjacent labels overlap. To delimit the
active areas of the menu, short lines are drawn between the slices,
like cuts in the crust, inside the circle of labels.

Dynamically changing pie menus don't work well with click ahead,
because the items keep moving around.  Pie menus are better for
selecting from a set of items that does not change, and best when the
items can be arranged to exploit the circular layout.

Pie menus with an odd number of items are
less symetric and harder to use. 
The fewer and evener the number of items in a pie menu, 
the easier it is to use.  
Certain numbers of items are well suited to various metaphors.  
(table xxx)

One solution to the problem of pie menus with too many items is to
dissolve large menus into smaller logically related submenus. Nested
pies work quite well as a gestural interface, because it's possible to
click ahead through them without visual feedback. If you think of it as
navagating through rooms in a building or city streets, you just
remember the directions, and chunk out the selection gestures one after
the other.

Another way around the problem is the scrolling spiral pie menu, that
encompasses many items, but only displays a fixed number of them at
once. By winding the cursor around the menu center, you can scroll
through all the items, like walking up or down a spiral staircase or
parking garage. 

When you pop up a pie menu near the edge of the screen, the menu
window may have to be moved by a certain offset in order to fit
completely on the screen, otherwise you couldn't select all the items.
But it would be quite unexpected were the menu to slip out from under
the click, leaving the cursor pointing at the wrong slice. So whenever
the menu is displayed on the screen, and it must be moved in order to
fit, it is important to "warp" the cursor by the same offset, relative
to its position at the time the menu is displayed. If a selection is
made, but the menu is not popped up on the screen due to click ahead
display premption, the cursor should not be warped.  Pen and touch
screen based pie menus can't warp your pen or finger, so pie menus
along the screen edge could pop up as semicircular fans.

While the menu display is prempted due to cursor motion, 
it's helpful to give some feedback, 
such as displaying the selected label near the cursor, 
or previewing the effect of the selection.

* explain their speed and accuracy

Pie menus are faster and have a lower error rate than linear "pull down"
menu.  According to Fitt's law, the "seek time" required to point the
cursor at a target depends on the distance to the target and the target
area.  Since the wedge shaped slices of a pie menu are all quite large
and very close to the cursor (their active area extends to the edge of
the screen), Fitt's law predicts good times for pie menus.  But the
rectangular target areas of a linear menu are very small in comparison,
and they're each a different distance (but the same direction) from the
cursor.

The results of Jack Callahan's controlled experiment, comparing the
seek time and error rates of eight-item pie and linear menus, supports
Fitt's law. Three types of eight-item menu task groupings were used:
Pie tasks (North, NE, East, etc...), linear tasks (First, Second,
Third, etc...), and unclassified tasks (Center, Bold, Italic, etc...).
Subjects with little or no mouse experience were presented menus in
both linear and pie formats, and told to make a certain selection from
each. They were able to make selections significantly faster, with
fewer errors, for all three task groupings, using pie menus.

[figures, discussion]

Buxton's experiment comparing different sized pie menus and input devices
  8 and 12 very good. rehersal. trackball bad. mouse good. pen great.

* two dimensions: direction and distance

Pies provide two dimensions of input:
direction and distance. 
The direction may dial around continuous range like a knob,
or select between slices of a pie like a menu;
the distance may pull out through a continuous range like a slider, 
or select between rings or bites of a slice like a secondary menu. 

  continuous or discrete
  two dimensional examples: font style/size, color hue/saturation

* metaphor, kinesthetics, and gesture

Idealy, pie menu designers should arrange the labels and submenus in
directions that reflect spatial associations and relationships between
them, making it easy to remember which direction does what.  Opposite
or complementary items can be places 180 degrees apart, and orthogonal
pairs 90 degrees apart. ...

A natural pie menu metaphor is geographical navagation:
driving around the intersections and streets of a city,
walking around the halls and rooms of a building, 
or climbing around the branches and leaves of a tree. 

Linear menus are like parallel parking and ladder climbing.

  designing kinesthetically pleasing pie menus
  example: window manager

* implementations and availability
  in X10 for the uwm window manager
  in SunView for the SDI game
  in NeWS for the Lite Toolkit
  in OpenWindows for The NeWS Toolkit
  safer than linear menus, probably not patented
  league for programming freedom
  take a look and feel free

My first attempt at implementing pie menus was on a Sun 3/160 running
the X10 window system, adding them to the "uwm" window manager (June
86), since there was no standard menu package at the time.  The user
could define nested menus in a ".uwmrc" file, and bind them to mouse
buttons (possibly modified by shift keys).  The default menu layout
was specified by an initial angle and a radius, which you could
override in any menu whose labels overlapped.  The popup window was
shaped as a rectangle large enough the encompass all the labels, with
a title at the top.

Then I linked this piemenuified window manager code into Mitch
Bradley's Sun Forth System, to make a Forth extensible window manager.
I used this interactivly programmable system to experiment with pie
menu tracking and window management techniques, and to administer and
collect data for Jack Callahan's experiment comparing pie menus with
linear menus.

While snowed in at home, Mark Weiser implemented Pie Menus for the
SunView window system (January 87), and they are featured in his "SDI"
game, the source code to which is available for free.

NeWS Lite Toolkit (May 87)

The NeWS Toolkit

Not only are pie menus quicker and easier than linear pull down menu,
they are probably even safer to use, because pull down menus are
patented by Apple Computer.

Earlier implementations of pull down menus at Xerox PARC did not
prevent Apple from patenting them, but Apple's patent and legal
department don't seem to prevent other people from using the idea,
either.

It's possible (though not very likely) that the abstract pie menu
concept was patented before 1969 (the earliest reference I could find
to it), and I could be in deep trouble for giving away my own code,
because of some obscure directional pastery vending machine control
patent.