Pie menus frame this kind of interaction as pop-up menus, which provide a "self revealing gestural user interface". The menu pops up and leads you through the possible selections. That feedback trains you to rehearse the gestures. Soon you begin to make the gesture without looking at the menu, then wait for the menu feedback to confirm you're doing the right thing. Finally you gain enough skill and confidence through "muscle memory" to make the gestures quickly without even looking at the screen or requiring any feedback.

It's best if the menus can provide real time in-world feedback, like applying the effect of the interaction immediately as the menu is tracking. That makes it feel more like immersive "direct manipulation" than indirect "menu selection". It's important that pie menus support "reselection", which makes them much more forgiving and differentiates them from traditional blind gesture recognition, so you at any time during tracking you can change the selection to any item you desire.

Pie menus completely saturate the entire possible gesture space with usable and accessible commands: there is no such thing as a syntax error, and you can always correct any gesture to select what you want, no matter how bad it started out, or cancel the menu, by moving around to the desired item or back to the center to cancel.

Handwriting and gesture recognition does not have this property, and it can be quite frustrating because you can't correct or cancel mistakes, and dangerous because mistakes can be misinterpreted as the wrong command. Most gestures are syntax errors. Blind gesture recognition doesn't have a good way to prompt and train you with the possible gestures, which only cover a tiny fraction of the possible gesture space. All the rest of the space of possible gestures is wasted, and interpreted as a syntax error (or worse, misinterpreted as the wrong gesture), instead of enabling the user to correct mistakes and reselect different gestures.

Even "fuzzy matching" of gestures trades off gestural precision with making it even harder to cancel or correct a gesture, without accidentally being misinterpreted as the wrong gesture. That's not the kind of an interface you would want to use in a mission critical application such as a car or airplane.

Another way to reframe the gestural, self revealing and reselectable qualities of pie menus is as navigation through a map, as opposed to climbing up a hierarchical menu tree. Instead of laboriously climbing up a tree of submenus, you simply navigate around a map of "sibmenus" -- sibling menus that you can easily move back and forth between by moving in opposite directions.

This demo of an iPhone app I developed called "iLoci" demonstrates the idea, enabling users to create their own memorable maps of "locations" instead of "menus", which they can edit by dragging around, that are related to each other by two-way reversible links. It exploits the "Method of Loci," an ancient memorization technique from the time before iPhones when people had to use their own brains to remember things, in order to leverage your spatial navigation memory and make it easy to learn your way around. http://vimeo.com/2419009

https://en.wikipedia.org/wiki/Method_of_loci
"The Method of loci (plural of Latin locus for place or location), also called the memory palace, is a mnemonic device introduced in ancient Roman and Greek rhetorical treatises (in the anonymous Rhetorica ad Herennium, Cicero's De Oratore, and Quintilian's Institutio Oratoria). In basic terms, it is a method of memory enhancement which uses visualization to organize and recall information. Many memory contest champions claim to use this technique to recall faces, digits, and lists of words. These champions’ successes have little to do with brain structure or intelligence, but more to do with their technique of using regions of their brain that have to do with spatial learning."

I like the idea of moving away from hierarchal menu navigation, towards spatial map navigation. It elegantly addresses the problem of personalized user created menus, by making linking and unlinking locations as easy as dragging and dropping objects around and bumping them together to connect and disconnect them. (Compare that to the complexity of a tree or outline editor, which doesn't make the directions explicit.) And it eliminates the need to a special command to move back up in the menu hierarchy, by guaranteeing that every navigation is obviously reversible by moving in the opposite direction. I believe maps are a lot more natural and easier for people to remember than hierarchies, and the interface naturally exploits "mouse ahead" (or "swipe ahead") and is obviously self revealing.

Here is another video demonstrating a prototype exploring this interface that I developed in Unity3D for Will Wright. It shows both an "iLoci" map editing interface, as well as traditional pop-up pie menus using "pull-out" distance parameters with real time in-world feedback to preview the effect of the selection (plus it also has cellular automata, at Will's request!): http://www.DonHopkins.com/home/StupidFunClub/MediaGraphDemo1...