\documentclass[twoside,openright]{uva-bachelor-thesis}

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% Title Page
\title{A generic architecture for gesture-based interaction}
\author{Taddeüs Kroes}
\supervisors{Dr. Robert G. Belleman (UvA)}
\signedby{Dr. Robert G. Belleman (UvA)}

\begin{document}

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\maketitle
\begin{abstract}
    % TODO
\end{abstract}

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\chapter{Introduction}
\label{chapter:introduction}

Surface-touch devices have evolved from pen-based tablets to single-touch
trackpads, to multi-touch devices like smartphones and tablets. Multi-touch
devices enable a user to interact with software using hand gestures, making the
interaction more expressive and intuitive. These gestures are more complex than
primitive ``click'' or ``tap'' events that are used by single-touch devices.
Some examples of more complex gestures are ``pinch''\footnote{A ``pinch''
gesture is formed by performing a pinching movement with multiple fingers on a
multi-touch surface. Pinch gestures are often used to zoom in or out on an
object.} and ``flick''\footnote{A ``flick'' gesture is the act of grabbing an
object and throwing it in a direction on a touch surface, giving it momentum to
move for some time after the hand releases the surface.} gestures.

The complexity of gestures is not limited to navigation in smartphones. Some
multi-touch devices are already capable of recognizing objects touching the
screen \cite[Microsoft Surface]{mssurface}. In the near future, touch screens
will possibly be extended or even replaced with in-air interaction (Microsoft's
Kinect \cite{kinect} and the Leap \cite{leap}).

The interaction devices mentioned above generate primitive events. In the case
of surface-touch devices, these are \emph{down}, \emph{move} and \emph{up}
events. Application programmers who want to incorporate complex, intuitive
gestures in their application face the challenge of interpreting these
primitive events as gestures. With the increasing complexity of gestures, the
complexity of the logic required to detect these gestures increases as well.
This challenge limits, or even deters the application developer to use complex
gestures in an application.

The main question in this research project is whether a generic architecture
for the detection of complex interaction gestures can be designed, with the
capability of managing the complexity of gesture detection logic. The ultimate
goal would be to create an implementation of this architecture that can be
extended to support a wide range of complex gestures. With the existence of
such an implementation, application developers do not need to reinvent gesture
detection for every new gesture-based application.

Application frameworks for surface-touch devices, such as Nokia's Qt \cite{qt},
do already include the detection of commonly used gestures like \emph{pinch}
gestures. However, this detection logic is dependent on the application
framework. Consequently, an application developer who wants to use multi-touch
interaction in an application is forced to use an application framework that
includes support for multi-touch gestures. Moreover, the set of supported
gestures is limited by the application framework of choice. To incorporate a
custom event in an application, the application developer needs to extend the
framework. This requires extensive knowledge of the framework's architecture.
Also, if the same gesture is needed in another application that is based on
another framework, the detection logic has to be translated for use in that
framework. Nevertheless, application frameworks are a necessity when it comes
to fast, cross-platform development. A generic architecture design should aim
to be compatible with existing frameworks, and provide a way to detect and
extend gestures independent of the framework.

Application frameworks are written in a specific programming language. To
support multiple frameworks and programming languages, the architecture should
be accessible for applications using a language-independent method of
communication. This intention leads towards the concept of a dedicated gesture
detection application that serves gestures to multiple applications at the same
time.

The scope of this thesis is limited to the detection of gestures on multi-touch
surface devices. It presents a design for a generic gesture detection
architecture for use in multi-touch based applications. A reference
implementation of this design is used in some test case applications, whose
goal is to test the effectiveness of the design and detect its shortcomings.

    \section{Structure of this document}

    % TODO: pas als thesis af is

\chapter{Related work}

    \section{Gesture and Activity Recognition Toolkit}

    The Gesture and Activity Recognition Toolkit (GART) \cite{GART} is a
    toolkit for the development of gesture-based applications. The toolkit
    states that the best way to classify gestures is to use machine learning.
    The programmer trains a program to recognize using the machine learning
    library from the toolkit. The toolkit contains a callback mechanism that
    the programmer uses to execute custom code when a gesture is recognized.

    Though multi-touch input is not directly supported by the toolkit, the
    level of abstraction does allow for it to be implemented in the form of a
    ``touch'' sensor.

    The reason to use machine learning is the statement that gesture detection
    ``is likely to become increasingly complex and unmanageable'' when using a
    set of predefined rules to detect whether some sensor input can be seen as
    a specific gesture. This statement is not necessarily true. If the
    programmer is given a way to separate the detection of different types of
    gestures and flexibility in rule definitions, over-complexity can be
    avoided.

    \section{Gesture recognition implementation for Windows 7}

    The online article \cite{win7touch} presents a Windows 7 application,
    written in Microsofts .NET. The application shows detected gestures in a
    canvas. Gesture trackers keep track of stylus locations to detect specific
    gestures. The event types required to track a touch stylus are ``stylus
    down'', ``stylus move'' and ``stylus up'' events. A
    \texttt{GestureTrackerManager} object dispatches these events to gesture
    trackers. The application supports a limited number of pre-defined
    gestures.

    An important observation in this application is that different gestures are
    detected by different gesture trackers, thus separating gesture detection
    code into maintainable parts.

    % TODO: This is not really 'related', move it to somewhere else
    \section{Processing implementation of simple gestures in Android}

    An implementation of a detection architecture for some simple multi-touch
    gestures (tap, double tap, rotation, pinch and drag) using
    Processing\footnote{Processing is a Java-based development environment with
    an export possibility for Android. See also \url{http://processing.org/.}}
    can be found in a forum on the Processing website \cite{processingMT}. The
    implementation is fairly simple, but it yields some very appealing results.
    The detection logic of all gestures is combined in a single class. This
    does not allow for extendability, because the complexity of this class
    would increase to an undesirable level (as predicted by the GART article
    \cite{GART}). However, the detection logic itself is partially re-used in
    the reference implementation of the generic gesture detection architecture.

    \section{Analysis of related work}

    The simple Processing implementation of multi-touch events provides most of
    the functionality that can be found in existing multi-touch applications.
    In fact, many applications for mobile phones and tablets only use tap and
    scroll events. For this category of applications, using machine learning
    seems excessive. Though the representation of a gesture using a feature
    vector in a machine learning algorithm is a generic and formal way to
    define a gesture, a programmer-friendly architecture should also support
    simple, ``hard-coded'' detection code. A way to separate different pieces
    of gesture detection code, thus keeping a code library manageable and
    extendable, is to user different gesture trackers.

% FIXME: change title below
\chapter{Design}
\label{chapter:design}

    % Diagrams are defined in a separate file
    \input{data/diagrams}

    \section{Introduction}

    This chapter describes the realization of a design for the generic
    multi-touch gesture detection architecture. The chapter represents the
    architecture as a diagram of relations between different components.
    Sections \ref{sec:driver-support} to \ref{sec:event-analysis} define
    requirements for the architecture, and extend the diagram with components
    that meet these requirements. Section \ref{sec:example} describes an
    example usage of the architecture in an application.

    \subsection*{Position of architecture in software}

        The input of the architecture comes from a multi-touch device driver.
        The task of the architecture is to translate this input to multi-touch
        gestures that are used by an application, as illustrated in figure
        \ref{fig:basicdiagram}. In the course of this chapter, the diagram is
        extended with the different components of the architecture.

        \basicdiagram{A diagram showing the position of the architecture
        relative to the device driver and a multi-touch application. The input
        of the architecture is given by a touch device driver. This output is
        translated to complex interaction gestures and passed to the
        application that is using the architecture.}

    \section{Supporting multiple drivers}
    \label{sec:driver-support}

    The TUIO protocol \cite{TUIO} is an example of a touch driver that can be
    used by multi-touch devices. TUIO uses ALIVE- and SET-messages to communicate
    low-level touch events (see appendix \ref{app:tuio} for more details).
    These messages are specific to the API of the TUIO protocol. Other touch
    drivers may use very different messages types. To support more than
    one driver in the architecture, there must be some translation from
    driver-specific messages to a common format for primitive touch events.
    After all, the gesture detection logic in a ``generic'' architecture should
    not be implemented based on driver-specific messages.  The event types in
    this format should be chosen so that multiple drivers can trigger the same
    events. If each supported driver would add its own set of event types to
    the common format, it the purpose of being ``common'' would be defeated.

    A minimal expectation for a touch device driver is that it detects simple
    touch points, with a ``point'' being an object at an $(x, y)$ position on
    the touch surface. This yields a basic set of events: $\{point\_down,
    point\_move, point\_up\}$.

    The TUIO protocol supports fiducials\footnote{A fiducial is a pattern used
    by some touch devices to identify objects.}, which also have a rotational
    property. This results in a more extended set: $\{point\_down, point\_move,
    point\_up, object\_down, object\_move, object\_up,\\ object\_rotate\}$.
    Due to their generic nature, the use of these events is not limited to the
    TUIO protocol. Another driver that can keep apart rotated objects from
    simple touch points could also trigger them.

    The component that translates driver-specific messages to common events,
    will be called the \emph{event driver}. The event driver runs in a loop,
    receiving and analyzing driver messages. When a sequence of messages is
    analyzed as an event, the event driver delegates the event to other
    components in the architecture for translation to gestures. This
    communication flow is illustrated in figure \ref{fig:driverdiagram}.

    Support for a touch device driver can be added by adding an event driver
    implementation. The choice of event driver implementation that is used in an
    application is dependent on the driver support of the touch device being
    used.

    \driverdiagram{Extension of the diagram from figure \ref{fig:basicdiagram},
    showing the position of the event driver in the architecture. The event
    driver translates driver-specific to a common set of events, which are
    delegated to analysis components that will interpret them as more complex
    gestures.}

    \section{Restricting events to a screen area}
    \label{sec:restricting-gestures}

    % TODO: in introduction: gestures zijn opgebouwd uit meerdere primitieven
    Touch input devices are unaware of the graphical input widgets rendered on
    screen and therefore generate events that simply identify the screen
    location at which an event takes place. In order to be able to direct a
    gesture to a particular widget on screen, an application programmer must
    restrict the occurrence of a gesture to the area of the screen covered by
    that widget. An important question is if the architecture should offer a
    solution to this problem, or leave it to the application developer to
    assign gestures to a widget.

    The latter case generates a problem when a gesture must be able to occur at
    different screen positions at the same time. Consider the example in figure
    \ref{fig:ex1}, where two squares must be able to be rotated independently
    at the same time. If the developer is left the task to assign a gesture to
    one of the squares, the event analysis component in figure
    \ref{fig:driverdiagram} receives all events that occur on the screen.
    Assuming that the rotation detection logic detects a single rotation
    gesture based on all of its input events, without detecting clusters of
    input events, only one rotation gesture can be triggered at the same time.
    When a user attempts to ``grab'' one rectangle with each hand, the events
    triggered by all fingers are combined to form a single rotation gesture
    instead of two separate gestures.

    \examplefigureone

    To overcome this problem, groups of events must be separated by the event
    analysis component before any detection logic is executed. An obvious
    solution for the given example is to incorporate this separation in the
    rotation detection logic itself, using a distance threshold that decides if
    an event should be added to an existing rotation gesture. Leaving the task
    of separating groups of events to detection logic leads to duplication of
    code. For instance, if the rotation gesture is replaced by a \emph{pinch}
    gesture that enlarges a rectangle, the detection logic that detects the
    pinch gesture would have to contain the same code that separates groups of
    events for different gestures. Also, a pinch gesture can be performed using
    fingers multiple hands as well, in which case the use of a simple distance
    threshold is insufficient. These examples show that gesture detection logic
    is hard to implement without knowledge about (the position of) the
    widget\footnote{``Widget'' is a name commonly used to identify an element
    of a graphical user interface (GUI).} that is receiving the gesture.

    Therefore, a better solution for the assignment of events to gesture
    detection is to make the gesture detection component aware of the locations
    of application widgets on the screen. To accomplish this, the architecture
    must contain a representation of the screen area covered by a widget. This
    leads to the concept of an \emph{area}, which represents an area on the
    touch surface in which events should be grouped before being delegated to a
    form of gesture detection.  Examples of simple area implementations are
    rectangles and circles.  However, area's could be made to represent more
    complex shapes.

    An area groups events and assigns them to some piece of gesture detection
    logic. This possibly triggers a gesture, which must be handled by the
    client application. A common way to handle framework events in an
    application is a ``callback'' mechanism: the application developer binds a
    function to an event, that is called by the framework when the event
    occurs. Because of the familiarity of this concept with developers, the
    architecture uses a callback mechanism to handle gestures in an
    application. Since an area controls the grouping of events and thus the
    occurrence of gestures in an area, gesture handlers for a specific gesture
    type are bound to an area. Figure \ref{fig:areadiagram} shows the position
    of areas in the architecture.

    \areadiagram{Extension of the diagram from figure \ref{fig:driverdiagram},
    showing the position of areas in the architecture. An area delegate events
    to a gesture detection component that trigger gestures. The area then calls
    the handler that is bound to the gesture type by the application.}

    Note that the boundaries of an area are only used to group events, not
    gestures. A gesture could occur outside the area that contains its
    originating events, as illustrated by the example in figure \ref{fig:ex2}.

    \examplefiguretwo

    A remark must be made about the use of areas to assign events the detection
    of some gesture. The concept of an ``area'' is based on the assumption that
    the set or originating events that form a particular gesture, can be
    determined based exclusively on the location of the events. This is a
    reasonable assumption for simple touch objects whose only parameter is a
    position, such as a pen or a human finger. However, more complex touch
    objects can have additional parameters, such as rotational orientation or
    color. An even more generic concept is the \emph{event filter}, which
    detects whether an event should be assigned to a particular piece of
    gesture detection based on all available parameters. This level of
    abstraction allows for constraints like ``Use all blue objects within a
    widget for rotation, and green objects for tapping.''. As mentioned in the
    introduction chapter [\ref{chapter:introduction}], the scope of this thesis
    is limited to multi-touch surface based devices, for which the \emph{area}
    concept suffices. Section \ref{sec:eventfilter} explores the possibility of
    areas to be replaced with event filters.

    \subsection*{Reserving an event for a gesture}

    The most simple implementation of areas in the architecture is a list of
    areas. When the event driver delegates an event, it is delegated to gesture
    detection by each area that contains the event coordinates. A problem
    occurs when areas overlap, as shown by figure \ref{fig:ex3}. When the
    white rectangle is rotated, the gray square should keep its current
    orientation. This means that events that are used for rotation of the white
    square, should not be used for rotation of the gray square. To achieve
    this, there must be some communication between the rotation detection
    components of the two squares.

    \examplefigurethree

    a

    --------

    % simpelste aanpak is een lijst van area's, als event erin past dan
    % delegeren. probleem (aangeven met voorbeeld van geneste widgets die
    % allebei naar tap luisteren): als area's overlappen wil je bepaalde events
    % reserveren voor bepaalde stukjes detection logic

    % oplossing: area'a opslaan in boomstructuur en event propagatie gebruiken
    % -> area binnenin een parent area kan events propageren naar die parent,
    % detection logic kan propagatie tegenhouden. om omhoog in de boom te
    % propageren moet het event eerst bij de leaf aankomen, dus eerst delegatie
    % tot laagste leaf node die het event bevat.

    % speciaal geval: overlappende area's in dezelfde laag v/d boom. in dat
    % geval: area die later is toegevoegd (rechter sibling) wordt aangenomen
    % bovenop de sibling links ervan te liggen en krijgt dus eerst het event.
    % Als propagatie in bovenste (rechter) area wordt gestopt, krijgt de
    % achterste (linker) sibling deze ook niet meer

    % bijkomend voordeel van boomstructuur: makkelijk te integreren in bijv GTK
    % die voor widgets een boomstructuur gebruikt -> voor elke widget die touch
    % events heeft een area aanmaken

    %For example, a button tap\footnote{A ``tap'' gesture is triggered when a
    %touch object releases a touch surface within a certain time and distance
    %from the point where it initially touched the surface.} should only occur
    %on the button itself, and not in any other area of the screen. A solution
    %to this problem is the use of \emph{widgets}. The button from the example
    %can be represented as a rectangular widget with a position and size. The
    %position and size are compared with event coordinates to determine whether
    %an event should occur within the button.

    \subsection*{Area tree}

        A problem occurs when widgets overlap. If a button in placed over a
        container and an event occurs occurs inside the button, should the
        button handle the event first? And, should the container receive the
        event at all or should it be reserved for the button?.

        The solution to this problem is to save widgets in a tree structure.
        There is one root widget, whose size is limited by the size of the
        touch screen.  Being the leaf widget, and thus the widget that is
        actually touched when an object touches the device, the button widget
        should receive an event before its container does. However, events
        occur on a screen-wide level and thus at the root level of the widget
        tree. Therefore, an event is delegated in the tree before any analysis
        is performed. Delegation stops at the ``lowest'' widget in the three
        containing the event coordinates. That widget then performs some
        analysis of the event, after which the event is released back to the
        parent widget for analysis. This release of an event to a parent widget
        is called \emph{propagation}. To be able to reserve an event to some
        widget or analysis, the propagation of an event can be stopped during
        analysis.
        % TODO: inspired by JavaScript DOM

        Many GUI frameworks, like GTK \cite{GTK}, also use a tree structure to
        manage their widgets. This makes it easy to connect the architecture to
        such a framework. For example, the programmer can define a
        \texttt{GtkTouchWidget} that synchronises the position of a touch
        widget with that of a GTK widget, using GTK signals.

    \section{Detecting gestures from events}
    \label{sec:gesture-detection}

    The events that are grouped by areas must be translated to complex gestures
    in some way. This analysis is specific to the type of gesture being
    detected.  E.g. the detection of a ``tap'' gesture is very different from
    detection of a ``rotate'' gesture. The architecture has adopted the
    \emph{gesture tracker}-based design described by \cite{win7touch}, which
    separates the detection of different gestures into different \emph{gesture
    trackers}. This keeps the different pieces of gesture detection code
    manageable and extendable. A single gesture tracker detects a specific set
    of gesture types, given a set of primitive events. An example of a possible
    gesture tracker implementation is a ``transformation tracker'' that detects
    rotation, scaling and translation gestures.

    % TODO: een formele definitie van gestures zou wellicht beter zijn, maar
    % wordt niet gegeven in deze thesis (wel besproken in future work)

    \subsection*{Assignment of a gesture tracker to an area}

        As explained in section \ref{sec:callbacks}, events are delegated from
        a widget to some event analysis. The analysis component of a widget
        consists of a list of gesture trackers, each tracking a specific set of
        gestures. No two trackers in the list should be tracking the same
        gesture type.

        When a handler for a gesture is ``bound'' to a widget, the widget
        asserts that it has a tracker that is tracking this gesture. Thus, the
        programmer does not create gesture trackers manually. Figure
        \ref{fig:trackerdiagram} shows the position of gesture trackers in the
        architecture.

        \trackerdiagram{Extension of the diagram from figure
        \ref{fig:widgetdiagram}, showing the position of gesture trackers in
        the architecture.}

    \section{Serving multiple applications}

    % TODO

    \section{Example usage}
    \label{sec:example}

    This section describes an example that illustrates the API of the
    architecture. The example application listens to tap events on a button.
    The button is located inside an application window, which can be resized
    using pinch gestures.

    % TODO: comments weg, in pseudocode opschrijven, uitbreiden met draggable
    % circle en illustrerende figuur
    \begin{verbatim}
    initialize GUI, creating a window

    # Add widgets representing the application window and button
    rootwidget = new rectangular Widget object
    set rootwidget position and size to that of the application window

    buttonwidget = new rectangular Widget object
    set buttonwidget position and size to that of the GUI button

    # Create an event server that will be started later
    server = new EventServer object
    set rootwidget as root widget for server

    # Define handlers and bind them to corresponding widgets
    begin function resize_handler(gesture)
        resize GUI window
        update position and size of root wigdet
    end function

    begin function tap_handler_handler(gesture)
        # Perform some action that the button is meant to do
    end function

    bind ('pinch', resize_handler) to rootwidget
    bind ('tap', tap_handler) to buttonwidget

    # Start event server (which in turn starts a driver-specific event server)
    start server
    \end{verbatim}

    \examplediagram{Diagram representation of the example above. Dotted arrows
    represent gestures, normal arrows represent events (unless labeled
    otherwise).}

\chapter{Test applications}

\section{Reference implementation in Python}
\label{sec:implementation}

% TODO
% alleen window.contains op point down, niet move/up
% een paar simpele windows en trackers

To test multi-touch interaction properly, a multi-touch device is required. The
University of Amsterdam (UvA) has provided access to a multi-touch table from
PQlabs. The table uses the TUIO protocol \cite{TUIO} to communicate touch
events. See appendix \ref{app:tuio} for details regarding the TUIO protocol.
The reference implementation is a Proof of Concept that translates TUIO
messages to some simple touch gestures (see appendix \ref{app:implementation}
for details).
% omdat we alleen deze tafel hebben kunnen we het concept van de event driver
% alleen met het TUIO protocol testen, en niet vergelijken met andere drivers

% TODO
% testprogramma's met PyGame/Cairo

\chapter{Suggestions for future work}

% TODO
% - network protocol (ZeroMQ) voor meerdere talen en simultane processen
% - gebruik formelere definitie van gestures ipv expliciete detection logic,
%   bijv. een state machine
% - volgende stap: maken van een library die meerdere drivers en complexe
%   gestures bevat
% - "event filter" ipv "area"

\section{A generic way for grouping events}
\label{sec:eventfilter}

\bibliographystyle{plain}
\bibliography{report}{}

\appendix

\chapter{The TUIO protocol}
\label{app:tuio}

The TUIO protocol \cite{TUIO} defines a way to geometrically describe tangible
objects, such as fingers or objects on a multi-touch table. Object information
is sent to the TUIO UDP port (3333 by default).

For efficiency reasons, the TUIO protocol is encoded using the Open Sound
Control \cite[OSC]{OSC} format. An OSC server/client implementation is
available for Python: pyOSC \cite{pyOSC}.

A Python implementation of the TUIO protocol also exists: pyTUIO \cite{pyTUIO}.
However, the execution of an example script yields an error regarding Python's
built-in \texttt{socket} library. Therefore, the reference implementation uses
the pyOSC package to receive TUIO messages.

The two most important message types of the protocol are ALIVE and SET
messages. An ALIVE message contains the list of session id's that are currently
``active'', which in the case of multi-touch a table means that they are
touching the screen. A SET message provides geometric information of a session
id, such as position, velocity and acceleration.

Each session id represents an object. The only type of objects on the
multi-touch table are what the TUIO protocol calls ``2DCur'', which is a (x, y)
position on the screen.

ALIVE messages can be used to determine when an object touches and releases the
screen. For example, if a session id was in the previous message but not in the
current, The object it represents has been lifted from the screen.

SET provide information about movement. In the case of simple (x, y) positions,
only the movement vector of the position itself can be calculated. For more
complex objects such as fiducials, arguments like rotational position and
acceleration are also included.

ALIVE and SET messages can be combined to create ``point down'', ``point move''
and ``point up'' events (as used by the Windows 7 implementation
\cite{win7touch}).

TUIO coordinates range from $0.0$ to $1.0$, with $(0.0, 0.0)$ being the left
top corner of the screen and $(1.0, 1.0)$ the right bottom corner. To focus
events within a window, a translation to window coordinates is required in the
client application, as stated by the online specification
\cite{TUIO_specification}:
\begin{quote}
    In order to compute the X and Y coordinates for the 2D profiles a TUIO
    tracker implementation needs to divide these values by the actual sensor
    dimension, while a TUIO client implementation consequently can scale these
    values back to the actual screen dimension.
\end{quote}

\chapter{Experimental program}
\label{app:experiment}

% TODO: rewrite intro
When designing a software library, its API should be understandable and easy to
use for programmers. To find out the basic requirements of the API to be
usable, an experimental program has been written based on the Processing code
from \cite{processingMT}. The program receives TUIO events and translates them
to point \emph{down}, \emph{move} and \emph{up} events.  These events are then
interpreted to be (double or single) \emph{tap}, \emph{rotation} or
\emph{pinch} gestures. A simple drawing program then draws the current state to
the screen using the PyGame library. The output of the program can be seen in
figure \ref{fig:draw}.

\begin{figure}[H]
    \center
    \label{fig:draw}
    \includegraphics[scale=0.4]{data/experimental_draw.png}
    \caption{Output of the experimental drawing program. It draws the touch
        points and their centroid on the screen (the centroid is used as center
        point for rotation and pinch detection). It also draws a green
        rectangle which responds to rotation and pinch events.}
\end{figure}

One of the first observations is the fact that TUIO's \texttt{SET} messages use
the TUIO coordinate system, as described in appendix \ref{app:tuio}.  The test
program multiplies these with its own dimensions, thus showing the entire
screen in its window. Also, the implementation only works using the TUIO
protocol. Other drivers are not supported.

Though using relatively simple math, the rotation and pinch events work
surprisingly well. Both rotation and pinch use the centroid of all touch
points. A \emph{rotation} gesture uses the difference in angle relative to the
centroid of all touch points, and \emph{pinch} uses the difference in distance.
Both values are normalized using division by the number of touch points. A
pinch event contains a scale factor, and therefore uses a division of the
current by the previous average distance to the centroid.

There is a flaw in this implementation. Since the centroid is calculated using
all current touch points, there cannot be two or more rotation or pinch
gestures simultaneously. On a large multi-touch table, it is desirable to
support interaction with multiple hands, or multiple persons, at the same time.
This kind of application-specific requirements should be defined in the
application itself, whereas the experimental implementation defines detection
algorithms based on its test program.

Also, the different detection algorithms are all implemented in the same file,
making it complex to read or debug, and difficult to extend.

\end{document}