\documentclass[twoside,openright]{uva-bachelor-thesis} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage{hyperref,graphicx,tikz,subfigure,float,lipsum} % Link colors \hypersetup{colorlinks=true,linkcolor=black,urlcolor=blue,citecolor=DarkGreen} % 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} % Title page \maketitle \begin{abstract} % TODO \end{abstract} % Set paragraph indentation \parindent 0pt \parskip 1.5ex plus 0.5ex minus 0.2ex % Table of content on separate page \tableofcontents \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. \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. \chapter{Design} \label{chapter:design} % Diagrams are defined in a separate file \input{data/diagrams} \section{Introduction} % TODO: rewrite intro? 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:daemon} 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. 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 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 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}. \driverdiagram Support for a touch 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. Because driver implementations have a common output format in the form of events, multiple event drivers can run at the same time (see figure \ref{fig:multipledrivers}). \multipledriversdiagram \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 also 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.} An area can be seen as an independent subset of a touch surface. Therefore, the parameters (coordinates) of events and gestures within an area should be relative to the area. 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{Area tree} \label{sec:tree} 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. If the architecture were to be used in combination with an application framework like GTK \cite{GTK}, each GTK widget that must receive gestures should have a mirroring area that synchronizes its position with that of the widget. Consider a panel with five buttons that all listen to a ``tap'' event. If the panel is moved as a result of movement of the application window, the position of each button has to be updated. This process is simplified by the arrangement of areas in a tree structure. A root area represents the panel, containing five subareas which are positioned relative to the root area. The relative positions do not need to be updated when the panel area changes its position. GUI frameworks, like GTK, use this kind of tree structure to manage widgets. A recommended first step when developing an application is to create some subclass of the area that synchronizes with the position of a widget from the GUI framework automatically. \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. Gestures such as a button tap or the dragging of an object using one finger are easy to detect by comparing the positions of sequential $point\_down$ and $point\_move$ events. A way to detect more complex gestures is based on a sequence of input features is with the use of machine learning methods, such as Hidden Markov Models \footnote{A Hidden Markov Model (HMM) is a statistical model without a memory, it can be used to detect gestures based on the current input state alone.} \cite{conf/gw/RigollKE97}. A sequence of input states can be mapped to a feature vector that is recognized as a particular gesture with some probability. This type of gesture recognition is often used in video processing, where large sets of data have to be processed. Using an imperative programming style to recognize each possible sign in sign language detection is near impossible, and certainly not desirable. Sequences of events that are triggered by a multi-touch based surfaces are often of a manageable complexity. An imperative programming style is sufficient to detect many common gestures. The imperative programming style is also familiar and understandable for a wide range of application developers. Therefore, the aim is to use this programming style in the architecture implementation that is developed during this project. However, the architecture should not be limited to multi-touch surfaces alone. For example, the architecture should also be fit to be used in an application that detects hand gestures from video input. A problem with the imperative programming style is that the detection of different gestures requires different pieces of detection code. If this is not managed well, the detection logic is prone to become chaotic and over-complex. To manage complexity and support multiple methods of gesture detection, the architecture has adopted the tracker-based design as described by \cite{win7touch}. Different detection components are wrapped in separate gesture tracking units, or \emph{gesture trackers} The input of a gesture tracker is provided by an area in the form of events. When a gesture tracker detects a gesture, this gesture is triggered in the corresponding area. The area then calls the callbacks which are bound to the gesture type by the application. Figure \ref{fig:trackerdiagram} shows the position of gesture trackers in the architecture. \trackerdiagram{Extension of the diagram from figure \ref{fig:areadiagram}, showing the position of gesture trackers in the architecture.} The use of gesture trackers as small detection units provides extendability of the architecture. A developer can write a custom gesture tracker and register it in the architecture. The tracker can use any type of detection logic internally, as long as it translates events to gestures. An example of a possible gesture tracker implementation is a ``transformation tracker'' that detects rotation, scaling and translation gestures. \section{Reserving an event for a gesture} \label{sec:reserve-event} A problem occurs when areas overlap, as shown by figure \ref{fig:eventpropagation}. When the white square 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 gesture trackers of the two squares. When an event in the white square is used for rotation, that event should not be used for rotation in the gray square. In other words, the event must be \emph{reserved} for the rotation gesture in the white square. In order to reserve an event, the event needs to be handled by the rotation tracker of the white before the rotation tracker of the grey square receives it. Otherwise, the gray square has already triggered a rotation gesture and it will be too late to reserve the event for rotation of the white square. When an object touches the touch surface, the event that is triggered should be delegated according to the order in which its corresponding areas are positioned over each other. The tree structure in which areas are arranged (see section \ref{sec:tree}), is an ideal tool to determine the order in which an event is delegated to different areas. Areas in the tree are positioned on top of their parent. An object touching the screen is essentially touching the deepest area in the tree that contains the triggered event. That area should be the first to delegate the event to its gesture trackers, and then move the event up in the tree to its ancestors. The movement of an event up in the area tree will be called \emph{event propagation}. To reserve an event for a particular gesture, a gesture tracker can stop its propagation. When propagation of an event is stopped, it will not be passed on the ancestor areas, thus reserving the event. The diagram in appendix \ref{app:eventpropagation} illustrates the use of event propagation, applied to the example of the white and gray squares. \section{Serving multiple applications} \label{sec:daemon} The design of the architecture is essentially complete with the components specified in this chapter. However, one specification has not yet been discussed: the ability address the architecture using a method of communication independent of the application programming language. If an application must start the architecture instance in a thread within the application itself, the architecture is required to be compatible with the programming language used to write the application. To overcome the language barrier, an instance of the architecture would have to run in a separate process. A common and efficient way of communication between two separate processes is through the use of a network protocol. In this particular case, the architecture can run as a daemon\footnote{``daemon'' is a name Unix uses to indicate that a process runs as a background process.} process, listening to driver messages and triggering gestures in registered applications. \vspace{-0.3em} \daemondiagram An advantage of a daemon setup is that is can serve multiple applications at the same time. Alternatively, each application that uses gesture interaction would start its own instance of the architecture in a separate process, which would be less efficient. \section{Example usage} \label{sec:example} This section describes an extended example to illustrate the data flow of the architecture. The example application listens to tap events on a button within an application window. The window also contains a draggable circle. The application window can be resized using \emph{pinch} gestures. Figure \ref{fig:examplediagram} shows the architecture created by the pseudo code below. \begin{verbatim} initialize GUI framework, creating a window and nessecary GUI widgets create a root area that synchronizes position and size with the application window define 'rotation' gesture handler and bind it to the root area create an area with the position and radius of the circle define 'drag' gesture handler and bind it to the circle area create an area with the position and size of the button define 'tap' gesture handler and bind it to the button area create a new event server and assign the created root area to it start the event server in a new thread start the GUI main loop in the current thread \end{verbatim} \examplediagram \chapter{Test applications} A reference implementation of the design is written in Python. Two test applications have been created to test if the design ``works'' in a practical application, and to detect its flaws. One application is mainly used to test the gesture tracker implementations. The other program uses areas in a tree, demonstrating event delegation and propagation. 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 and its test applications are a Proof of Concept, %meant to show that the architecture design is effective. %that translates TUIO messages to some common multi-touch gestures. \section{Reference implementation} \label{sec:implementation} % TODO % een paar simpele areas en trackers % Geen netwerk protocol The reference implementation is written in Python and available at \cite{gitrepos}. The following component implementations are included: \textbf{Event drivers} \begin{itemize} \item TUIO driver, using only the support for simple touch points with an $(x, y)$ position. \end{itemize} \textbf{Gesture trackers} \begin{itemize} \item Basic tracker, supports $point\_down,~point\_move,~point\_up$ gestures. \item Tap tracker, supports $tap,~single\_tap,~double\_tap$ gestures. \item Transformation tracker, supports $rotate,~pinch,~drag$ gestures. \end{itemize} \textbf{Areas} \begin{itemize} \item Circular area \item Rectangular area \item Full screen area \end{itemize} The implementation does not include a network protocol to support the daemon setup as described in section \ref{sec:daemon}. Therefore, it is only usable in Python programs. Thus, the two test programs are also written in Python. \section{Full screen Pygame program} % TODO The first test application was initially implemented without application of the architecture design. This application was a Python port of a Processing\footnote{} program found on the internet, with some adaptations to work with the TUIO protocol. \section{GTK/Cairo program} % TODO \chapter{Conclusions} % TODO \chapter{Suggestions for future work} \section{A generic way for grouping events} \label{sec:eventfilter} % TODO % - "event filter" ipv "area" \section{Using a state machine for gesture detection} % TODO % - gebruik formelere definitie van gestures ipv expliciete detection logic, % bijv. een state machine \section{Daemon implementation} % TODO % - network protocol (ZeroMQ) voor meerdere talen en simultane processen % - volgende stap: maken van een library die meerdere drivers en complexe % gestures bevat \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: 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. % 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. \chapter{Diagram demonstrating event propagation} \label{app:eventpropagation} \eventpropagationfigure \end{document}