The related work done on this topic falls into four main categories:
\begin{itemize}
\item Previous work on SDAZ.
\item Orders of Control
\item Fitts' Law studies.
\item Physiological analysis.
\end{itemize}

\section{Previous Work on SDAZ}

\citeasnoun{ih:1} identified the problem of disorientation caused by rapid scrolling, and proposed Speed-Dependent Automatic Zooming (SDAZ) as an attempt to solve this. An SDAZ system couples an automatic zoom control with scrolling in such a way that when the user scrolls rapidly, the system automatically zooms-out to reduce blurring. \citename{ih:1} created several applications that used SDAZ to scroll: a web browser, a map browser, a sound editor, an image viewer, and a dictionary viewer. They concluded that the sound editor, image viewer and dictionary viewer were unsuccessful and not worth pursuing further as applications for SDAZ because SDAZ did not appear appropriate for applications of that nature. However, they believed that the web browser and map browser were worth further investigation --- though their informal preliminary evaluation of the systems showed no significant difference between SDAZ and scrollbars.

The idea that there are potential gains to be made by coupling zooming and scrolling has already been validated by Fisheye systems. \citename{gs:1} compared performance of three types of Fisheye systems with two normal scrolling systems at path following, and found the performance of the Fisheye systems to be significantly better. This shows that there are potential gains to be made by coupling the concepts of scrolling and zooming.

\citeasnoun{cs:1} picked up on the ideas of \citename{ih:1} and performed a more formal evaluation of SDAZ and scrollbars on a document browser and a map browser. They found SDAZ to be a 22\% faster on the document browsing tasks, which involved the locating of pictures and headings. On the map browsing task they found that participants were 43\% faster using SDAZ to locate targets. Their analysis of user preferences also indicated that participants preferred the SDAZ system to the standard scrollbar system.

% Interestingly, this 43\% figure can be predicted from the other. The scrollbar system that they were comparing it to used both a horizontal and vertical scrollbar, while the SDAZ system could move in any direction. Hence to reach a target in the diagonal direction, the user had to move each scrollbar one unit. Whereas SDAZ  by using the idea that SDAZ is the same improvement rate as was being obtained equivalent to a two-dimensional 

An earlier paper written by us this year for a COSC 411 (Advanced Human-Computer Interaction) assignment, investigated the maximum speed of information flow that users found tolerable. A modified version of this paper has been accepted for publication in January 2004 \cite{wsc:1}. Users had to estimate, at two different magnifications, what they felt a ``comfortable'' and ``maximum-tolerable'' scrolling speed would be. Our conclusions of this work focused on the applications of our results to SDAZ systems. We suggested that an appropriate maximum scroll rate at full magnification was probably somewhere between 1.5 and 2.7 pages per second, with the optimum likely being much closer to 1.5. We also investigated our theory that in SDAZ systems the magnification could be altered automatically in such a way as to always keep information on the screen for a fixed length of time regardless of the scroll speed. Our data, however, did not support this idea and suggested that the desirable on-screen-time of data is dependent on magnification. Our results did serve to validate the fundamental idea of SDAZ --- our data showed that incorporating zooming ``allows for much more rapid navigation through the document space while maintaining the same level of user comfort.''

\section{Orders of Control}
\label{ordersofcontrol}
%Make sure this label is in the order of control section

Computer control systems generally fall into one of two categories: position control, or rate control \cite{zss:1}. Position control, also known as zero order control, maps the device's displacement to displacement with the system being controlled. For example, a scrollbar is a zero order control system as there is a linear relationship between the position of the mouse when dragging the scroll thumb and the position within the document. Rate control, also known as first order control, maps the input device's displacement to velocity within the controlled system. For example, in rate-based scrolling the distance the mouse moves corresponds to the speed at which the document scrolls. The relationship can be modelled by a first order differential equation, hence the name ``first order control'' \cite{poulton:1}.

One known advantage of position control systems is that they support reversible actions better \cite{bbkf:1}. It is very easy, for example, for a user to grab the scroll thumb to go up a couple of pages to check something and then come straight back to where they were working before very rapidly. \citename{bbkf:1} point out that this is not as easy to do with a rate control system. Our analysis in Section \ref{Tax} and our experimental results (see Chapter \ref{expresults}) agree strongly with this.

It seems to be accepted that for such tasks as navigation in large spaces, rate control systems are better \cite{bbkf:1}. \citename{zss:1} point out that when scrolling through a large document space it is desirable to control not only the position of the document but also the rate of the information flow so that the user can comfortably scan the document, and suggest that a rate control system would be superior to a position control system for doing this. They argue that with a position control device, the user may not be able to control the speed of movement continuously and that physical constraints (such as reaching the edge of the mouse pad) would mean the user has to stop scrolling and the re-engage when scrolling over a long distance.

The SDAZ system proposed by \citename{ih:1} and examined by \citename{cs:1} is a rate control system. SDAZ can thus be viewed as a modified version of rate-based scrolling. Therefore the natural comparison to perform with SDAZ is to compare it to a standard rate-based system, with the question in mind of ``do the modifications make it superior to the standard system?'' Though \citename{cs:1} demonstrated that SDAZ was superior to standard position control systems, it does not necessarily validate the idea behind SDAZ as it has not been compared to rate control systems. Therefore our evaluation of SDAZ seeks to compare it directly to a standard rate-based system --- we also include scrollbars in our evaluation for completeness, but they are not the focus of our comparison.

\section{Fitts' Law}
\label{fittslaw}
 \citeasnoun{gbm:1} suggested that Fitts' Law \cite{fitts:1} could be extended beyond modelling acquisition of a single visible target, to a model of navigation in general. Fitts' Law is a very well understood and heavily researched model that has long been used to model target acquisition (See, for example, such studies as \citeasnoun{ceb:1}, \citeasnoun{epp:1}, \citeasnoun{jm:1}, \citeasnoun{gharm:1}, and \citeasnoun{macfitts:2}).

Fitts' Law states that the time for target acquisition is linearly dependent on the Index of Difficulty (IoD):
%\begin{displaymath}
\begin{equation}\label{fittsmath}
T=a+b\:\textrm{IoD}
\end{equation}
%\end{displaymath}
The IoD, which is measured in bits, is calculated as a logarithm of the ratio of distance to target over target width:
\begin{displaymath}
\textrm{IoD}=\log_{2}(\frac{D}{W}+1)
\end{displaymath}

\citeasnoun{gbm:1} suggested that Fitts' Law could be extended from a model of visible target acquisition to a model of navigation in general. In particular, they had in mind the ability to model multi-scale pointing systems. Multi-scale target acquisition is where the user is provided with two controls (usually scrollbars) one of which performs fine-grained movements within the navigation space and the other course-grained movements. Therefore to locate the target, the user first moves the course-grained bar to approximately the right position and then makes minor adjustments with the finer-grained control. Such controls are usually used where the information space is very large compared to the level of accuracy required. In a large information space (for example a thousand page document), a normal scroll thumb becomes very small and moving it one pixel can jump multiple pages through the document, making navigation extremely difficult. The relevance of \citename{gbm:1}'s research to our work is the idea that Fitts' Law can be used to accurately model scrolling.

\citeasnoun{hcbm:1} took this idea a step further and proposed ``a formal experimental paradigm designed to help evaluate scrolling techniques'' using Fitts' Law as the basis for this paradigm. They believe that the Fitts' Law parameters of distance and tolerance are suitable for being used to provide experimenters with a practical method to quantify scrolling techniques. They propose the use of the standard ``reciprocal tapping task'' \cite{fitts:1}  where the user moves back and forth several times between the two targets as rapidly as possible. After discarding the data from the first couple of taps (as the user is still getting a feel for where the target is) the mean time it took for each distance is calculated for each scrolling system. A graph can then be plotted comparing time against IoD for each system, which should give a linear relationship according to Equation \ref{fittsmath}. This can yield interesting comparisons between scrolling systems --- for example, one system might be better for short distances and another better for long distances.

\section{Physiological Analyses}

It is worth having some idea of exactly what causes fast moving objects to blur. The contents of this section are dealt with at greater length in our earlier work \cite{wsc:1}.

Blurring occurs when information is moving too rapidly across the retina of our eyes for our visual systems to process properly. A comfortable image velocity is around 2 degrees per second \cite{kelly:1}, though a person with good sight can tolerate an image retinal velocity of up to 3 deg/s without blurring occurring \cite{mobe:1}. The human eye has a built-in functionality whereby it naturally tracks moving objects, thereby reducing their retinal velocity and stopping blurring. This is known as smooth-pursuit eye movement \cite{eb:1}. The use of smooth-pursuit eye movement allows us to watch objects that are moving in excess of 9 deg/s \cite{eb:1}, perhaps even up to 100 deg/s \cite{tsps:1}, as the tracking of the target reduces the retinal image velocity to a manageable level.

Blurring is caused, therefore, when the smooth-pursuit system cannot be used properly. In document scrolling, for example, this can occur because the user must fix on a feature of the document and start following it as it moves across the screen with their smooth-pursuit system in order to identify what it is. By the time they have identified it and found that it is not the piece of information they are looking for and jumped their eyes back to another prominent feature, other information may have scrolled off the screen. The user will likely then give up trying to track all the targets and hence just see the information on the screen as a blur.

\citeasnoun{cmn:1} provide a model of human cognitive capabilities which suggests it takes about 200ms to spot a prominent feature in a display. It then takes about 150ms for the smooth-pursuit mechanism to activate \cite{rashbass:1}, and the image must then be stabilised on the retina for 100--125ms before it can be identified (\citeasnoun{bu:1}, \citeasnoun{cmn:1}).

The situation in document scrolling is more complex however. There is the presence of multiple prominent moving features on the display at once, and the fact that information is continually disappearing of one edge of the screen and more is appearing on the other.

We are also unaware of any previous work (apart from our own) that investigates the effect magnification has on the human ability to recognise moving targets.
