\section{A Taxonomy of Navigation}
Some types of navigation are performed effectively by current methods, while other types are not. It is worth examining different types of document navigation in order to gain an understanding of the strengths and weaknesses in current methods of navigation and to obtain insight into just how SDAZ systems would complement the standard techniques.

We are not aware of any existing taxonomies for the classification of different navigation actions. We propose the following characterisation of the different types of document navigation:
\begin{itemize}
\item Spatial

This is where the user knows where in their document their target is. For example ``I want to look at chapter three which is one-third of the way through this document.'' This is analogous to picking up a book and knowing approximately which section of the book you want to look at.

\item End-Point

This is where it is desirable to navigate to the very start or very end of the document. This might often form the first part of a two part navigation action - for example ``I want to go to the page that is two pages from the end of the document''.

\item Pagination

This is where the user wants of make minor adjustments to the information displayed on their screen. For example the user might be focusing on an item near the bottom of the screen and want to centre the screen on that location, or perhaps to look at the previous page.

\item Search-For

This is where the user enters a keyword into a search tool and the tool takes the user to all such instances of the word in the document.

\item Paging

This is where the user is reading or skim-reading the document and wants to keep centred the part they are examining as they move slowly and linearly through the document.

\item Section Jump

This is where the user wishes to navigate to a section heading. For example ``I want to go to the 'Related Work' heading'' or ``I want to go to chapter 4''.

\item Visual Browsing

This is where the user is unfamiliar with the document and wants to get a feel for its contents. The user wants to get an overview of the type of information contained in the document, important sections and graphics.

\item Visual Search

This is where the user has a known visual target in mind. For example ``I want to find the red graph'' or ``I want to find a particular page and I can remember what it looked like''.

\end{itemize}

It is clear that the current tools achieve some of these tasks effectively. For example, a scroll bar seems by far the most effective tool for Spatial navigation. The user can grab the scroll-thumb and move it to the appropriate location. Even if the document is too large for use of the scroll-thumb to accurately acquire the target, it will still be best for the scrollbar to adjust the position as close to the target as possible and then to acquire the target by using Visual Search. End point navigation is also a solved-problem: It is standard practise for Ctrl-Home and Ctrl-End to navigate instantaneously to the beginning and end of a document. Pagination also is easily achieved by use of the Pg-Up and Pg-Down buttons, similarly most applications achieve Search-For navigation by providing a ``Find'' utility.

It is in Paging that rate-based scrolling finds its niche.  Paging can be accommodated in small documents by dragging the scroll thumb slowly, however in large documents this is impractical as the smallest movement of the thumb may jump so far as to skip information. Use of the Pg- keys is not always adequate as the sudden jump these cause disorientates the user who has to re-orientate themselves before continuing to read. Far more satisfactory for this task is rate-based scrolling where the document scrolls continuously at a speed controlled by the user. This allows the user to keep their focus at the centre of the screen, to not be distracted by sudden jumps of the document, and to have full control over the speed of the document's movement.

Section Jump is performed most effectively by the user of an overview+detail system, where one window contains a listing of the main sections in the document allowing one click to jump straight to them, while the other contains the document itself. The major disadvantage of such systems is that the extra window adds to the screen clutter.

However, current methods do not so effectively achieve Visual Search, and Visual Browsing. It is in these areas, as well as Paging and Section Jump, that we believe SDAZ has most to offer. The most obvious advantage of SDAZ is in Visual Search, on which we focus our formal evaluation later in this report. SDAZ provides a unparallelled way of smoothly navigating through large documents without the limitation of blurring that occurs in rate-based scrolling. (\textbf{MORE}) Visual Browsing is facilitated by SDAZ through the zoom-out. Whenever the user scrolls rapidly, the automatic zoom-out allows the user to view a wider area of the document giving them a better feel for its overall contents. In Paging, SDAZ retains all the advantages of rate-based scrolling since at low speeds it is equivalent to rate-based scrolling. In performing a Section Jump, SDAZ is perhaps not as good as an overview+detail system. However, since section headings are likely to be large and bold, they will stand out when zoomed-out (though perhaps not readable) and could be easily navigated to if the user had a moderate knowledge of where in the document to find the section they were looking for and so could obtain their target by Visual Search.

In the evaluation performed by \citename{ih:1} the zoom-out was semantic based --- section headings and graphics were kept fairly large while body text was shrunken further. By using our taxonomy it can be seen that this would have resulted in a trade-off between Visual Search and Section Jump. Their system did not preserve page layouts which we believe would have reduced its usefulness for performing Visual Search, and their system became increasingly an overview+detail system as it zoomed out probably increasing its ability to perform a Section Jump. The destruction of page layouts by the zoom-out would also be detrimental to the Visual Browsing functionality.


\section{Physiological Considerations}
The question of maximum rates of visual flow is also an issue for research into Rapid Serial Visual Presentation (RSVP). RSVP displays items in the information set in very quick succession. It ``is the electronic equivalent of riffling a book in order to assess its content'' \cite{ds:1}. With modern computing technology, the limiting factor on the speed at which the data can be displayed is the capacity of the human observer to process the information being presented. RSVP was originally studied from a psychological standpoint but more recently from a human-computer interaction perspective.

\citeasnoun{fo:1} first used RSVP to explore the nature of human visual perception. He performed four similar experiments in which words were displayed in rapid succession and participants were then asked to record what they had seen. He found that syntactically simpler sentences require less time for participants to perceive them accurately. Increased informational content required an increase in the duration of exposure to the visual system, otherwise it resulted in decreased performance.

Research into human visual perception has found that the human eye summates signals over a period of 120-125ms (\citeasnoun{cmn:1}, \citeasnoun{bu:1}). Though the more recent signals are given more weight \cite{sz:1}.

This might lead us to believe that we could predict the level of blurring by simply using the data's displacement in a 120ms time slot. \citename{bu:1}, however, found that observed blurring is significantly less than this model would predict. This is because the human visual system reduces blur by tracking moving objects with smooth-pursuit eye movement \cite{eb:1}. Tracking moving targets with the eye reduces the relative velocity of the image across the retina.

Visual accuracy can usually tolerate an image retinal velocity of up to 3 degrees per second \cite{mobe:1}, with a comfortable velocity being around 2 deg/s \cite{kelly:1}. However, the introduction of smooth-pursuit eye movement allows movement 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.

In some cases this smooth-pursuit mechanism can be ignored. For example, RSVP sometimes deals with image durations of 100ms or even less \cite{spence:1}. This is too short a duration for the smooth-pursuit system to activate \cite{mobe:1}.

\section{Document Scrolling}
\subsection{A Theoretical Estimation}
In the case of document scrolling, the user will attempt to read each main heading as it flashes past and recognize each major image. Given that we are dealing with image velocities of approximately 20 deg/s, it will be necessary that the smooth-pursuit system activates to track the target. Thus, we can predict the time required as follows:
\begin{itemize}
\item The time taken to recognize a portion of the document as being an important landmark in the document. $\approx$200ms according to \citename{cmn:1}'s model, as it requires one cycle of both the visual system and the cognitive system.
\item The time taken for the smooth-pursuit system to activate and reduce the retinal flow to an acceptable level. $\approx$150ms according to \citeasnoun{rashbass:1}.
\item The time taken to identify the image ($\approx$100ms according to \citename{spence:1}) or read the heading. The normal reading rate is approximately 280 words per minute \cite{km:1}. Thus, given a one to three word section heading, it will take 200-600ms to read.
\end{itemize}
Therefore a crude approximation would say that information must be visible for 450-950 milliseconds to be recognized properly.

\section{Discussion of Units}

The introduction of the idea of different levels of magnification (in such systems as SDAZ, for example) means that two distinct measurements of speed need to be separated.

Let us define \emph{document speed} as the rate at which navigation through the information space is occurring. This will be measured primarily in units such as pages/second or lines/second. It is this value that it is desirable to maximize in order to acquire the target more rapidly.

Let us define \emph{viewer speed} as the rate at which information moves across the display. We believe it is most convenient to measure this value in terms of \emph{screen time}. That is, using units of seconds. Alternative units that might be used for this include cm/s, pixels/s and degrees/s. These alternative units can be calculated as functions of screen resolution, physical screen size, and viewer distance from the screen. Since, we are dealing with image velocities of significantly greater than 3 deg/s, the smooth-pursuit system is reducing the actual retinal image velocities to manageable levels, rendering the actual image velocity in deg/s somewhat irrelevant. The more generalizable unit therefore, should be \emph{screen time}, which is in agreement with our theoretical analysis.

Given these definitions there will be a relationship between document speed and viewer speed as a function of magnification:
\[
Viewerspeed = Magnification / Documentspeed
\]

\section{Fitts' Law}

\textbf{FITTS' LAW!!!!!!!!!!!}
