One of the purposes of the Transformation component is to provide general transfor- mations that are independent from the visual encodings; this means that they do not directly modify these encodings; the changes in the time domain, however, indirectly modify the visual space. Extending the time domain, for example, results in more points being represented: depending on the encoding this might increase clutter. While the interpretation of the functionality of the operators also depends on the application, it is possible to discuss alternatives of these interpretations for the operators. This is covered in the following subsections.
7.2.1
Time mapped to Position
As discussed in chapter 5, mapping time to the positional channel is a common approach for interactive time visualisation. The effects of temporal transformations on this channel depend on how the other axis is used: if the other channel is used to display the distribution of events or objects over time through identifier variables or distribution of values over time through attribute or variables. For some trajectory visualisations, spatial variables are also combined with time.
The property of the time domain with the strongest influence on this channel is the number of time points, which can be altered by extent operators or by changing granularities. Reducing the number of points requires deciding what to do with the associated data points; various strategies exist depending on the type of data that is being displayed along with time. Regarding the time axis itself, the visual space can be reduced as needed (fig. 7.1 (a)) or remaining time points can be repositioned (fig. 7.1 (c)).
(a) (b) (c)
Fig. 7.1 Example of the effect of (a) trimming the time domain. In (b), the visual space is reduced, whereas in (c), the points are repositioned to keep the same scale.
For the other axis, the choice depends on various characteristics of the data and the encodings, such as the number of points that are being aggregated or the type of data. For quantitative variables, for example, if two points are aggregated into one after a transformation, a new derived attribute must be calculated and it will change the position of the point on the screen.
7.2.2
Time mapped to Size
Time is usually mapped to size through unanchored durations or anchored intervals. In the first case, duration is treated a normal quantitative attribute, which can be derived from the time domain or not – in the latter case, the operator will have no effect. If the duration is derived from the time domain, then changes in the granularity and bounds of the domain will also change the durations; effects of segmenting the time domain depend on the treatment of durations derived from instants that belong to different segments.
Changing the granularities used to derive the durations, within the framework, means that the durations have to be re-calculated, possibly resulting in a new range of durations. The design decisions discussed for position apply in the same way for size. In fig. 7.2 (b), the size of the single bar was calculated as the average of the previous two time points, whereas in fig. 7.2 (c) the size is assigned to the greatest value. The same principle applies to other types of variables; for categorical attributes, if the value of the attribute is different, the visualisation designer must choose the appropriate derivation for the new value.
(a) (b) (c)
Fig. 7.2 Example of the effect of (a) trimming the time domain. In (b), the visual space is reduced, whereas in (c), the points are repositioned to keep the same scale.
7.2.3
Time mapped to Colour
Displaying time through the colour channel often means using a appropriate single hue colour scales based on the sequential nature of time. This means, in an HSL colour space, varying saturation and lightness. For only a few time points, however, if the objective is to simply differentiate the time points, with order not being of any particular importance, it is also possible to use a non-sequential colour scale.
An example of mapping time to colour is the time curve (Bach et al., 2016a) (see ap- pendix A for the specification with the framework), which is a 2D projection of the temporal domain based on the similarity of time points (Figure 7.3a). In this visu- alisation, the spatial distribution of the time points does not reflect any temporal ordering. As there is not an intrinsic temporal component in the 2D projection, the authors mapped the temporal order to the colour channel and also to the criteria used to connect points.
In the original paper, the authors used a continuous colour scale spanning the whole temporal extent. With this scheme, while it is possible to identify the temporal ordering of events, it is difficult to identify the temporal location when events occur irregularly in time, as in the case of the curves in fig. 7.3a – even though line thickness indicates the length of the interval between two data points. One alternative is to change the granularity of the domain used for colouring, for example, by rolling up to a coarser granularity, such as in fig. 7.3b. In this case, one of the factors to consider when choosing the appropriate granularity is that the colour change might suggest an interruption during a burst of activity.