on how records are mapped to marks. For example, selecting a bar in an ordinal–quantitative pane will result in a bar chart, whereas selecting a line mark results in a line chart. The mark set currently supported in Polaris includes the rectangle, circle, glyph, text, Gantt bar, line, polygon, and image. There are two types of marks; single tuple marks and multituple marks. Multituple marks form a single graphical entity from a set of marks; an example is a polygon mark where each vertex of the polygon is a single tuple.

Following Cleveland, ⁸ we further structure the space of graphics by the number of independent and dependent variables. For example, a graphic where both axes encode independent variables is different than a graphic where one axis encodes an independent variable and the other encodes a dependent variable ( y = f (x)). By default, dimensions of the database are interpreted as independent variables and measures as dependent variables. We briefly discuss the defining characteristics of the three families within our categorization. It should be noted that these rules allow us to automatically choose a default mark given the types of the fields on the axes.

ordinal–ordinal graphics: The characteristic member of this family is the table, either of numbers or of marks encoding attributes of the source records.

In ordinal–ordinal graphics, the axis variables are typically independent of each other, and the task is focused on understanding patterns and trends in some function f (O ,O )

xy

AE R, where R represents the fields encoded in the retinal properties of the marks. This can be seen in the heatmap in Figure 3, where the analyst is studying gene expression as a function of experiment and gene. Figure 6(a) shows another example where lines of source code are color-encoded with the number of cache misses attributable to that line. ordinal–Quantitative graphics: Well-known representatives of this family of graphics are the bar chart, the dot plot, and the Gantt chart.

In an ordinal–quantitative graphic, the quantitative variable is often dependent on the ordinal variable, and the

analyst is trying to understand or compare the properties of some set of functions f (O) AE Q. The cardinality of the record set affects the structure of the graphics in this family: When the cardinality of the record set is one, the graphics are simple bar charts or dot plots. When the cardinality is greater than one, additional structure may be introduced to accommodate the additional records (e.g., a stacked or clustered bar chart).

The ordinal and quantitative values may be independent variables, such as in a Gantt chart. Here, each pane represents all events in a category; each event has a type as well as a beginning and end time. Figure 6(c) shows a table of Gantt charts, with each Gantt chart displaying the thread scheduling and locking activity on a CPU within a multiprocessor computer.

Quantitative–Quantitative graphics: Graphics of this type are used to understand the distribution of data as a function of one or both quantitative variables and to discover causal relationships between the two quantitative variables, such as in a scatterplot matrix. Figure 3 illustrates another example of a quantitative–quantitative graphic: the map. In this figure, the analyst is studying election results by county.

3. 3. Visual mappings

Each record in a pane is mapped to a mark. There are two components to the visual mapping. The first component, described in Section 3. 2, determines the type of graphic and mark. The second component encodes fields of the records into visual or retinal properties of the selected mark. The visual properties in Polaris are based on Bertin’s retinal variables: ⁴ shape, size, orientation, color (value and hue), and texture.

Allowing analysts to explicitly encode different fields of the data to retinal properties of the display greatly enhances the data density and the variety of displays that can be generated. However, in order to keep the specification succinct, analysts should not be required to construct the mappings. Instead, they should be able to simply specify that a field be

figure 3: the families of graphics within our taxonomy with examples of well-known charts from each family. the taxonomy structures the space of graphics into three families by the types of fields assigned to their axes and then further structures each family by the number of independent and dependent variables. using this taxonomy we can derive the type of graphic within each pane from the table axes expressions and the mark type.