Exact or Rounded Curve Point Representation

The options under Representation in the Global Options dialog box only apply to reference axes graphs, and these graphs must not have time line scaling.

The Exact and Rounded options let you specify how the points in the curve are distributed over the reference axis. In the discussion of these options, the reference axis is assumed to be the x-axis.

These options are important when, as is most often the case, the number of pixels in the window is not an even multiple of the number of points in the curve. SAP Statistics must decide two questions:

  • How the points are to be spread over the width of the window?
  • How the gridlines are to be spread over the width of the window, and how they should be labelled?

Both considerations depend on how the number of curve points compares to the number of window pixels:

  • More curve points than window pixels:

SAP Statistics must choose a selection of the points to display.

Example: For a 700-point curve and a 200-pixel window, the system can choose 200 of the 700 curve points for display: approximately every third or fourth (that is, every "3.5th") curve point.

  • Fewer curve points than window pixels:

The system can display all points in the data, but must decide which pixel to assign each point to.

Example: For a 200-point curve and a 700-pixel window, the system can display all 200 points: at intervals of approximately one point every three or four (that is, every "3.5th") pixels.

The two options under Representation solve these questions as follows:

  • Exact

The data points in the graph are all the same distance apart, and each point lies on a gridline.

With an Exact representation, the system assigns one point to every nth pixel (more points than pixels) or exactly n pixels to every point (fewer points than pixels).

A gridline is drawn for each point displayed, and is labelled with the point's x-value. (The above figure shows a graph with Markered curves with an Exact representation of three curves. Compare with the following figure.)

Achieving this regularity provides a more accurate representation of the input, but often makes inefficient use of the display space. For example, with 700 pixels and 200 points, only 600 pixels can be used (by displaying a point on every third pixel). The other available 100 pixels are not used, so that an empty stripe appears at the right end of the graph.

  • Rounded

The system does not maintain the same distance between data points, and the points do not necessarily lie on gridlines.

With a Rounded representation, the system does not use a whole number (such as the n factor mentioned for Exact) to assign points to pixels or pixels to points. Instead, the quotient of the larger number and the smaller (pixels and points) is used to drive the assignment in an irregular fashion.

For example, for 700 pixels and 200 points, the quotient 3.5 is used, instead of 3. Every "3.5th" pixel is pinpointed for assignment: the number of each is rounded down if the result is fractional. Thus the first five points, (theoretically assigned to pixels 0, 3.5, 7, 10.5, 14), would be actually be placed on pixels 0, 3, 7, 10, 14.

Using the Rounded method, the distance between pixels with points on them will vary slightly from point to point. In this example, sometimes every third, sometimes every fourth.

A similar calculation is performed when there are more points than pixels, except that every "3.5th" point is assigned to a pixel. In this case, the display sometimes shows every third point and sometimes every fourth.

With Rounded, gridlines are assigned by dividing the number of pixels by the optimal number of gridlines, and labelling each with the x-value of data point that is nearest. (The optimal number of gridlines is derived from the the window width and the size of the character strings needed to label the reference axis.) There is no guarantee that the point for that label falls exactly on the gridline shown.

The following figure shows a Rounded representation of three curves. Compare with it with the preceding figure, which shows an Exact representation.

The Rounded option makes maximum use of the display area because it is not restricted to using a number of pixels that is an even multiple of the number of curve points. This can make a substantial difference for example when there are 1000 pixels and 501 curve points.

A graph shown using the Rounded option may not be as accurate a depiction of the input. However, in most cases, the variable distances between points in the graph may be neither visible nor important.