The diagram plane or space is spanned by axes, which determine the scaling of the data to be displayed. The 2D diagram uses at a minimum one vertical Y axis and one horizontal X axis, and the 3D diagram also uses a Z axis, which is pointed toward the viewer. Please note that, contrary to the typical labeling in mechanics, the vertical axis in FlexPro is also called the Y axis in a 3D diagram. While 3D diagrams use a fixed number of three axes, one each for the X, Y, and Z directions, several Y and X axes can be used for a 2D diagram. This makes it possible to display curves with different physical units in the same diagram. If you use more than one Y axis, then you can alternatively stack them on top of each other.
Dynamic Number of Axes
If you have a list containing several data sets with different units above an axis and display the list in a 2D Diagram, FlexPro automatically displays several scales: one per unit. You can also refer to the Dynamic Axes and Curves option in the Diagram Wizard.
To scale the axes of 2D and 3D diagrams, you can use the linear, logarithmic with base 10, 2 or e, offset reciprocal, third octave, octave, probability, probit and logit scale types.
With linear scaling you can choose whether you would like to specify a fixed division interval or whether the division interval should be determined automatically so that there are a fixed number of divisions.
The linear scaling with metric division option lets you establish a fixed relationship between the length of an axis and the physical unit of the curve displayed against this axis. You can set the scale freely. For example, if you set 0.1 V/mm as the scale and 1 V as the division interval, the divisions of the axis will be exactly 1 cm apart. If you enlarge the diagram and the length of the axis changes accordingly, the number of divisions will increase automatically. The distance between the divisions will remain constant.
By selecting Linear, division by data set or Logarithmic, division by data set you can determine at which positions on the axis divisions are to be drawn by using a data set or a formula. The procedure used depends on the data set or formula that you specify for labeling:
•Data series: The values are taken from the data series in sequential order, and a division is drawn at the corresponding position. All numerical data types are allowed. The process ends when all values have been read.
•Formula with one argument (function): The function is called with an ascending index as the argument. The first index is a null value. The result of the function determines the position of the axis division. All numerical data types are allowed for the result. The process ends when a value lies outside of the starting or end value of the axis, or when a void floating point value or the value Empty is passed.
The reciprocal scaling option uses the transformation X' = 1 / X.
Use Offset reciprocal scaling to convert from Kelvin to °C. The transformation is X' = 1 / (X + 273.15).
The probability scaling option is used to linearize normal distribution functions. If the Y axis of a diagram has been probability-scaled, these types of distribution functions appear as straight lines and can easily be compared.
Probit scaling option corresponds to probability scaling, although here standard deviations are considered, where 50% corresponds to the value of 5. The value range of a probability or probit-scaled axis lies in the interval [0.0001%, 99.9999%].
Logit scaling is similar to probability scaling. As a transformation, however, the Logit function X' = X / (100 - X) is used. The value range of a logit-scaled axis is within the interval [0.1%, 99.9%].
The scaling types Third octave and Octave are logarithmic scaling options with the divisions corresponding to the third octave or octave series.
You can define an output unit for the axis. All curves are then converted to this unit before output. If you do not define an output unit, the axis is assigned the unit of the first curve whose data has a unit; all additional curves are transformed to this unit.
When the axis is displayed at both borders of a 2D diagram, you can assign a different unit to the second scaling, such as m/s for scaling on the left border and km/for scaling on the right border.
You can set the scaling of the axis manually by specifying the physical values that correspond to both ends of the axis. Alternatively, you can specify data sets or FPScript formulas that provide end values. With Autoscaling these end values are automatically determined from the curves to be displayed. This means that the curves are displayed with optimal spread. If you select Data minimum/maximum the extreme values of the curves displayed on the axis are used. By selecting Data range lower limit/upper limit the data range values entered on the General tab of the data sets are used. You can exclude individual curves from autoscaling. Autoscaling is often used with the Extend end values attribute. This means that the extreme values found are not used directly as axis end values; instead, a correction takes place first, so that the end values of the axis come to lie on a division. The options Symmetric scaling and Align zero point with that of the previous axis extend the start or end value of the axis so that the zero point is exactly in the middle of the axis or is aligned with that of the previous axis. The axis end values can be calculated dynamically using an FPScript formula. In 2D diagrams with several axes, you can also link the end values of neighboring axes.
If all of the diagram axes have the same physical unit, you can achieve an undistorted picture using isometric axis adjustment. This corrects the axis end values corrected so that they correspond to the axis length ratios. The isometric axis adjustment means for example, that with a 2D diagram, circular curves are also displayed as circles and not as ellipses.
Usually the X axis is aligned from left to right, the Y axis is aligned from bottom to top and the Z axis is aligned from back to front. However, the orientation can be switched around for each axis. You can also add orientation arrows to the axes, which point in the direction of the increasing scalar values.
You can define an axis origin for all 2D diagram axes and for the Y axis of a 3D diagram. For 2D diagrams, the axis origin determines the point of intersection of the corresponding axis of the axis system unless this axis is positioned at the edge of the diagram. If you have activated floor lines for the X axis, then a floor line parallel to the X axis is displayed at the height of the axis origin of the corresponding Y axis. You can choose whether the floor line should be drawn only for columns and surfaces or for any curves.
For a 3D diagram, the axis origin determines the location of the floor, unless it was positioned at one of the end values of the axis. This floor determines, for instance, the plane on which the 3D columns are placed and is displayed as a frame with divisions.
You can provide an axis with divisions and subdivisions that can be labeled with the values corresponding to their position on the axis.
The divisions are shown as small dashes on the axis, and you can change their type, length and color. The position of the divisions on the axis result from the axis scaling. You can either specify the amount that should correspond to one division interval or you specify the number of division intervals. It is also possible to specify the positions of the divisions as data series or, to calculate them using an FPScript function, which obtains the index of the division to be calculated as the argument.
With the division origin, you determine the value from which the division is to start at the top and bottom. This does not have to lie between the starting value and end value of the axis. When the subdivisions are applied, the division intervals are split up into a certain number of subdivisions. You can specify this number. Logarithmic axes are treated separately: With a division of 1 and either a subdivision total of 2 or a subdivision total of 8 and the Avoid overlapping option selected, only positions 2 and 5 are labeled, for instance, "10² 2 5 10³".
The axes divisions and subdivisions, for which you have enabled the option Account for this axis when drawing the grid on the Appearance tab of the Properties dialog box, also determine the location of the grid lines, if a grid is to be displayed.
You can label the divisions and subdivisions of an axis with any values taken from a data set or calculated using a function. For labeling you can use a data series, a signal or a formula with an argument (function). FlexPro then labels the divisions and subdivisions as follows:
The values are taken from the data series one by one and written onto the axis.
All data types, including strings, are permitted. The values have to be stored in the same order in the data set in which the labeling of the axis occurs.
The division labeling then proceeds from the division origin to the end value and then to the starting value of the axis. This is why you should set the division origin to the starting value of the axis.
Labeling of the divisions with text originating from a data set.
The value resulting from the axis division is searched for in the X component of the signal and the corresponding Y value is then written onto the axis. If necessary, interpolation is performed.
Display signals against any measured quantity, which does not have to be monotone, e.g., time signals over a space coordinate.
The value resulting from the axis division is passed to the function as an argument and the result of the function is written onto the axis. All data types are allowed for the result, including strings.
Linearization of any characteristic line.
The axis will continue to be scaled according to the scaling configured and, if applicable, the values established through automatic scaling.
You can add an axis label to each axis of a diagram. You can specify the axis label text directly or use the text from the curves displayed on the axis, which also have an Axis Labeling tab in their Properties dialog box. You can enter any text in which you can embed Fields for accessing header information of the displayed data sets. FlexPro offers a variety of pre-defined fields for labeling axes so that you do not have to program these yourself.
If you display multiple curves and use their axis labels, then these form text stacked vertically written on the axis. However, you can turn this option off for individual curves to show the time information only once on the X axis, for instance. The axis labels of the individual curves can be colored in with the respective color of the curve to make label assignment easy.
The data that you display above an axis should all have the same physical unit. You can add this unit to the axis label, display it between the last two divisions or behind each division.
The axes of 2D diagrams can be displayed at either edge of the diagram, at both edges or in the axis origin of an assigned axis pointing in the other direction. Several Y axes in a 2D diagram can be displayed as stacked instead of side-by-side. Here, the diagram is divided into several areas, and you can adjust the size of these areas. It is also possible to limit the area across which an axis is stretched. You can, for instance, create a second Y axis that only stretches over an area of 0% to 10% of the height of the diagram to overlay a digital channel in a narrow band as a step line. You can also display several X axes side by side.