The Contour Definition Menu can be spawned in one of two ways from the Plot Definition Menu: by selecting Contour as a Plot Tools option or by setting one of the plot axis to be a function Contour. In the first case the menu is made immediately visible. In the second case the menu is created silently, that is it does not pop immediately up onto the screen. In both cases the menu is added to the Menu List in the lower section of the Control Panel and if it is in the background it may be brought to the foreground from that listing.
When spawned from the Plot Tools option the default menu appears as:
When spawned from the Function Of option the default menu appears as:
The contour definition menu sets all of the options available to the contour routines. This includes how to perform the interpolation to empty grid points, how the contour should be output, and if necessary how to set up the internal contour grid.
When the contour menu is spawned from the Plot Tools option the default settings are sufficient to produce an acceptable smoothing of the data. When the contour menu is spawned as a result of a Function Of axis setting several fields must be set before a contour can be made.
FORMAT identifies the input format the data. In general this is correctly set when the menu is popped up. The options are:
| Option | Definition |
|---|---|
| X vs Y | Full Cartesian input. Data is input as a set of intensities as a function of X, Y, and possibly Z. |
| XY vs Z | Half Cartesian input. Data is input as a set of intensities as a function of [X2 + Y2]½ (XY) and Z. This option is not currently implemented. |
| Phi vs Theta | Angular input. Data is input as a set of intensities as a function of the angles Phi (phase angle) and Theta (elevation angle). |
METHOD identifies how the input data is to be processed. The options are:
| Option | Definition |
|---|---|
| RANDOM(3D) | Full Cartesian input data provided from a 3D data source (Z values are included). The contour will be made to a cut through the data set. Selection of this option will bring up one instance of the 3D PLANE DEFINITION menu. The plane to contour is selected through this menu. |
| RANDOM(2D) | Full Cartesian input data provided from either a 2D or 3D data source. The contour is done using all data and ignoring the Z component of the data (all data collapsed to X-Y plane). Specifying a Random processing means that there is no ordering to the data input and that neighboring data points cannot be easily inferred. |
| ORDERED GRID (2D) | Input and usage similar to Random(2D) except input data constitutes a rectangular grid. The input is been blocked into columns of data, all columns having the same length. Graphically the points surrounding a data point in at row J in column I will be the points at J, J+1, and J-1 in the adjacent columns of data (I-1 and I+1) and at J+1 and J-1 in the current column of data (I). The spacing between adjacent rows and/or columns in the grid can be irregular. Used often with spiral data with the spiral spokes forming the data columns which advance in phase. |
| HOLLOW GRID (2D) | The input data is pregridded and not all of the grid position may be filled. The contour will fill the missing values using the existing grid values. This option is set when the menu is invoked from the Plot Tools option and cannot be changed. |
| PREGRIDDED (2D) | The input data is fully pregridded. Any empty grid points are to be left empty. All subsequent smoothing and production of contour lines will occur from the contour grid as received. |
DISPLAY AS sets the contour output format. The options include:
| Option | Definition |
|---|---|
| COLOR FILL | Output is the color encoded contour grid |
| COLOR CONTOURS | Output is a series of color encoded lines of constant intensity |
| CONTOURS | Output is a series of lines of constant intensity |
| FILL w/CONTOURS | Output is the color encoded contour grid with a series of lines of constant intensity overlaying it. |
GRID sets whether the set of nearest neighbors to all of the contour grids needs to be recomputed when the contour program is being multiple times. The options are:
| Option | Definition |
|---|---|
| CONSTANT | The input data has the same X, Y, Z for each call to the contouring routine. There is no need to relocate the nearest values to the contour grid points. If the nearest neighbor array doesn't exist (first call) it will be created. Not only must the X, Y, Z values be the same, the input order cannot change. |
| RECALCULATE | Need to re-establish the nearest neighbors to the contour grid points. |
DUMP MESH indicates whether the contour mesh should be dumped to an file in ASCII format. The options are:
| Option | Definition |
|---|---|
| NO | Do not dump mesh |
| YES | Dump the mesh. File the mesh is dumped to is named MESH. The file contains a rectangular grid of values, the values being the interpolated value at each mesh point. |
NEG DATA is accessible only if the input intensity data is to have its logarithm data prior to the contour. The option sets the action to take place if an input data value is less than or equal to 0. The options are:
| Option/ | Definition |
|---|---|
| TINY | Set the log of the value to -60.0 |
| SMALL | Set the log of the value to the log of the minimum color scale value divided by 5. |
| IGNORE | Drop the data value from the input data. |
NEG DATA brings up a single instance of the 1-D CUT Menu. This allows cuts to be defined through a completed contour along which the contour intensity is computed and plotted as a line-plot together with the contour.
CLOSE closes the Contour Definition Menu window.
The X Mesh Info option line establishes the contour mesh in the X direction. The entire line of options is disabled if Method has been set to either HOLLOW GRID or PREGRIDDED.
POINTS establishes the number of grid points along the contour mesh X-Axis.
MINIMUM sets the value associated with the left-most column of the contour mesh.
MAXIMUM sets the value associated with the right-most column of the contour mesh.
SCALING specifies the algorithm to use to compute the centers and edges of the contour mesh grids along in X direction using the Minimum and Maximum X mesh values. The options are:
| Option | Definition |
|---|---|
| LINEAR | The plot grid centers are linearly spaced in X between the centers of the first and last grid. |
| LOG | The plot grid centers are logarithmically spaced in X between the centers of the first and last grid. |
The Y Mesh Info option line establishes the contour mesh in the Y direction. The entire line of options is disabled if Method has been set to either HOLLOW GRID or PREGRIDDED.
POINTS establishes the number of grid points along the contour mesh Y-Axis.
MINIMUM sets the value associated with the bottom row of the contour mesh.
MAXIMUM sets the value associated with the top row of the contour mesh.
SCALING specifies the algorithm to use to compute the centers and edges of the contour mesh grids along in Y direction using the Minimum and Maximum Y mesh values. The options are:
| Option | Definition |
|---|---|
| LINEAR | The plot grid centers are linearly spaced in Y between the centers of the first and last grid. |
| LOG | The plot grid centers are logarithmically spaced in Y between the centers of the first and last grid. |
The Cyclic In X option line establishes if the data is cyclic in the X direction of the contour mesh. In this case the left and right edge of the contour mesh represent the same data. The options are:
| Option | Definition |
|---|---|
| NO | The contour mesh is not cyclic in X |
| YES | The contour mesh is cyclic in X |
The second two entry boxes in the Cyclic In X option line are enabled only if the CYCLIC option has been set to YES. These the values of the left and right mesh edges respectively. This is generally either -180 and 180 (the default setting) or 0 and 360.
The Fit Info option line defines how the interpolation of the values assigned to the contour mesh points is performed.
ORDER establishes the order of the 2D or 3D least squares fit used to establish the contour mesh value from the surrounding data. In general a first order fit is sufficient. Higher order fits have a tendency to \become unstable, adding artificial peaks and valleys to the data.
WEIGHT sets the exponent of the weighting factor used in conjunction with any data included in the least squares fit. The weighting factor is of the form (1/r)exp. A positive value causes data closer to the grid point to have a higher weighting factor in the interpolation. A negative value does the opposite. A value of 0 weights all data the same.
The Neighbor Info option line defines the extent of data
PATTERN is accessible only if the Method option has been set to ORDERED GRID. The option specifies the data points to be used in the interpolation of the contour grid points. The data points are specified as a pattern of points surrounding the grid point being interpolated, the size of the pattern being given in the MIN INCL option on this line. The PATTERN options are:
TRIANGLE:
The used data points form a triangular pattern around the contour grid being interpolated. The pattern is shown below for MIN INCL of 1 (red), 2 ( orange), and 3 (cyan ). The data point starts in the black box.
The used data points form a diamond pattern around the contour grid being interpolated. The pattern is shown below for MIN INCL of 1 (red), 2 (orange), 3 (cyan), and 4 (blue). The data point starts with the black box.
SQUARE:
The used data points form a square pattern around the contour grid being interpolated. The pattern is shown below for MIN INCL of 1 (orange), 2 (cyan), and 3 (blue). The data point starts in the black box.
All of the input data are used in the interpolation.
MIN INCL specifies the minimum number of data points to be used in the interpolation of the contour grid points. If the Method option has been set to ORDERED GRID then the MIN INCL defines the size of the data pattern. In all cases the data points identified to be used in the interpolation are those nearest to the contour mesh position.
QUADS specifies the number of quadrants surrounding the grid point in which data must exist for the interpolation to be attempted. Four quadrants ensures that the data used surround the contour grid point. The number of quadrants is internally reduced for grid points which are on the boundary of the contour mesh. The need to satisfy the QUADS restriction can increase the number of points used in the interpolation over that given in the MIN INCL option.
MAX RADIUS specifies the largest distance a point can be from the contour grid and still be included in the interpolation. The units of the radius is given in the next option.
BASE specifies the units of the MAX RADIUS option. They are:
| Option | Definition |
|---|---|
| ABSOLUTE | The radius is specified in whatever units are defined for the X and Y Axes. |
| GRID | The radius is specified in terms of contour grids. |
COLOR FILL SUBGRIDS is enabled only when the Display As option is set to either Color Fill or Fill w/Contours. The value specifies how the rectangular area between four contour mesh grid points grids is to be sub-gridded. The sub-gridding allows for a secondary smoothing in the color output. A value of 2 subdivides the are into 4 sub-grids, a value of 3 into 9 grids, etc. The color assigned to each sub-grid is formed by a linear interpolation of the colors assigned to the three nearest contour mesh points.
The Contour Info options are enabled only when the Display As option is set to any option but Color Fill.
CONTOURS set the total number of contour lines to be drawn between the MIN VAL and MAX VAL options set in the following two entry boxes.
MIN VAL sets the value (minimum value) associated with the first output contour line.
MAX VAL sets the value (maximum value) associated with the last output contour line.
LINE COLOR is enabled only when the Display As option is set to either Contours or Fill w/Contours. This is the color of the displayed contour lines. There are 8 total colors to choose from.
If the contour is output as as set of contour lines then those lines maybe labeled with their contour value. The Contour Label option line contains the options used in labeling the contour lines.
DISPLAY establishes if numerical labels are to be assigned to the contour lines. This option is only enabled if Display As has been set to either COLOR CONTOURS or CONTOURS. The options include:
| Option | Definition |
|---|---|
| NO | Do not label contours |
| YES | Contours are to be labeled |
COLOR is enabled only when the DISPLAY option is YES. The option sets the label color to use when outputting the contour line labels. There are 8 possible colors.
FORMAT is enabled only when the DISPLAY option is YES. The option establishes the format to use when labeling the contour lines. The format is specified in standard C notation. Formats used must be applicable for floating point values. In this case %.0f mimics an integer.
SIZE is accessible only when the DISPLAY option is YES. The option establishes the font size to use when labeling the contour lines. Valid sizes run from 3 to 32767 with character size increasing with value. At a size of 1000 a single character will completely fill the plot page.
SKIP is accessible only when the DISPLAY option is YES. The option establishes how often the contour lines which are to be labeled. The first drawn contour line is always labeled. If that is said to be contour line 0, then successive contour lines are labeled only if SKIP divides evenly into the line number. All contour lines are labeled with a SKIP of 1, every other contour line with a SKIP of 2, every third contour line with a SKIP of 3, and so on.
The Grid Value option line contains options which allow the contour grid to be visualized.
DISPLAY establishes if the contour grid should be output in the plot. The options include:
| Option | Definition |
|---|---|
| NO | Do not show the contour grid |
| YES | The contour grid should be shown |
COLOR is accessible only when the DISPLAY option is YES. The option sets the color used when outputting the contour grid. There are 8 possible colors plus the option BY-VALUE in which the grid point color is encoded according to the value assigned it.
FORMAT is accessible only when the DISPLAY option is YES. The option is currently not implemented. The contour grid points are always output as a +.
SIZE is accessible only when the DISPLAY option is YES. The option establishes the font size to use when outputting the contour grid points. Valid sizes run from 3 to 32767 with character size increasing with value. At a size of 1000 a single character will completely fill the plot page.
The Data Value line sets the options which allow the input data values to be visualized.
DISPLAY establishes if the input data should be displayed in the plot. The options include:
| Option | Definition |
|---|---|
| NO | Do not show the input data |
| YES | The input data should be shown |
COLOR is accessible only when the DISPLAY option is YES. The option sets the color used when outputting the input data values. There are 8 possible colors plus the option BY-VALUE in which the input data indicator is color encoded according its value.
FORMAT is accessible only when the DISPLAY option is YES. There are two possible formats. If the format specified is a valid C format then the value of the input data will be shown according to the indicated format. Formats used must be applicable for floating point values and a format of %.0f mimics an integer. If the format is not a valid C format then the format string is output at the location of the data. A format of + will output a + at the location of each of the input data value.
SIZE is accessible only when the DISPLAY option is YES. The option establishes the font size to use when outputting the input data values or points. Valid sizes run from 3 to 32767 with character size increasing with value. At a size of 1000 a single character will completely fill the plot page.
DELETE PAGE deletes the current Contour Definition and all menus associated with it.
The following examples show the effects of some of the options available through the Contour Definition Menu. All of the options are demonstrated for the case where the Contour Definition Menu is invoked from the Plot Tools options. Here is one example:
In its default configuration shown above, the Contour Definition Menu is set to display a Color Filled contour with a smoothing resolution of 4. The following figure shows two plots. The lower plot is the original uncontoured data set while the upper plot shows the results of running the data through the contour filter with the default option settings.
This results in:
The order of the least squares fit in the interpolation of the data to the contour mesh points is set to 2. Note that the minimum number of neighbors has been set to 12. The larger value is needed because of the larger number of coefficients used in the fit.
The upper plot shows the data with a second order fit applied to it and the lower plot with the default first order fit. There are only few and minor differences for this data set.
The Display As for the upper plot is set to Color Contours (menu shown below) while the lower plot is set to Fill w/Contours which is a Filled contour overlayed with the contour lines of the top plot but now output in only while and reduced in number. Note that to get the contour lines the Contour Info line of options has be filled in.
Grid Values, Data Values Option
The Grid Values Display Option is set to Yes for the upper plot. The contour mesh points are plotted as +'s and color encoded according to their value. Note that the Display As is set to CONTOURS and that the number of contours to output is set to 0. This suppresses all contour output other than the grid values.
The lower panel shows the same data but with the Data Values Display Option is set to Yes.
The plots generated are shown below and indicate that the majority of the unfilled contour mesh points are along the phi direction.
The Display As is set to Color Fill for both the upper and lower plots. In the upper plot the Subgrids Option is set to 4 and to 1 for the lower plot. Note that the number of X and Y mesh points has be reduced to 30 for the 90 used in the above plots. Increased interpolation through the subgrid option generally provides a smoothing comparable to using a higher density of contour mesh points and at a much faster overall computation time.
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