Streamlines, A Field Flow Visualization Utility

David I. Brown
NCAR, P.O. Box 3000
Boulder, Colorado 80307-3000

Table of Contents

1.0 PREFACE

The streamline field flow plotting utility described here was originally written in the early 1970's and has previously been known as STRMLN. Over the years, a number of enhancements have been made, but the basic capabilities and interface have not changed much. Late in 1992 a more extensive revision was undertaken. Both the interface and functionality of the package underwent a major upgrade. There were several goals: first, make the package work more like other utilities in the NCAR Graphics toolkit suite; second, make it easier to use in combination with the other utilities; third, allow easier access to standard coordinate system mappings, including especially the EZMAP transformations; and fourth, improve the information content of the final plot. Most of these goals have been at least partially realized in the current version of the package, although, as usual, not all the envisioned improvements could be accomplished in the time allotted to the task. Since it might be confusing to retain the name of a now obsolete entry point as the utility name, and moreover, as it now seems unwise to share the package name with any entry point name, the new name for the NCAR Graphics streamline plotting utility is simply Streamlines.

2.0 INTRODUCTION

This document describes the NCAR Graphics utility, known as Streamlines, designed to allow a user to plot a streamline representation of field flow given two arrays containing the components of the field vectors on a uniform grid in a user-defined coordinate system.

In the past, subroutines within the STRMLN utility were assigned names meaningful to the programmer, but there was no comprehensive naming convention in place. Beginning with NCAR Graphics Version 3.2, however, all new routines, whether user-entry points or not, are six characters long and begin with the key letters, 'ST'. The old entry points are still supported through a compatibility version of the STRMLN subroutine, and some, though not all, of the features provided by the new routines are available through these entry points by appropriately setting the compatibility mode internal parameter, CPM.

This section is intended to give an overall view of Streamlines and selected aspects of its design; it covers some details, but, in general, one should refer to the sections SUBROUTINES and PARAMETERS for detailed descriptions of subroutines and parameters mentioned. (Parameters are mentioned by name; all the names are of the form XXX, where XXX is a three-character mnemonic.) The section ERROR MESSAGES describes error messages written by Streamlines. The section EXAMPLES describes the examples available for Streamlines. It is assumed that the reader is familiar with NCAR Graphics in general and has some knowledge of (or can find and read the documentation for) the utilities AREAS and EZMAP.

Note that currently a Streamlines plot gives information about the instantaneous directional characteristics of the field flow. Variations in flow intensity can be shown by enabling the progressive step-wise coloring feature using flow magnitude as the scalar value. For the future, enhancements are planned to allow Streamlines also to represent field intensity using a continuously varying line width.

2.1 Streamlines User Entry Point Routines

The code to draw a streamline flow field plot (unless using the obsolete entries points discussed at the end of this section) must include a call to the routine STINIT followed at some point by a call to STREAM. Before and after the STINIT call you may use several internal parameter setting routines to alter the behavior of the streamline plotting code. You must set some of these parameters before the call to STINIT in order to have any (or the correct) effect. In other cases, you can safely set the parameter between the call to STINIT and the call to STREAM. However, there is currently little benefit in delaying any of the parameter setting calls. You are encouraged, therefore, to make all parameter setting calls before calling STINIT.

You may be wondering why the Streamlines utility requires two calls where formerly only a call to STRMLN was required. The answer is twofold. First, the interface to Streamlines is now almost identical to the new interface to the companion utility, Vectors, so that if you know one of the utilities you will have less to learn and remember to use the other effectively. Second, future enhancements to the Streamline utility are planned that will allow you to use parameter getting routines to obtain information about the target data sets after the STINIT call; then, using parameter setting routines, you will be able to adjust the behavior of the STREAM routine to best fit the requirements of the data.

All the internal parameters have default values; only those which are to have values different from the default need to be set. The user may call routines to set the values of parameters as follows:

In general, once a parameter is given a value by a call to one of these routines, it retains that value until a similar call resets it. Thus, many of the parameter-setting calls do not need to be repeated for each new streamliner field flow plot.

The user may retrieve the value of an internal parameter at any time by calling one of the parameter getting routines:

The core functionality of the Streamlines utility is contained in the two routines that are required in order to create a streamline field flow plot, STINIT and STREAM.

Streamlines contains four user-modifiable routines that are not invoked directly by the user, but by Streamlines itself. Three of the routines, STUMXY, STUIXY, and STUMTA, are provided for the user to implement custom mappings from data to user coordinate space. The fourth, STUMSL, draws streamline segments when the parameter, MSK, is set to enable masking to an area map. The default versions of these routines contain simple code that may handle a basic case, but little more. These routines are as follows:

Two Streamlines routines are supplied to provide compatibility with pre-Version 3.2 codes. You may choose from a variety of compatibility options by setting the compatibility mode parameter CPM appropriately; this facility offers considerable flexibility in making a transition to the new version of the utility.

2.2 Using Streamlines

In order to use Streamlines, you must make the following sequence of calls:

  1. Optionally call parameter-setting routines.

  2. Call STINIT to initialize the streamline flow field plot.

  3. Call STREAM to draw the streamlines.

  4. Optionally call PERIM(1,0,1,0) if you want to place a border around the plot.

  5. Call FRAME to advance the plotter frame.

Assuming that step 1 is null and that all default parameter values are used, the resulting plot will look similar to what would have been drawn by STRMLN.

2.3 Coordinate Systems in Streamlines

In order to understand the process of transforming the data contained in the vector field component input arrays into streamlines following particular paths on an output plot, it would be helpful to differentiate unambiguously each stage of the transformation pipeline within the context of the coordinate systems defined by NCAR Graphics. In this discussion, the following terms are used:

Note that all reliance on the integer metacode coordinate system has been eliminated from the Streamline utility as of Version 3.2.

Given the default values of the parameters XC1, XCM, YC1 and YCN, the mapping from grid to data coordinate space is an identity transformation. That is, the data coordinate space extends from (1.0,1.0) to (REAL(M), REAL(N)). However, you may assign any desired boundaries to the data coordinate system by setting XC1, XCM, YC1 and YCN to values of your choice. For satisfactory results these choices need to be consistent with the user coordinate boundaries established by the SET call and the mapping established by the MAP parameter. In general, the location of an array element A(I,J) in data coordinate space is given as:

Xdata = XC1 + (I - 1)*(XCM - XC1)/(M - 1)
Ydata = YC1 + (J - 1)*(YCN - YC1)/(N - 1)
where (XC1,YC1) is the lower boundary of the data coordinate space and (XCM,YCN) is the upper boundary.

2.4 Coordinate Space Mapping

If the parameter MAP has values between 0 and 2 Streamlines handles the mapping from data space to user and NDC space internally, using routines STMPXY, STIMXY, and STMPTA. If MAP has any other value the user-modifiable routines STUMXY, STUIXY, and STUMTA are called to perform a mapping defined by the user. Note that Streamlines uses three routines to perform mappings similar to those accomplished in one routine by other utilities in NCAR Graphics. This is because in order to handle non-linear mappings properly, Streamlines must map points both in both directions of the transformation pipeline, and in addition must map the directional angle from grid to NDC space at each incremental point of the streamline. New points on the streamline are generated using a constant reference increment size in NDC space, avoiding the discontinuities that can occur from using grid coordinate based increments that can vary greatly in size after applying a non-linear mapping.

The mappings handled internally by Streamlines are as follows:

When a user-defined mapping is required, you must modify the user-definable mapping routines, STUMXY, STUIXY, and STUMTA, to respond in a consistent way to the MAP code you choose to identify your mapping. In the standard distribution, the default versions of these routines are all located in the single source file, 'stumxy.f'. If the Streamlines routines are loaded from a binary library, you can usually replace the library version just by compiling the routines and explicitly linking its object with the NCAR Graphics library.

2.5 How Streamlines Are Constructed

If you are creating your own mapping routines, it may be helpful to have some idea of how streamlines are created. The steps of the iterative streamline construction process may be summarized as follows:

  1. Find the next grid box eligible for starting a streamline, and generate the normalized interpolated vector components for the point at the center of this box.

  2. Convert the grid coordinate point to data coordinates and call STMPXY to map the point to user coordinates. Then use the SPPS routines CUFX and CUFY to find the point in NDC space.

  3. Given the coordinates of the point in data, user, and NDC space, and also the normalized interpolated vector component values, call STMPTA to determine the streamline directional angle at the point relative to NDC space.

  4. Using the directional angle, the normalized device point coordinates, and the NDC differential magnitude value (indirectly specified by the internal parameter, DFM) generate the next point of the streamline in NDC space.

  5. Convert this point back to user coordinates using the SPPS calls, CFUX and CFUY. Then call STIMXY to map the user coordinates back to data coordinates. Finally convert the data coordinates to grid coordinates and generate the normalized interpolated vector component values for this new point.

  6. Repeat steps three through five until a streamline termination condition is met. Go back to the original starting point of the stream and perform the same steps in the other direction to complete the streamline. Then start over at step one until no eligible streamline starting grid boxes remain.

In contrast, when Streamlines is emulating the pre-Version 3.2 mapping method, the steps are somewhat different. Here is a summary:

  1. Find the next grid box eligible for starting a streamline, and generate the normalized interpolated vector components for the point at the center of this box.

  2. Call FX and FY to convert the point in grid coordinates into user coordinates. (Any transitional mapping from grid to data coordinates must be handled within these functions.) Then use the SPPS routines CUFX and CUFY to find the point in NDC space.

  3. Use the function ATAN2 applied directly to the normalized interpolated vector components to determine the streamline directional angle. (This is used only to establish the direction of the directional arrowheads)

  4. Add the interpolated components, which are normalized to represented a fractional distance in grid coordinate space, to the grid coordinates of the point to generate a new point. Generate the normalized interpolated vector components of this new point.

  5. Repeat steps two through four until a streamline termination condition is met. Go back to the original starting point of the stream and perform the same steps in the other direction to complete the streamline. Then start over at step one until no eligible streamline starting grid boxes remain.

Clearly, somewhat less processing is involved when the older mapping technique is used, so if execution time is a primary concern, and the mapping is linear (or you can afford to ignore the non-linearities), you may prefer to use the older mapping method. You can do this, even when using the Version 3.2 interface, simply by setting the compatibility mode parameter, CPM, to a positive value.

When the mapping is non-linear, the Version 3.2 approach has two primary advantages: (1) the directional arrows always point in the correct direction, and (2) the likelihood of discontinuities appearing in the streamline as the result of grid box stretching and distortion over the transformation is greatly reduced. If discontinuities do appear they can generally be eliminated simply by setting the differential magnitude parameter, DFM, to a suitably small value. Note, however, that Streamlines still chooses stream starting points and places the directional arrowheads relative to the grid coordinate system. Over non-linear mappings, therefore, the arrowheads and the streams may be crowded in some areas of the plot and sparse in others. Future versions of the Streamlines utility plan to address these problems.

2.6 The SET Call

The mapping into the plotter frame depends on the boundaries of the user coordinate space and the viewport defined in NDC space. If the user coordinates are not log-scaled and neither axis is mirrored user coordinates and GKS world coordinates are the same. In this case, and it is possible to define the user/world coordinate boundaries (also known as the window) and map them to the viewport using GKS calls. However, this document only discusses the SPPS routine, SET, since it accomplishes all the same goals and works under all conditions recognized by NCAR Graphics.

A call to the SPPS routine SET has the form

      CALL SET (VPL,VPR,VPB,VPT,WDL,WDR,WDB,WDT,LL)
All arguments are REAL except for LL, which is an INTEGER. The first four arguments must all be between 0 and 1, inclusive; they define a rectangular area on the plotter frame known as the "viewport". The next four arguments define the boundaries of the user coordinate space (the "window"). The final argument indicates whether the mapping of user coordinates into the viewport is to be linear or logarithmic in X and Y. See the documentation of the SPPS utility for further details.

By default, Streamlines calls SET. However, by setting the parameter SET to zero, you may prevent Streamlines from doing making the call. In this case, however, you must do your own SET call or depend on some other utility (such as EZMAP) to have done it.

If Streamlines calls SET, it always uses LL = 1, requesting a linear-linear mapping from the window to the viewport. The viewport is positioned as specified by the current values of the parameters VPL, VPR, VPB, VPT, and VPS. The first four of these specify the boundaries of a "viewport area", in which the viewport is to be centered and made as large as possible; the final one determines how the shape of the viewport is to be chosen. You could, for example, render several plots within a single plotter frame by setting these parameters to define separate non-overlapping areas for each plot.

By default, the user coordinate boundaries are set equal to the data coordinate boundaries, which, in turn, default to the grid coordinate boundaries (1: M, 1: N) unless the parameters XC1, XCM, YC1, YCN have non-default values. You may override this behavior by setting parameters WDL, WDR, WDB, and WDT to non-default values, explicitly specifying the values used to define the window in the SET call. Normally you would modify the window setting parameters only when the parameter MAP has a non-default value, but Streamlines is still expected to perform the SET call. Whereas the viewport area may be set to any part of the plotter frame, without fear of losing the plot, you must be careful setting WDL, WDR, WDB, and WDT, or the region of interest is not likely to match up with the viewport.

When MAP is set to 1, specifying an EZMAP projection, you should give the SET parameter a value of 0, since EZMAP must take charge of the SET call to perform the requested map transformation. If you want to adjust the viewport size or position in this case, do it using the EZMAP call MAPPOS.

When MAP is set to 2, specifying a polar coordinate mapping, you may choose either to leave the SET parameter defaulted and set the user coordinate boundary parameters WDL, WDR, WDB, and WDT appropriately, or else to set the SET parameter to zero and make your own call to the SET routine.

Note that, as long as the parameter MAP is zero, a SET call performed by Streamlines will define the window in such a way as to be consistent with the ranges of the X and Y coordinates it generates. If MAP is set non-zero, then you will probably need to set XC1, XCM, YC1, and YCN to transform the grid coordinates into the range of data coordinates expected by Streamlines mapping routine. The call to SET must specify user coordinate boundaries commensurate with the range generated by the data coordinate to user coordinate transformation; if Streamlines is to do the call, then you will need to set WDL, WDR, WDB, and WDT to accomplish this.

2.7 Streamline Modes

Streamlines has two modes: normal streamline mode and "curly" vector mode. In normal mode, a streamline begins at the center of a grid box, and once started, it steps both in the flow direction and opposite the flow direction. It continues in both directions until it steps outside the data grid, approaches within a certain minimum distance of an existing streamline, or stops making progress because it approaches a critical point in the field. In contrast, a "curly" vector begins at a grid point (i.e. one of the corners of a grid box), and its length is predetermined based on the magnitude of the flow at that point. It may extend in both directions or only in one direction, depending on the value of the parameter VPO. However, each step along the path of a curly vector is determined in the same way as a step along the path of normal streamline.

2.7.1 Curly Vector Mode

By default, Streamlines is in normal streamline mode. Set the parameter STM to 1 in order to activate curly vector mode. Although curly vectors are generated using the same basic algorithm as streamlines, a number of specialized parameters, similar to those used by the Vectors package, are used to control their appearance.

2.7.1.1 Reference length and magnitude

The basic length of each curly vector is determined in relation to a vector reference magnitude specified by the parameter VRM and a vector reference length specified, as a fraction of the viewport width, by the parameter VRL. Vectors belonging to the dataset whose magnitude is equal to the reference magnitude are drawn at the reference length. By default, if VRM is set to 0.0, the reference magnitude is the maximum magnitude in the vector field, but it may be set to any arbitrary value. The default reference length is determined dynamically based on the viewport and the size of the dataset along each dimension.

2.7.1.2 Minimum length and magnitude

By default the size of each vector differs from the reference length by the ratio of its magnitude to the reference magnitude. A common result of this strictly proportional representation is that low magnitude vectors become too small to be rendered clearly. As a result, their direction, especially, becomes difficult to decipher. Streamlines provides a parameter, VFR, that allows you to specify, as a fraction of the reference length, a minimum vector arrow length. When this resource is set to a value greater than 0.0, the smallest magnitude vector is rendered at the specified fraction of the reference length, and intermediate magnitude vectors are rendered at proportionally intermediate lengths. Setting VFR to 1.0 causes all vector arrows to be drawn at the reference length.

2.7.1.3 Ensuring uniform arrow sizing over a series of plots

In order to ensure that within a series of plots of related data a particular length always represents the same vector magnitude, you must always first set the reference magnitude using parameter VRM explicitly. Otherwise, whatever magnitude happens to be the maximum in each plot will be rendered at the reference length. In addition, because VFR sets a size for the smallest magnitude vector in each plot, you must leave it set to its default value of 0.0.

2.7.1.4 Controlling the spacing between vector arrows

You can control the spacing of curly vectors using the same parameters you use to set the spacing for starting streamlines in normal streamline mode. The starting grid increment parameter SGD can be used to set a stride through the grid space to thin the curly vectors uniformly in grid space. This can work well if the transformation from data space to NDC is linear. However, if the transformation is non-linear, you may find that the minimum distance parameter SMD provides better results. It marks grids points as ineligible in such as way that you are ensured each curly vector starting point is spaced a minimum distance in NDC space from each neighbor in the plot. However, it does requires that you provide a larger workspace, and processing make take a bit longer.

2.7.1.5 Arrow Position

Using the VPO parameter, you can control whether the tail, the head, or the center of vector arrow is positioned at the location of the grid point in data space. Based on this parameter, curly vector are generated by stepping in the flow direction, opposite the flow direction, or in both directions for half the total length each.

2.8 Color Threshold Level Control

Streamlines now supports progressive coloring based upon the interpolated magnitude or other associated scalar value at each step-wise location of the streamline. Streamlines will not set up a color palette. You must call the GKS routine GSCR to assign RGB values for each color index you intend to use. Currently, a maximum palette of 255 colors is allowed. As in all of NCAR Graphics, the color indices used can range from 1 to 255, with index 0 reserved for the background color. You are also responsible for setting up the GKS color index array used by Streamlines to determine the color to use for data within a certain range. For example, assuming (1) a palette of 14 colors is desired, (2) the desired RGB values have previously been stored in a 3 x n array called "RGB", and (3) a consecutive series of GKS indices starting at N + 1 is to be used (where N is a previously initialized value between 0 and 255 - 14) you could accomplish both these tasks in a single simple loop:

      DO 100 I=1,14,1
        CALL GSCR (1,I+N,RGB(1,I),RGB(2,I),RGB(3,I))
        CALL STSETI('PAI -- Parameter Array Index', I)
        CALL STSETI('CLR -- GKS Color Index', I+N)
      100 CONTINUE
The setting of the color threshold value control parameter, CTV, determines how Streamlines handles the selection of color threshold values. If you want Streamlines to choose the threshold values, set CTV to a positive value: 1 to color by vector magnitude or 2 to color by scalar array. Set the number of levels parameter NLV to select the number of threshold levels (and the number of colors, with a maximum of 255) to use. When Streamlines chooses the threshold levels, it finds the maximum and minimum values in the data, then simply divides the range into NLV equally spaced divisions. The resulting NLV threshold values are stored into the threshold level array, TVL. The first value stored is the minimum data value plus one division increment while the last value is the maximum data value itself. As each vector is processed its color is chosen by finding the first entry in the threshold level array greater than or equal to the data value associated with the vector, retrieving the array subscript for this entry, and then setting the GKS polyline color index to the value in the color index array, CLR, accessed by the same subscript. Assuming as above that 14 levels are desired, the following code would tell Streamlines to choose the color levels based on data in the scalar array:

      CALL STSETI('NLV - Number of Threshold Levels', 14)
      CALL STSETI('CTV - Color Threshold Value Control', 2)
To set up the threshold level array yourself, make CTV negative: -1 to color by vector magnitude or -2 to color by scalar array value. When CTV is less than or equal to 0, Streamlines will not touch the values in the TVL array. Set NLV as before to the number of levels desired, then set the first NLV members of the threshold array to the desired threshold values, keeping in mind from the preceding description how Streamlines chooses the color index based on the threshold array values. A basic rule to observe is that the threshold values should increase monotonically as the array subscripts increase. Note also that if the data value associated with a location on the streamline is larger than all the values in the threshold value array, it will be assigned the color subscripted by the index for the maximum data value. Again assuming 14 colors and also that the desired threshold values are stored in an array called "TVALS", the following code would set up the threshold array and inform Streamlines not to modify its contents:

      CALL STSETI('NLV - Number of Threshold Levels', 14)
      CALL STSETI('CTV - Color Threshold Value Control', -2)
      DO 200 I=1,14,1
        CALL STSETI('PAI -- Parameter Array Index', I)
        CALL STSETR('TVL -- Threshold Value Array', TVALS(I))
  200 CONTINUE
You can also use the color threshold control parameter to retain a threshold array set up by a previous plot (within the same program execution). Suppose you have a program to create several plots using scalar arrays with varying maximum and minimum values. When Streamlines picks the threshold values, the color associated with a particular data value may change from plot to plot. To ensure that a given data value is associated with the same color for the complete series of plots, pick one plot (preferably the one with the greatest range) and by setting CTV to a positive value, allow Streamlines to set up the threshold array. For the subsequent plots, set CTV negative. All plots will then use the same threshold array, and therefore the colors will be associated with identical ranges of data.

2.9 Masked Streamline Overlays Using an Area Map

At times you may need to overlay a streamline flow field over a plot created by another NCAR Graphics utility, such as Conpack. There may be certain areas, such as the boxes containing contour level labels, where you do not want the streamlines to appear. Beginning with Version 3.2, the Streamlines utility supports streamline masking based on the contents of a area map previously established using routines from the Areas utility. Most of the information required to use the area map routines is documented elsewhere, either in the descriptions of the Conpack utilities that work with area maps or in the actual documentation of the Areas utility itself. You create the area map and the underlying plot just as you normally would. Then, in order to create the streamline overlay, you would need to take the following steps:

EXTERNAL STUMSL

2.10 Special Values

If the data at a particular grid point is unavailable or unreliable, a "special" value, typically a value outside the possible range of valid data, may be assigned to the array element associated with the grid point in question. Since Streamlines has two vector field component arrays as input, it uses several parameters to control processing of special value data points. Each of the two input arrays may have its own separately defined special value. The parameters USV and VSV are used to set the special values for the U and V vector field component arrays, respectively.

The parameter SVF controls special value processing. When SVF is set to its default value, 0, Streamlines assumes that the data contains no special values. If the data actually does contain special values, the resulting plots hopefully will look strange enough that you will realize that special values need to be taken into account. When SVF has any other value, special value processing is enabled. In this case, Streamlines overrides the interpolation method flag and insists on using the 4-point bi-linear interpolation method. This is because the other available interpolation method generally requires 16 surrounding good data points to determine the vector component values at any point in the streamline. If the 16 point method were used with special values present, not only would 32 special value checks, rather than 8, need to be performed at each step of the streamline construction, but also Streamlines would be required to omit the streamlines from a larger portion of the field plot, because only one special value out of the 32 array elements checked would be enough to cause termination of the streamline.

As it is, Streamlines checks the U and V data arrays at each of the four corner points of the grid box, each time a streamline under construction enters a new grid cell. If any of the eight values checked is a special value, then the streamline is terminated and a new one begun if possible.

2.11 Supplementary Text and Plot Information

2.12 Streamlines' Grid Window

Note that the grid window for Streamlines is not the same as the grid window for AUTOGRAPH, since the former is expressed with respect to the plotter frame and the latter is expressed with respect to the AUTOGRAPH "graph window". There is an easy conversion from one to the other, however. If AGFL, AGFR, AGFB, and AGFT specify the AUTOGRAPH graph window and AGDL, AGDR, AGDB, and AGDT specify the AUTOGRAPH grid window and CGDL, CGDR, CGDB, and CGDT specify the Streamline grid window, then the following relationships ensure coincidence of the AUTOGRAPH and Streamlines' grid windows:

CGDL=AGFL+AGDL*(AGFR-AGFL)
CGDR=AGFL+AGDR*(AGFR-AGFL)
CGDB=AGFB+AGDB*(AGFT-AGFB)
CGDT=AGFB+AGDT*(AGFT-AGFB)
Note what happens when AGFL and AGFB are 0's and AGFR and AGFT are 1's, which is the default situation; in that case CGDL=AGDL, CGDR=AGDR, CGDB=AGDB, and CGDT=AGDT.

2.13 GKS Considerations

Certain assumptions are made by Streamlines about the state of GKS, as follows:

  1. Like all the utilities in NCAR Graphics, Streamlines assumes that GKS has been opened and that the desired workstations have been opened and activated. The statement

          CALL OPNGKS
    calls the SPPS routine OPNGKS, the GKS equivalent of which is

          CALL GOPKS (6,0)
      CALL GOPWK (1,2,1)
      CALL GACWK (1)
    creating a single metacode workstation associated with FORTRAN unit 2.

  2. Similarly, at the end of one's program, the workstations must be deactivated and closed and then GKS must be closed. The statement

          CALL CLSGKS
    calls the SPPS routine CLSGKS, the GKS equivalent of which is

          CALL GDAWK (1)
      CALL GCLWK (1)
      CALL GCLKS
  3. It is assumed that the aspect source flags for various quantities are set to "individual". (NCAR GKS does this by default, but other packages may not.) To make sure that all the aspect source flags are set correctly, use the following code:

          DIMENSION IASF(13)
      ...
      DATA IASF / 13*1 /
      ...
      CALL GSASF (IASF)
  4. Streamlines uses the GKS polyline color index set by the most recent call to GSPLCI for rendering the streamlines.

3.0 SUBROUTINES

All Streamlines routines added for NCAR Graphics Version 3.2 and later have six-character names beginning with the letters 'ST. Current user entry points and user modifiable routines are described in detail in alphabetical order in this section. Obsolete routines appear in the section following entitled OBSOLETE SUBROUTINES.

3.1 STGETC (CNM,CVL)

This routine is used to get the current value of a parameter of type CHARACTER

3.1.1 Usage

Use the statement 

      CALL STGETC (CNM,CVL)
at any time to retrieve in CVL the current character value of the parameter whose name is CNM.

3.1.2 Arguments

CNM (CHARACTER, input) is the name of a parameter whose character value is to be retrieved. Only the first three characters of CNM are examined. The three characters may either be entirely upper or entirely lower case; mixed case is not recognized. It is recommended that the rest of the character string be used to improve the readability of the code. For example, instead of just 'ZFT', use 'ZFT - Zero Field Text String'.

CVL (CHARACTER, output) is a variable in which the value of the parameter specified by CNM is to be returned.

3.2 STGETI (CNM,IVL)

This routine is used to get the current value of a parameter of type INTEGER.

3.2.1 Usage

Use the statement 

      CALL STGETI (CNM,IVL)
at any time to retrieve in IVL the current integer value of the parameter whose name is CNM.

3.2.2 Arguments

CNM (CHARACTER, input) is the name of a parameter whose integer value is to be retrieved. Only the first three characters of CNM are examined. The three characters must either be entirely upper or entirely lower case; mixed case is not recognized. It is recommended that the rest of the character string be used to improve the readability of the code. For example, instead of just 'PLR', use 'PLR - Polar Input Mode'.

IVL (INTEGER, output) is a variable in which the value of the parameter specified by CNM is to be returned.

3.3 STGETR (CNM,RVL)

This routine is used to get the current value of a parameter of type REAL.

3.3.1 Usage

Use the statement 

      CALL STGETR (CNM,RVL)
at any time to retrieve in RVL the current real value of the parameter whose name is CNM.

3.3.2 Arguments

CNM (CHARACTER, input) is the name of a parameter whose real value is to be retrieved. Only the first three characters of CNM are examined. The three characters must either be entirely upper or entirely lower case; mixed case is not recognized. It is recommended that the rest of the character string be used to improve the readability of the code. For example, instead of just 'ARL', use 'ARL - Arrowhead Length'.

RVL (REAL, output) is a variable in which the value of the parameter specified by CNM is to be returned.

3.4 STINIT (U,LU,V,LV,P,LP,M,N,WRK,LW)

STINIT performs initialization tasks required before STREAM may be called to create a streamline field flow plot. Information about the input data arrays is copied into internal common block variables and the coordinate system mappings and boundaries are established.

3.4.1 Usage

Call STINIT before the first invocation of STREAM, and again any time you modify the contents of the input data arrays. You may precede an STINIT call with any number of calls to the parameter setting routines, STSETC, STSETR and STSETI. Although it is possible to call STSETC, STSETI or STSETR between calls to STINIT and STREAM, changing the setting of many of Streamline's parameters at this point will result in incorrect behavior. When in doubt, set parameters before the STINIT call.

Set up the two vector component arrays prior to calling STINIT. To permit multiple purpose use of the array space, the STINIT argument list includes both the actual size and an assumed size for the first dimension of each input array. Due to FORTRAN array ordering conventions, only the assumed size needs to be specified for the second dimension. (Note: when using the C bindings, mentally exchange all references to first and second dimensions in this discussion.) The arguments LU, LV, and LP contain the actual size of the first dimensions of arrays U, V, and P respectively. Since the grid locations for each of the data arrays are assumed to coincide, a single argument, M, represents the assumed size of the first dimension for all the arrays. Similarly, the argument, N, is the assumed size of the second dimension. The only requirement for the actual second dimension size is that it be greater than or equal to N for each array.

WRK is an work array used for various purposes within the Streamlines oode. Its actual dimension and the associated size specifier, LW, must be given values ranging from a minimum of 2*M*N to 5*M*N, depending on the parameter settings in effect. Given the default value of all parameters, Streamlines uses the WRK array only to store normalized values of the U and V vector components while the streamlines are calculated, and a size of 2*M*N is sufficient. If the streamline minimum distance parameter, SMD, has a positive non-zero value, then another 2*M*N must be added. If coloring the streamlines based on vector magnitude (CTV equal to 1 or -1), an additional M*N is required. Note that there is no problem specifying an array bigger than required: if memory is not a problem you can simply specify the dimension size as 5*M*N to ensure that Streamlines will work will any combination of parameter settings.

3.4.2 Arguments

U (REAL 2-dimensional array, dimensioned LU xn: n >= N, input): By default, assumed to contain the first dimensional Cartesian components of the vector field. However, if PLR is non-zero, it is treated as containing the vector magnitudes.

LU (INTEGER, input): Actual value of the first dimension of array U.

V (REAL 2-dimensional array, dimensioned LV x n: n >= N, input): By default, assumed to contain the second dimensional Cartesian components of the vector field. However, if PLR is non-zero, it is treated as containing the vector angles.

LV (INTEGER, input): Actual value of the first dimension of array V

P (REAL 2-dimensional array, dimensioned LP x n: n >= N, input): Array of scalar data that may be used as a basis for progressively coloring the streamlines. The grid points are assumed to coincide with the grid points of the U and V arrays. Required only if CTV has an absolute value of 2; otherwise this argument is ignored and may be assigned a dummy value.

LP (INTEGER, input, DUMMY): Actual value of the first dimension of array P

M (INTEGER, input): Number of contiguous elements along the first dimensional axis containing data to be processed in each of the arrays, U and V.

N (INTEGER, input): Number of contiguous elements along the second dimensional axis containing data to be processed in each of the arrays, U and V.

WRK (REAL, array dimensioned n: n >= LW, input/output): Work array used for various purposes.

LW (INTEGER, input): Assumed size of the array WRK. Must be at least 2*M*N for Streamlines to operate with default parameter settings up to 5*M*N to allow any combination of parameter settings.

3.5 STREAM (U,V,P, IAM,STUMSL,WRK)

This routine plots a streamline representation of field flow data, based on conditions established by STINIT and the current values of a set of user-modifiable internal parameters associated with the Streamlines utility.

3.5.1 Usage

A call to STINIT must precede the first call to STREAM, and is again required any time the vector array data changes or any of the coordinate space control parameters are modified. However, you may modify certain rendering control parameters between multiple invocations of STREAM. See the section, PARAMETERS, for more information.

Arguments to STINIT establish the sizes of the two or three data arrays and the WRK array. STINIT places these values into common block variables where they become available to STREAM. Therefore no size arguments need appear in the STREAM argument list. When there is no scalar data array, and area masking is not enabled, the third, fourth, and fifth arguments to STREAM may have dummy values and the invocation would be something like:

      CALL STREAM(U,V,IDM,IDM,IDM,WRK)

where IDM is an arbitrary variable, INTEGER or REAL, that need not have been initialized. However, any time the color threshold control parameter, CTV has an absolute value of 2, the auxiliary scalar data array is expected, and the P scalar array variable needs to be specified.

The masking capability supported by Streamlines allows you to overlay streamlines on top of graphics produced by other utilities, such as CONPACK contour plots, without encroaching on areas, like label boxes, that should appear in the foreground. Normally the area map should be generated and used in the normal way (as described in the AREAS and CONPACK documentation) before calling any routines in the Streamlines utility. When the parameter MSK has a non-zero value, masking is enabled and a previously created area map must be passed to STREAM. STREAM examines the map, returning an error if the map appears to be invalid or the number of area groups is beyond the range it can handle (currently 64). Otherwise, it only uses the map as an argument to the Areas utility subroutine, ARDRLN. The user must also pass in a user-definable masked drawing subroutine. A simple version of this subroutine, named (like the argument) STUMSL, is supplied with the Streamlines utility, and may suffice for basic masked drawing operations. There is a separate entry describing the arguments and usage of STUMSL in this section.

Note that in order to keep the interface as simple as possible, Streamlines locally declares the area identifier and area group arrays passed to the masked drawing subroutine. The dimension of these arrays is set to the value of the FORTRAN PARAMETER IPAGSZ, currently set to 64.

3.5.2 Arguments

U (REAL 2 dimensional array, dimensioned as specified in last call to STINIT, input): By default, assumed to contain the first dimensional axis components of the vector field. However, if PLR is non-zero, it is treated as containing the vector magnitudes.

V (REAL 2 dimensional array, dimensioned as specified in last call to STINIT, input): By default, assumed to contain the second dimensional axis components of the vector field. However, if PLR is non-zero, it is treated as containing the vector angles.

P (REAL 2 dimensional array, dimensioned as specified in last call to STINIT, input): Array of scalar data used as a basis for progressively coloring the streamlines. The grid points are assumed to coincide with the grid points of the U and V arrays. Required only if CTV has an absolute value of 2; otherwise this argument is ignored and may be assigned a dummy value.

IAM (INTEGER array, unknown dimension, input): Area map array previously established by calls to routines in the Areas utility. It is checked to see that the number of area groups is within the limits allowed by Streamlines, then simply passed through to an Areas routine for further processing. Required only if MSK is set to a non-zero value; otherwise it is ignored and may be assigned a dummy value.

STUMSL (EXTERNAL subroutine, input): User-definable masked drawing subroutine. See the entry, "STUMSL", in this section for a discussion of the usage and argument list required for this subroutine. Required only if MSK is set to a non-zero value; otherwise it is ignored and may be assigned a dummy value.

WRK (REAL array, dimensioned as specified in last call to STINIT, input/output): Work array used to store normalized values of the U and V vector components while the streamlines are calculated. It also holds bit flags indicating whether a grid location is eligible for starting a streamline or placing a directional arrowhead.

3.6 STRSET

Resets all parameters to their initial default values.

3.6.1 Usage

To reset all parameters to their default values:

      CALL STRSET
There are no arguments

3.6.2 Arguments

None.

3.7 STSETC (CNM,CVL)

This routine is called to set the value of a parameter of type CHARACTER.

3.7.1 Usage

Use the statement 

      CALL STSETC (CNM,CVL)
to give the parameter whose name is CNM the character value CVL.

3.7.2 Arguments

CNM (CHARACTER, input) is the name of a parameter to be given a character value. Only the first three characters of CNM are examined. The three characters may either be entirely upper or entirely lower case; mixed case is not recognized. It is recommended that the rest of the character string be used to improve the readability of the code. For example, instead of 'ZFT', use 'ZFT - Zero Field Text String'.

CVL (CHARACTER, input) is an expression, the value of which is to be given to the parameter specified by CNM.

3.8 STSETI (CNM,IVL)

This routine is called to set the value of a parameter of type INTEGER.

3.8.1 Usage

Use the statement

      CALL STSETI (CNM,IVL)
to give the parameter whose name is CNM the integer value IVL.

3.8.2 Arguments

CNM (CHARACTER, input) is the name of a parameter to be given an integer value. Only the first three characters of CNM are examined. The three characters must either be entirely upper or entirely lower case; mixed case is not recognized. It is recommended that the rest of the character string be used to improve the readability of the code. For example, instead of 'CKP', use 'CKP - Check Progress Iteration Count'.

IVL (INTEGER, input) is an expression, the value of which is to be given to the parameter specified by CNM.

3.9 STSETR (CNM,RVL)

This routine is called to set the value of a parameter of type REAL.

3.9.1 Usage

Use the statement 

      CALL STSETR (CNM,RVL)
to give the parameter whose name is CNM the real value RVL.

3.9.2 Arguments

CNM (CHARACTER, input) is the name of a parameter to be given a real value. Only the first three characters of CNM are examined. The three characters may either be entirely upper or entirely lower case; mixed case is not recognized. It is recommended that the rest of the character string be used to improve the readability of the code. For example, instead of 'DFM', use 'DFM - Differential Magnitude'.

RVL (REAL, input) is an expression, the value of which is to be given to the parameter specified by CNM.

3.10 STUIXY (XUS,YUS,XDA,YDA,IST)

The user-modifiable routine STUIXY inversely maps a single point on the streamline from user to data coordinate space.

3.10.1 Usage

STUIXY is a user-modifiable routine provided to support custom mappings of the data coordinate space. The user does not invoke it directly. Instead, whenever the parameter MAP specifies a mapping not handled by Streamlines internally (i.e., when MAP is set to a value other than 0, 1, or 2), Streamlines calls STUIXY once for each incremental step in the creation of a streamline. The default version of STUIXY simply performs an identity mapping. In order to implement a custom mapping, you must pick a unique mapping code (a positive integer greater than 2), and then modify each of the three routines, STUMXY, STUIXY, and STUMTA to recognize and respond consistently to the chosen code. In the standard distribution of NCAR Graphics, these three routines reside in a single file, "stumxy.f". STUMXY maps a point from data to user coordinate space, STUIXY inversely maps a point from user to data coordinate space, and STUMTA, which is likely to be the most difficult to implement, finds the tangent angle of the streamline at a point in NDC space. The user does not call STUIXY.

STUIXY has access to a common block called STMAP that contains a number of variables used to record the current transformation state. In order to accommodate a variety of mapping implementations, STMAP provides more information than normally required. Consider the values stored in STMAP as strictly read-only. One essential member of this common block is IMAP, which contains the value currently assigned to the MAP parameter.

In STUIXY, the implementor of a custom mapping needs to add code of the form:

      IF (IMAP .EQ. <chosen_map_code>) THEN
          ...map XUS to XDA
          ...map YUS to YDA
          ...if error, set IST to a negative value
          RETURN
      ENDIF
Note that after the return from STUIXY, Streamlines checks to ensure that XDA and YDA are within the current boundaries of the data coordinate system.

When implementing a custom mapping, you may wish to look at the coding of the pre-defined mappings (0, identity mapping; 1, EZMAP projections; and 2, polar coordinate mapping) in the file "stmpxy.f". For these mappings, the subroutine STIMXY is the equivalent of STUIXY; it has an identical interface and may serve as a model for your implementation. For more information, see the section titled Coordinate Systems in Streamlines.

3.10.2 Arguments

XUS (REAL, input): The X coordinate of a point in the user coordinate system.

YUS (REAL, input): The Y coordinate of a point in the user coordinate system.

XDA (REAL, output): The X coordinate of the point in the data coordinate system.

YDA (REAL, output): The Y coordinate of the point in the data coordinate system.

IST (REAL, output): Status of the mapping operation: 0 indicates success, negative values indicate that the mapping failed; positive values are reserved and should not be used by the implementor of a mapping routine.

3.11 STUMSL (XCS,YCS,NCS,IAI,IAG,NAI)

This routine is the user-definable external subroutine used to draw masked streamlines. The default version of the routine draws any polyline all of whose area identifiers are greater than or equal to zero.

3.11.1 Usage

"STUMSL" is the name given to the default version of the masked streamline drawing routine, and it is also the name given to the argument through which the external subroutine is passed to STREAM. However, you may choose any acceptable FORTRAN identifier as the name of a user-defined version of the routine. The substitute routine must have an argument list equivalent to the default version of STUMSL. Also, whether or not the default version is used, the subroutine that calls STREAM should contain an external declaration of the routine, such as:

      EXTERNAL STUMSL
If the MSK parameter is greater than 0, signifying that masking is to be performed, Streamlines sends one or more sets of X and Y polyline coordinate arrays to the area masking routine, ARDRLN, for each streamline. ARDRLN subdivides the polyline into pieces such that each smaller polyline has a single area identifier with respect to each area identifier group, then makes a call to STUMSL for each polyline piece. While the default version of STUMSL only checks to see that none of the area identifiers are negative, a user-defined version could perform more complicated decision processing based on knowledge of the meaning of specific area identifier groups and/or area identifier values. Note that, before invoking STUMSL, ARDRLN modifies the user coordinate space by making the following calls:

      CALL GETSET(VPL,VPR,VPB,VPT,WDL,WDR,WDB,WDT,LLG)
      CALL SET(VPL,VPR,VPB,VPT,VPL,VPR,VPB,VPT,1)
These calls temporarily turn the user to NDC mapping into an identity, allowing the user to call any of the routines, CURVE, CURVED, or the GKS routine GPL, to render the polygon piece, without worrying about a possible non-identity mapping between user and world coordinates.

The current version of Streamlines supports masked drawing with up to 64 area groups. Streamlines will exit with an error message if an area map with more than 64 groups is passed to it.

3.11.2 Arguments

XCS (REAL array, assumed size NCS, input): Array of X coordinates of the points defining the polyline with the given set of area identifiers.

YCS (REAL array, assumed size NCS, input): Array of Y coordinates of the points defining the polyline with the given set of area identifiers.

NCS (INTEGER, input): Number of points; assumed size of the X and Y coordinate arrays, XCS and YCS.

IAI (INTEGER array, assumed size NAI, input): Array of area identifier values. Each value represents the area identifier with respect to the area group in the area group array with the same array index.

IAG (INTEGER array, assumed size NAI, input): Array of area-identifier groups.

NAI (INTEGER, input): Number of area identifier groups. The current version of Streamlines supports up to 64 area groups.

3.12 STUMTA (XDA,YDA,XUS,YUS,XND,YND,DU,DV,TA,IST)

Given the coordinates of a point on the streamline in data, user, and NDC space, and the interpolated, normalized components of the vector at the point relative to data coordinate space, the user-modifiable routine STUMTA finds the directional angle of the streamline relative to NDC space at the point.

3.12.1 Usage

STUMTA is a user-modifiable routine provided to support custom mappings of the data coordinate space. The user does not invoke it directly. Instead, whenever the parameter MAP specifies a mapping not handled by Streamlines internally (i.e., when MAP is set to a value other than 0, 1, or 2), Streamlines calls STUMTA once for each incremental step in the creation of a streamline. The default version of STUMTA simply returns the angle implied by the incremental vector components passed to it: that is, it returns ATAN2(DV,DU). In order to implement a custom mapping, you must pick a unique mapping code (a positive integer greater than 2), and then modify each of the three routines, STUMXY, STUIXY, and STUMTA to recognize and respond consistently to the chosen code. In the standard distribution of NCAR Graphics, these three routines reside in a single file, "stumxy.f". STUMXY maps a point from data to user coordinate space and STUIXY inversely maps a point from user to data coordinate space. STUMTA, which is likely to be the most difficult to implement, finds the tangent angle of the streamline at a point in NDC space.

STUMTA has access to a common block called STMAP that contains a number of variables used to record the current transformation state. In order to accommodate a variety of mapping implementations, STMAP provides more information than normally required. Consider the values stored in STMAP as strictly read-only. One essential member of this common block is IMAP, which contains the value currently assigned to the MAP parameter.

When implementing a non-linear mapping, an iterative differential technique will most likely be required. Look at the routine, STMPTA, in 'stmpxy.f', which handles the pre-defined mappings, for examples of the method. Both the default transformation (MAP set to 0), in order to account for possible log scaling of the user coordinate axes, and also the EZMAP projection (MAP set to 1) use such a technique. Basically the idea is that the vector components must be proportionally reduced in size enough that an effectively "instantaneous" angle can be calculated, but they must not become so small that the calculation is adversely affected by the floating point precision available for the machine. Additionally, checks must be put in place to prevent the increment from stepping off the edge of the coordinate system space. The pre-defined mappings step in the opposite direction to find the angle whenever an increment in the original direction would fall off the edge.

3.12.2 Arguments

XDA (REAL, input): The X coordinate of a point on the streamline in the data coordinate system.

YDA (REAL, input); The Y coordinate of a point on the streamline in the data coordinate system.

XUS (REAL, input): The X coordinate of the point in the user coordinate system.

YUS (REAL, input): The Y coordinate of the point in the user coordinate system.

XND (REAL, input): The X coordinate of the point in NDC space.

YND (REAL, input): The Y coordinate of the point in NDC space.

DU (REAL, input): The interpolated value of the normalized component of the vector at the point, with direction parallel to the X axis of the data coordinate system.

DV (REAL, input): The interpolated value of the normalized component of the vector at the point, with direction parallel to the Y axis of the data coordinate system.

TA (REAL, output): The directional angle of the streamline at the point relative to NDC space.

IST (REAL, output); Status of the mapping operation: 0 indicates success, negative values indicate that the mapping failed; positive values are reserved and should not be used by the implementor of a mapping routine.

3.13 STUMXY(XDA,YDA,XUS,YUS,IST)

The user-modifiable routine STUMXY maps a single point on the streamline from data to user coordinate space. The argument list for STUMXY parallels that of the internal Streamlines routine, STMPXY, used for the predefined mappings employed when the MAP parameter has a value between 0 and 2.

3.13.1 Usage

STUMXY is a user-modifiable routine provided to support custom mappings of the data coordinate space. The user does not invoke it directly. Instead, whenever the parameter MAP specifies a mapping not handled by Streamlines internally (i.e., when MAP is set to a value other than 0, 1, or 2), Streamlines calls STUMY as needed during the process of creating a streamline. The default version of STUMY simply performs an identity mapping. In order to implement a custom mapping, you must pick a unique mapping code (a positive integer greater than 2), and then modify each of the three routines, STUMXY, STUIXY, and STUMTA to recognize and respond consistently to the chosen code. In the standard distribution of NCAR Graphics, these three routines reside in a single file, "stumxy.f". STUMXY maps a point from data to user coordinate space, STUIXY inversely maps a point from user to data coordinate space, and STUMTA, which is likely to be the most difficult to implement, finds the tangent angle of the streamline at a point in NDC space. The user does not call STUIXY.

STUMXY has access to a common block called STMAP that contains a number of variables used to record the current transformation state. In order to accommodate a variety of mapping implementations, STMAP provides more information than normally required. Consider the values stored in STMAP as strictly read-only. One essential member of this common block is IMAP, which contains the value currently assigned to the MAP parameter.

In STUMXY, the implementor of a custom mapping needs to add code of the form:

      IF (IMAP .EQ. <chosen_map_code>) THEN
          ...map XDA to XUS
          ...map YDA to YUS
          ...if error, set IST to a negative value
          RETURN
      ENDIF
Note that after the return from STUMY, Streamlines checks to ensure that XUS and YUS are within the current boundaries of the user coordinate system.

When implementing a custom mapping, you may wish to look at the coding of the pre-defined mappings (0, identity mapping; 1, EZMAP projections; and 2, polar coordinate mapping) in the file "stmpxy.f". For these mappings, the subroutine STMPXY is the equivalent of STUMXY; it has an identical interface and may serve as a model for your implementation. For more information, see the section titled Coordinate Systems in Streamlines.

3.13.2 Arguments

XDA (REAL, input): The X coordinate of a point on the streamline in data coordinate space.

YDA (REAL, input): The Y coordinate of a point on the streamline in data coordinate space.

XUS (REAL, output): The X coordinate of the point in user coordinate space.

YUS (REAL, output): The Y coordinate of the point in user coordinate space.

IST (REAL, output) Status of the mapping operation: 0 indicates success, negative values indicate that the mapping failed; positive values are reserved and should not be used by the implementor of a mapping routine.

4.0 OBSOLETE SUBROUTINES

4.1 EZSTRM (U,V,WORK,IMAX,JMAX)

EZSTRM is a front-end to STRMLN with a simpler interface. Like STRMLN, it may be used to create a streamline field flow plot in a single call.

4.1.1 Usage

U and V are 2-dimensional vector component arrays. IMAX must be given the value of the actual size of the first dimension of both these arrays (implying that the first dimensions must be the same for both), while JMAX is the assumed size of the second dimension. The WORK array must, at minimum, be of length 2*IMAX*JMAX. Assuming the default value of the compatibility mode parameter, CPM, Streamlines always performs a SET call and will draw a perimeter around the plot using a call to PERIM when accessed through the EZSTRM interface. By modifying the value of CPM, however, you may take more control over the utility than originally possible using this entry point. For instance, you can override the default value of the SET parameter, or use the Version 3.2 coordinate system mapping routines instead of the old FX and FY functions. Nevertheless, when creating new code, users are strongly encouraged to use the STINIT/STREAM interface, since its capabilities are greater and more likely to improve with time.

4.1.2 Arguments

U (REAL 2-dimensional array, dimensioned IMAX xn: n >= JMAX, input) By default, assumed to contain the first dimensional Cartesian components of the vector field. However, if PLR is non-zero, it is treated as containing the vector magnitudes.

V (REAL 2-dimensional array, dimensioned IMAX xn: n >= JMAX, input) By default, assumed to contain the second dimensional Cartesian components of the vector field. However, if PLR is non-zero, it is treated as containing the vector angles.

WORK (REAL array, dimensioned n: n>= 2*IMAX*JMAX working space): User provided work array used to store the normalized vector component values, and also to keep track of the grid boxes eligible for starting a streamline or placement of a directional arrow.

IMAX (INTEGER, input) Actual size of the first dimension of arrays U and V

JMAX (INTEGER, input) Assumed size of the second dimension of arrays U and V.

4.2 FX (X,Y)

Given the X and Y coordinates of a point on the streamline in the grid coordinate system, the function FX returns the X coordinate of the point in user coordinate space.

4.2.1 Usage

The user does not invoke the function, FX, directly. In older versions of NCAR Graphics, the user modified the functions, FX and FY, in order to implement custom mappings from grid coordinates to user coordinates. These functions were used throughout NCAR Graphics, not just in the Streamlines utility. For compatibility with existing code, calls to any of the Streamlines primary entry points predating Version 3.2 (EZSTRM or STRMLN), by default use FX and FY to map from grid to user coordinates. However, by appropriately setting the compatibility mode parameter, CPM, the user can choose whether the FX and FY functions or the new mapping routines are invoked when using any of the primary entry points supported by Streamlines.

Unlike the Version 3.2 mapping routines, whose input coordinates are in the data coordinate system, FX takes input in the grid coordinate system. Therefore, any required conversions into the data coordinate system must be performed within the function prior to the mapping into user coordinates. The common block STMAP, available for inclusion within the FX routine, supplies the information necessary to perform the conversion into data coordinate space, as well as for the mapping from data to user coordinates. The default version of FX simply performs an identity mapping from grid to user coordinate space.

4.2.2 Arguments

X (REAL, input): The X coordinate of a point on the streamline in the grid coordinate system

Y (REAL, input) The Y coordinate of a point on the streamline in the grid coordinate system

4.3 FY (X,Y)

Given the X and Y coordinates of a point on the streamline in the grid coordinate system, the function FX returns the X coordinate of the point in user coordinate space.

4.3.1 Usage

The user does not invoke the function, FY, directly. In older versions of NCAR Graphics, the user modified the functions, FX and FY, in order to implement custom mappings from grid coordinates to user coordinates. These functions were used throughout NCAR Graphics, not just in the Streamlines utility. For compatibility with existing code, calls to any of the Streamlines primary entry points predating Version 3.2 (EZSTRM or STRMLN), by default use FX and FY to map from grid to user coordinates. However, by appropriately setting the compatibility mode parameter, CPM, the user can choose whether the FX and FY functions or the new mapping routines are invoked when using any of the primary entry points supported by Streamlines.

Unlike the Version 3.2 mapping routines, whose input coordinates are in the data coordinate system, FY takes input in the grid coordinate system. Therefore, any required conversions into the data coordinate system must be performed within the function prior to the mapping into user coordinates. The common block STMAP, available for inclusion within the FY routine, supplies the information necessary to perform the conversion into data coordinate space, as well as for the mapping from data to user coordinates. The default version of FY simply performs an identity mapping from grid to user coordinate space.

4.3.2 Arguments

X (REAL, input): The X coordinate of a data point in the grid coordinate system

Y (REAL, input): The Y coordinate of a data point in the grid coordinate system

4.4 STRMLN (U,V,WORK,IMAX,IPTSX,JPTSY,NSET,IER)

STRMLN plots a streamline representation of a flow field, given two 2-dimensional vector component arrays, U and V. Certain characteristics of the plot may be controlled by adjusting the values given to the input arguments. Other less frequently changed characteristics may be affected by modifying the initial values assigned to members of the common blocks STR02 and STR03 at the beginning of the executable code section of STRMLN. In addition, depending on the value given to the compatibility parameter, CPM, certain options may be controlled by setting internal parameters using STSETx routines.

4.4.1 Usage

Beginning with version 3.2 of NCAR Graphics, the STRMLN entry point has been recoded as a front end to the STINIT/STREAM interface to Streamlines. The compatibility mode parameter, CPM, controls the degree to which a call to the Version 3.2 STRMLN emulates the older call. Appropriate settings of CPM can separately answer each the following three questions regarding the level of emulation:

Given the default value of CPM, all these questions are answered in the affirmative, and a call to STRMLN gives a reasonably faithful emulation of the older version's behavior. However, even in this case, it is possible to use the parameter setting routines to control the behavior of features that have no counterpart in the older version of STRMLN, as long as the feature is accessible without calling the new interface. For instance, you could control the streamline linewidth by setting the LWD parameter, but on the other hand you could not draw streamlines masked to an area map because doing so requires direct invocation of STREAM with the proper input arguments.

The following two tables show how the STRMLN input arguments and STR02/STR03 common block members map into internal parameters currently supported by Streamlines:

Input ArgumentInternal Parameter
NSETSET (NSET = 0 is approximately equivalent to SET = 1)

Common Block MemberInternal Parameter
INITASGD
INITBAGD
ITERPCKP
ITERCCKX
IGFLGTRP
ICYCCYK
IMSGSVF
UVMSGUSV
UVMSGVSV
DISPLVNL
AROWLARL (AROWL as fraction of grid box size is converted to ARL as fraction of viewport width)
CSTOPSSP (CSTOP as fraction of grid box size is converted to SSP as fraction of viewport width)
DISPLDFM (DISPL as fraction of grid box size is converted to DFM as fraction of viewport width)
DISPC/DISPLCDS (The critical displacement multiplier CDS is calculated as the ratio of DISPC to DISPL)

See the parameter descriptions in the next section for an explanation of the meaning of these parameters. Descriptions of the behavior of NSET and the STR02 and STR03 common block members is available in the source code for STRMLN.

4.4.2 Arguments

U (REAL 2-dimensional array, dimensioned IMAX x n: n >= JPTSY, input): By default, assumed to contain the first dimensional Cartesian components of the vector field. However, if PLR is non-zero, it is treated as containing the vector magnitudes.

V (REAL 2-dimensional array, dimensioned IMAX x n: n >= JPTSY, input): By default, assumed to contain the second dimensional Cartesian components of the vector field. However, if PLR is non-zero, it is treated as containing the vector angles.

WORK (REAL array, dimensioned n: n>= 2*IPTSX*JPTSY, working space): User provided work array used to store the normalized vector component values, and also to keep track of the grid boxes eligible for starting a streamline or placement of a directional arrow.

IMAX (INTEGER, input): Actual value of the first dimension of arrays U and V.

IPTSX (INTEGER, input): Number of contiguous elements along the first dimensional axis containing data to be processed in each of the arrays, U and V.

JPTSY (INTEGER, input): Number of contiguous elements along the second dimensional axis containing data to be processed in each of the arrays, U and V.

NSET (INTEGER, input) Flag that controls how and when the SET call is invoked. If NSET is 0, STRMLN makes a SET call to establish a standard viewport and window boundaries coincident with the array coordinate boundaries. PERIM is called to draw a border. If NSET is greater than zero, STRMLN does not call SET or PERIM. If NSET is less than zero, STRMLN calls SET to establish window boundaries coincident with the array grid coordinate boundaries but does not modify the viewport or call PERIM.

IER (INTEGER, output) If no error involving the ICYC common block variable (or, depending on the compatibility mode, the CYK internal parameter) is detected IER contains the value 0 on exit from STRMLN. If, when STRMLN is invoked, ICYC (or CYK) is erroneously set to indicate that the data is cyclic, STRMLN still processes the data using non-cyclic interpolation formulas, but returns the value of -1 in IER.

5.0 PARAMETERS

The behavior of Streamlines is controlled by parameters stored in internal common blocks accessible to its routines that require access to them.

5.1 Parameter Names

Each of the parameters of Streamlines is identified by a three-character name that in general has some mnemonic relationship to its function. For example, SSP is the name of a parameter that specifies the amount of space Streamlines tries to maintain between adjacent streamlines and MSK is the name of a parameter that allows the user to specify whether or not to mask the streamlines to an area map.

5.2 Parameter Types

Each parameter is intrinsically of type INTEGER, or REAL, but the type of the parameter is not implied by the form of its name; one must read the description of the parameter to determine its type. Note that Streamlines does not currently support any parameters of type CHARACTER.

5.3 Parameter Defaults

Each parameter has a default value which is intended to yield a reasonable, useful, default behavior. To modify the behavior of Streamlines routines, one changes the values of the appropriate parameters at the appropriate time.

5.4 Parameter Access

The value of a parameter may be set using STSETI or STSETR. Each of these routines has as its first argument a character string beginning with the three-character name of the parameter and as its second argument an expression of the type implied by the last character of the routine name ("I" for "INTEGER" or "R" for "REAL"). Similarly, the current value of a parameter may be retrieved using STGETI or STGETR, each of which has as its first argument the name of the parameter and as its second argument a variable of the type implied by the last character of the routine name.

In general, once a parameter is given a particular value, it retains that value until it is given a new value by the user. However, a number of parameters are read-only to the user; their values may be retrieved by the STGETx routines but an attempt to set them using the STSETx routines will result in an error. These parameters are intended to provide the user with useful information about the state of the program that may be helpful in determining how to perform the next operation.

5.5 Parameter-Name Arguments

Only the first three characters of the parameter-name argument in calls to the parameter access routines are examined. The user is encouraged to add additional text in order to make the code more understandable. For example, a call to set the streamline spacing might read

      CALL STSETR ('SSP - Streamline Spacing',0.02)
Note that since the dimension of the parameter name variable is defined as 'CHARACTER*(*)', there is no limit to the number of characters used to comment the call.

5.6 Automatic Type Conversion

Normally, one would use STSETI to set parameters of type INTEGER and STSETR to set parameters of type REAL. However, since automatic conversion is done as necessary, this need not be the case. One could, for example, use either of the two statements

      CALL STSETI ('USV - U Array Special Value',-9999)
      CALL STSETR ('USV - U Array Special Value',-9999.0)
to set the U array special value (which is intrinsically REAL) to -9999.0. The first has the virtue of being two characters shorter. Similarly, one could use either of the two statements

      CALL STSETI ('TRP - Interpolation Method',1)
      CALL STSETR ('TRP - Interpolation Method',1.0)
to set the interpolation method parameter (which is intrinsically INTEGER) to 1. (In this case, of course, the first of the two statements seems to make better sense.) If a REAL parameter is to be given a non-integral value (like 3.14159), then STSETR must be used, of course. Note that the argument passing rules of FORTRAN must still be respected: an INTEGER argument passed to STSETR will have the usual "undefined" results.

5.7 Automatic Restriction of Parameter Values

Some parameters may take on any possible value of the proper type. Others are restricted to a certain range. In some cases, out-of-range parameters are simply constrained to some value within the range. In other cases, where it seems dangerous to second-guess what the user has in mind, an error is returned and the program halts.

5.8 Parameters Categorized

This section contains a list of all Streamlines parameters categorized by function along with a short descriptive phrase. It also notes which of the categories may safely be set in between the call to STINIT and STREAM. The section following is an alphabetical listing of all parameters including a detailed description.

5.8.1 Miscellaneous Control Parameters

These parameters provide miscellaneous control of the Streamlines utility. When using the STINIT/STREAM interface, these parameters may be set between the calls to STINIT and STREAM.

CPM - Compatibility Mode - Integer
SST - Streamline Statistics Output Flag - Integer
TRP - Interpolation Method - Integer

5.8.2 Coordinate System Control

These parameters (along with the mapping subroutine, STMPXY or STUMXY) establish the mapping through a series of coordinate systems starting with the array indices that define the basic grid and ending with the Normalized Device Coordinates. Any non-default values must be set prior to calling STINIT.

SET - SET Call Flag - Integer
XC1 - X Coordinate at Index 1 - Real
XCM - X Coordinate at Index M - Real
YC1 - Y Coordinate at Index 1 - Real
YCN - Y Coordinate at Index N - Real
WDB - Window Bottom - Real
WDL - Window Left - Real
WDR - Window Right - Real
WDT - Window Top - Real
VPB - Viewport Bottom - Real
VPL - Viewport Left - Real
VPR - Viewport Right - Real
VPT - Viewport Top - Real
VPS - Viewport Shape - Real
TRT - Transformation Type - Integer
MAP - Map Transformation Code - Integer

5.8.3 Input Data Control

These parameters control the interpretation of the input data, and allows the user to place restrictions on the range of data represented. Any non-default values must be set prior to calling STINIT.

PSV - P Array Special Value - Real
SVF - Special Value Flag - Integer
USV - U Array Special Value - Real
VSV - V Array Special Value - Real
PLR - Polar Input Mode - Integer
CYK - Cyclical Data Flag - Integer

5.8.4 Color Control

These parameters are used to control the set up of the color threshold array and the color index array. If CTV has a positive value, STINIT modifies NLV members of the TVL threshold array. Otherwise, these parameters may be set between the call to STINIT and STREAM.

CTV - Color Threshold Value Control - Integer
NLV - Number of Color Levels - Integer
CLR - Array of GKS Color Indices - Integer Array
TVL - Array of Threshold Values - Real Array
SPC - Special Color - Integer

5.8.5 General Rendering Control

These parameters allow the user to control the rendering of the streamline flow field plot. Parameters in this category may be set between the call to STINIT and STREAM.

STM - Streamline Mode - Integer
GBS - Grid Based Spacing - Integer
MSK - Mask To Area Map Flag - Integer
LWD - Streamline Linewidth - Real
DFM - Streamline Differential Magnitude - Real
SSP - Streamline Spacing Value - Real
SGD - Stream Starting Grid Increment - Integer
SMD - Streamline Minimum Distance - Real
AGD - Arrow Head Placement Grid Increment - Integer
AMD - Arrow Head Minimum Distance - Real
ARL - Arrow Head Length - Real
CDS - Critical Displacement Multiplier - Real
CKP - Check Progress Iteration Count- Integer
CKX - Check Crossover Iteration Count- Integer
VNL - Vector Normalization Value - Real

5.8.5 Curly Vector Rendering Control

These parameters apply only when curly vector mode is in effect (STM set to 1).

VRL - Vector Reference Length - Real
VRM - Vector Reference Magnitude - Real
VFR - Minimum Vector Fractional Length - Real
AFR - Arrow Head Fractional Minimum Size - Real
VPO - Vector Positioning Mode - Integer

5.8.5 Read-Only Informational Parameters

These parameters may be used to retrieve information about the state of the Streamlines utility. The may be retrieved at any time, but may not contain useful information at all stages of the processing.

DMN - NDC Minimum Vector Size - Real
DMX - NDC Maximum Vector Size - Real

5.8.6 Supplementary Text Control Parameters

These parameters control the placement of the Zero Field Text Block. Parameters in this category may be set between the call to STINIT and STREAM.

ZFC - Zero Field Text Block Color - Integer
ZFP - Zero Field Text Block Positioning Mode - Integer
ZFS - Zero Field Text Block Character Size - Real
ZFT - Zero Field Text String - Character* 36
ZFX - Zero Field Text Block X Coordinate - Real
ZFY - Zero Field Text Block Y Coordinate - Real

5.9 Parameter Description

Parameter descriptions follow, in alphabetical order. Each description begins with a line giving the three-character mnemonic name of the parameter, the phrase for which the mnemonic stands, and the intrinsic type of the parameter. Note that the phrases such as "the value of XXX is x" where 'XXX' is the name of a parameter and x is an INTEGER or REAL value, are freely used to mean "the Streamlines internal common block variable associated with parameter XXX holds the value x".

5.9.1 AFR - Arrow Head Fractional Minimum Size - Real

In curly vector mode, the arrowhead may vary between a minimum size and a maximum size in proportion to the the vector magnitude of the grid point. This parameter specifies the minimum size of the arrowhead as a fraction of the maximum size, which is controlled by the parameter ARL. AFR has an effect only when STM has the value 1.

5.9.2 AGD - Arrow Head Placement Grid Increment - Integer

This parameter allows you a degree of control over directional arrowhead spacing in the field flow plot. Streamlines allows a maximum of one directional arrowhead for each grid box, where a grid box is the space between adjacent integer grid coordinates in the grid coordinate system along both dimensions. However, Streamlines actually places an arrowhead only if both lower grid indices, modulo the value of AGD, are equal to 0. If AGD is set to 2, for instance, Streamlines places an arrowhead on the first streamline to enter each grid box with even-numbered lower grid indices.

If the transformation pipeline is everywhere linear from grid coordinate space to NDC space, then the spacing of the arrowheads should be more or less uniform over the field flow plot. However, if there is a non-linearity anywhere in the pipeline, the arrowheads will probably be more crowded in some areas than in others. In that case, a more uniform distribution of the arrowheads may be achieved using the parameter AMD.

Note that in curly vector mode, there is always one arrowhead per vector. Therefore, AGD has an effect only when STM has the value 0.

5.9.3 AMD - Arrow Head Minimum Distance - Real

AMD allows you to specify, as a fraction of the viewport width, a minimum distance between adjacent directional arrowheads along a single streamline. If the data grid is transformed in such a way that adjacent grid cells become very close in NDC space, as for instance in many map projections near the poles, you can use this parameter to help reduce the otherwise cluttered appearance of these regions of the plot. Note that currently, whenever AMD has a positive value, the first arrowhead that would otherwise be drawn for each streamline is always eliminated. If AMD is less than or equal to 0.0, then no arrowheads are eliminated. AMD has an effect only when STM has the value 0. The default value of AMD is 0.0.

Note that in curly vector mode, there is always one arrowhead per vector. Therefore, AMD has an effect only when STM has the value 0.

5.9.4 ARL - Arrow Head Length - Real

ARL defines the length of each of the two lines used to create the directional arrow head. If the parameter GBS is set to 0, ARL has units "fraction of viewport width"; if GBS is set to 1, ARL has the units "fraction of grid box width". The default value of ARL is 0.012 when GBS has the value 0 and 0.33 when GBS has the value 1. Setting GBS causes ARL to be reset to its appropriate default value.

5.9.5 CDS - Critical Displacement Multiplier - Real

CDS specifies the minimum amount the streamline must grow as a multiple of the basic differential step size each time the stream progress is checked in order for the streamline not to be terminated. The nominal differential step size is specified by DFM in NDC space, and the progress is checked each CKP iterations. Points of convergence or divergence typically cause stream growth to diminish and the streamline eventually to be terminated. The default value of CDS is 2.0, meaning that any time a streamline does not increase in length a minimum of 2.0*DFM in NDC over the previous check, it is discontinued and a new streamline is begun if possible.

5.9.6 CKP - Check Progress Iteration Count- Integer

The parameter CKP specifies the number of iterations through the streamline building loop between each check of the streamline growth. If the distance between current position of the streamline and the position saved at the time of the previous check is less than a minimum amount, defined as the value of CDS times the value of DFM in NDC space, then the current streamline is terminated and a new one begun if possible. The default value of CKP is 35.

5.9.7 CKX - Check Crossover Iteration Count- Integer

CKX specifies the number of iterations through the streamline building loop between checks for streamline crossover, that is, one streamline growing closer than a certain distance (as specified by the parameter SSP) to previously created streamline. A negative value of CKX causes Streamlines to check for crossover only when a new grid box is entered. At each crossover check, the current streamline position is compared with a sampling of previous streamline positions retained in an internal circular list. The length of this list is fixed by the FORTRAN PARAMETER IPLSTL, currently set to 750. Since up to this number of comparisons are performed at each crossover check, the frequency with which these checks are performed can have a noticeable impact on performance. CKX has an effect only when STM has the value 0. By default, CKX has the value -99, causing Streamlines to check for crossover only on entrance to a new grid box.

5.9.8 CLR - Array of GKS Color Indices - Integer Array

This parameter represents an array containing the GKS color index to use for coloring each streamline step segment when the scalar quantity is less than or equal to the threshold value with the same index in the TVL threshold value array. In order to access a particular element of the CLR array, you must first set the value of PAI, the parameter array index parameter, to the value of the array element's index. All elements of the array are set to one initially. Note that the Streamlines utility makes no calls to set the GKS color representation (GSCR), nor ever modifies the contents of the CLR array; therefore you are responsible for creating a suitably graduated color palette and assigning the color index values into the CLR array, prior to calling STREAM. Typically, assuming the desired RGB values have been previously stored in a 2-dimensional 3 x n array called RGB, you loop through the calls that set up the color representation and color index as in the following example for a fourteen color palette:

      DO 100 I=1,14,1
        CALL GSCR (1,I,RGB(1,I),RGB(2,I),RGB(3,I))
        CALL STSETI('PAI -- Parameter Array Index', I)
        CALL STSETI('CLR -- GKS Color Index', I)
  100 CONTINUE
See the descriptions of CTV, NLV, and TVL for details on configuring the scalar-value based coloring scheme.

5.9.9 CPM - Compatibility Mode - Integer

Controls the degree of compatibility between versions of the Streamlines utility prior to NCAR Graphics 3.2 and the current version. You can independently control three behaviors using the nine settings provided:

Note, however, that when using the Version 3.2 entry points STINIT and STREAM, only the third behavior option has any meaning. Note also that curly vector and progressive streamline coloring are not available if the old coordinate mapping routines are used.

When CPM is set to 0, its default value, the Streamlines utility's behavior varies depending on whether you access it through one of the pre-Version 3.2 entry points (STRMLN and EZSTRM), or through the STINIT/STREAM interface. Otherwise, positive values result in invocation of the older coordinate mapping routines (FX and FY). Negative values cause the Version 3.2 mapping routines to be used instead. When using the pre-Version 3.2 interface only, odd values of CPM cause the data values in the common blocks, STR02 and STR03, to override corresponding values initialized in the Version 3.2 STDATA block data subroutine, or set by the user calling STSETx routines. Values of CPM with absolute value less than or equal to two cause the NSET argument to STRMLN to take precedence over the SET parameter.

Here is a table of the nine settings of CPM and their effect on the operation of the Streamlines utility:

ValueUse FX and FYUse STR02, STR03Use NSET
-4nonono
-3noyesno
-2nonoyes
-1noyesyes
0old - yes; new - no (*)yesyes
1yesyesyes
2yesnoyes
3yesyesno
4yesnono

(*) Old means EZSTRM or STRMLN entry point; new, STINIT/STREAM. Only the first column is applicable to the behavior of the STINIT/STREAM interface

5.9.10 CTV - Color Threshold Value Control - Integer

In conjunction with NLV, this parameter controls streamline coloring and the setting of threshold values. The vectors may be colored based on the vector magnitude or on the contents of a scalar array (STINIT/STREAM input argument, P). A table of supported options follows:

ValueAction
-2Color streamlines based on scalar array data values; the user is responsible for setting up threshold level array, TVL
-1Color streamlines based on vector magnitude; the user is responsible for setting up values of threshold level array.
0 (default)Color streamlines according to the current GKS polyline color index value. Threshold level array, TVL and GKS color index array, CLR are not used.
1Color streamlines based on vector magnitude; STINIT assigns values to the first NLV elements of the threshold level array, TVL.
2Color streamlines based on scalar array data values; STINIT assigns values to the first NLV elements of the threshold level array, TVL.

Note that if streamlines are to be colored by magnitude (CTV set equal to 1 or -1) you must supply Streamlines with work space equal to the size of STINIT arguments N and M multiplied together. In other words, you must add an additional M*N to the minimum size of the WRK array and value of the LW argument, for a total of 3*M*N if SMD is not set to a value greater than 0.0 or to 5*M*N if it is.

5.9.11 CYK - Cyclical Data Flag - Integer

Use this parameter to specify that the data in the vector field arrays is cyclical: that is, it repeats with a period of M-1 (M, the input parameter to STINIT) along the first dimensional axis. If the flag is set to specify that the data is cyclical, Streamlines checks to see if the field data meet certain criteria. If they do, then an internal cyclical flag is set, causing the normalized vector interpolation routines to consider data from the opposite ends of the dataset when interpolating near the first dimensional dataset boundaries. If the criteria are not met, then Streamlines sets an error flag, retrievable by the user through the parameter ERR; processing continues without interruption, except that Streamlines now interpolates near the first dimensional end points without consideration of data at the opposite end. The test the data must pass in order to be deemed cyclical is that for each subscript value along the second dimensional axis, the first element and the last element along the first dimensional axis must be identical. A value of 0 for CYK means that the data is to be considered non-cyclical; any other value means that Streamlines should test for the cyclical condition. The default value of CYK is 0.

5.9.12 DFM - Streamline Differential Magnitude - Real

DFM specifies the length of the differential magnitude step size used by Streamlines. If the parameter GBS is set to 0 DFM has units "fraction of viewport width"; if GBS is set to 1, DFM has the units "fraction of grid box width". When the Version 3.2 mapp