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Last data update: 2014.03.03

R: Plots velocities as arrows or as trajectory plots.

Quiver and flow paths

R Documentation

Plots velocities as arrows or as trajectory plots.

Description

Function quiver2D displays velocity vectors as arrows, using ordinary graphics.

Function quiver2Drgl displays velocity vectors as arrows using rgl.

Function flowpath displays the flow paths of particles, based on velocity vectors.

Usage

quiver2D(u, ...)

## S3 method for class 'matrix'
quiver2D(u, v, x = NULL, y = NULL, 
           colvar = NULL, ..., 
           scale = 1, arr.max = 0.2, arr.min = 0, speed.max = NULL,  
           by = NULL, type = "triangle", col = NULL, NAcol = "white", 
           breaks = NULL, colkey = NULL, mask = NULL,
           image = FALSE, contour = FALSE, 
           clim = NULL, clab = NULL, 
           add = FALSE, plot = TRUE) 

## S3 method for class 'array'
 quiver2D(u, v, margin = c(1, 2), subset, ask = NULL, ...)
                    
quiver2Drgl (u, v, x = NULL, y = NULL, colvar = NULL, ..., 
           scale = 1, arr.max = 0.2, arr.min = 0, speed.max = NULL, 
           by = NULL, type = "triangle", 
           col = NULL, NAcol = "white", breaks = NULL,
           mask = NULL, image = FALSE, contour = FALSE,
           colkey = NULL, clim = NULL, clab = NULL, add = FALSE, plot = TRUE)

flowpath(u, v, x = NULL, y = NULL, startx = NULL, starty = NULL, ...,
           scale = 1, numarr = 0, arr.length = 0.2, maxstep = 1000, 
           add = FALSE, plot = TRUE)

Arguments

`u`	A matrix (`quiver2D`) or array (`quiver2D.array`) with velocities in x-direction. For `quiver2D` the number of rows should be = Nx or Nx+1 (Nx = length(x), if x given), the number of columns should be = Ny or Ny+1 (Ny = length(y), if y given).
`v`	A matrix (`quiver2D`) or array (`quiver2D.array`) with velocities in y-direction. For `quiver2D` the number of rows should be = Nx or Nx+1, the number of columns should be = Ny or Ny+1.
`x`	Vector with x-coordinates of the velocities. If `NULL`, it is taken to be a sequence between (0, 1), and with length = `nrow(u)`.
`y`	Vector with y-coordinates of the velocities. If `NULL`, it is taken to be a sequence between (0, 1), and with length = `ncol(v)`.
`startx`	Vector with the start position in x-direction of the flow paths. Length > =1. If not specified, then all combinations of `x` and `y` at the outer margins will be used as starting point.
`starty`	Vector with start position in y-direction of flow paths. Length = length of `startx`.
`colvar`	The variable used for coloring. It need not be present, but if specified, it should be a vector of dimension equal to `c(nrow(u), ncol(v))`. Values of `NULL`, `NA`, or `FALSE` will toggle off coloration according to `colvar`.
`col`	Colors to be used for coloring the arrows as specified by the `colvar` variable. If `col` is `NULL` and `colvar` is specified, then a red-yellow-blue colorscheme (jet.col) will be used. If `col` is `NULL` and `colvar` is not specified, then `col` will be "black".
`NAcol`	Colors to be used for `colvar` values that are `NA`.
`breaks`	a set of finite numeric breakpoints for the colors; must have one more breakpoint than color and be in increasing order. Unsorted vectors will be sorted, with a warning.
`scale`	Scaling factor for the arrows. When `scale = 1`, the longest arrow will fill a grid cell in x- and y- direction. When `scale = 2`, it will be twice as long.
`arr.max`	Maximal size of the arrowhead, in cm (approximately). The arrows are scaled according to the velocity (`sqrt(u^2 + v^2)`). `arr.max` is associated with the maximal velocity.
`arr.min`	Minimal size of the arrowhead, in cm (approximately). Set `arr.min` = `arr.max` for constant size.
`speed.max`	Speed that corresponds to `arr.max`. Everything with speed larger than `speed.max` will be depicted with size equal to `arr.max`. If unspecified (`max(sqrt(u^2 + v^2))`).
`by`	Number increment for plotting the vectors; one value or two (x, y) values. For example, setting `by = 2` will plot every second velocity value in `x` and in `y` direction. Setting `by = c(1, 2)` will plot all vectors in `x` and every second vector in `y`. Useful if the vector density is too high.
`colkey`	A logical, `NULL` (default), or a `list` with parameters for the color key (legend). List parameters should be one of `side, plot, length, width, dist, shift, addlines, col.clab, cex.clab, side.clab, line.clab, adj.clab, font.clab` and the axis parameters `at, labels, tick, line, pos, outer, font, lty, lwd, lwd.ticks, col.box, col.axis, col.ticks, hadj, padj, cex.axis, mgp, tck, tcl, las`. The defaults for the parameters are `side = 4, plot = TRUE, length = 1, width = 1, dist = 0, shift = 0, addlines = FALSE, col.clab = NULL, cex.clab = par("cex.lab"), side.clab = NULL, line.clab = NULL, adj.clab = NULL, font.clab = NULL`) See colkey from package `plot3D`. The default is to draw the color key on side = 4, i.e. in the right margin. If `colkey` = `NULL` then a color key will be added only if `col` is a vector. Setting `colkey = list(plot = FALSE)` will create room for the color key without drawing it. if `colkey = FALSE`, no color key legend will be added.
`type`	The type of the arrow head, one of `"triangle"` (the default) or `"simple"`, which uses R-function arrows.
`contour, image`	If present, then a contour2D or image2D plot will be added to the quiver plot. They should be a `list` with arguments for the contour2D or `image2D` function.
`clim`	Only if `colvar` is specified, the range of the colors, used for the color key.
`clab`	Only if `colkey` is not `NULL` or `FALSE`, the label to be written on top of the color key. The label will be written at the same level as the main title. To lower it, `clab` can be made a vector, with the first values empty strings.
`margin`	A vector giving the subscripts which the plotting function will be applied over. The plotting function will loop over the index that is not in `margin`. For instance, `c(1, 2)`, indicates to plot rows(x) and columns(y) and to loop over index `3`; `c(2, 1)` will do the same but transposed. `margin` should be a vector with two numbers inbetween `1`, and `3`.
`ask`	A logical; if `TRUE`, the user is asked before each plot, if `NULL` the user is only asked if more than one page of plots is necessary and the current graphics device is set interactive, see par(ask) and dev.interactive.
`add`	If `TRUE`, will add to current plot. Else will start a new plot. Note: to use this in a consistent way, the previous plot should have been done with one of the `plot3D` functions.
`mask`	A `matrix` or `list` defining the grid cells outside the domain as `NA`. Use a list with argument `NAcol` to specify the color that the masked cells (that are `NA`) should get; the default is `"black"`. The unmasked cells are left `"white"`. If `x` and `y` are a vector, then `mask` can be a `matrix` with dimension equal to `length(x), length(y)`. If either `x` or `y` is itself a `matrix`, then `mask` should be a `list` that contains the `x`, `y`, and `z` values (and that are named 'x', 'y', 'z'). A `mask` cannot be combined with `add = TRUE`.
`plot`	If `FALSE`, will not plot the flow paths, but will return the matrix with path values instead.
`numarr`	The number of arrows added on the flow paths.
`arr.length`	Constant size of the arrowhead, in cm (approximately).
`maxstep`	Maximum number of steps for calculating the flow paths.
`...`	Additional arguments passed to the plotting methods (arrows2D), The arguments after ... must be matched exactly.
`subset`	A logical expression indicating over which elements to loop; missing values are taken as `FALSE`.

Details

S3 function quiver2D plots vectors specified by u, v at the coordinates x, y.

flowpath uses the velocities u, v at the coordinates x, y to create trajectories, starting at points startx, starty. It can also be used to return the flow path points by setting plot equal to FALSE. It uses very simple Euler integration and may not be very accurate.

Value

flowpath returns (as invisible) a 2-column matrix with the x-y coordinates of the flow paths. Separate flow paths are separated with NA.

quiver2D returns (as invisible) a list containing the coordinates of the arrows (x0, x1, y0, y1), the color of each arrow (col), the length of the arrowhead (length) and the maximal speed corresponding to arr.max (speed.max). This output can be used e.g. with function arrows.

Note

There was a slight error in the scaling of the arrows in versions previous to 1.0.3, which has been corrected. See last example.

Examples

## =======================================================================
##  EXAMPLE 1: 
## =======================================================================
 pm <- par("mfrow")
 par(mfrow = c(2, 2))

# generate velocities
 x  <- seq(-1, 1, by = 0.2)
 y  <- seq(-1, 1, by = 0.2)
 dx <- outer(x, y , function(x, y) -y)
 dy <- outer(x, y , function(x, y) x)

# velocity plot, with legend
 F <- quiver2D(u = dx, v = dy, x = x, y = y)
 legend("topright", bg = "white", 
   legend = paste("max = ", format(F$speed.max, digits = 2))) 

# different color for up/downward pointing arrows
 quiver2D(u = dx, v = dy, x = x, y = y, colvar = dx > 0, 
        col = c("red", "blue"), colkey = FALSE,
        arr.max = 0.4, arr.min = 0.1)

# different scale
 quiver2D(u = dx, v = dy, x = x, y = y, by = 2, scale = 2)

# three flow paths
 flowpath(u = dx, v = dy, x = x, y = y, startx = 0.1, starty = 0.1)
 flowpath(u = dx, v = dy, x = x, y = y, 
          startx = c(0.9, -0.9), starty = c(0.0, 0.0), col = "red",
          numarr = 2, add = TRUE)

## =======================================================================
##  EXAMPLE 2: note: has changed in version 1.0.3 - uses contour2D!
## =======================================================================
 par(mfrow = c(1, 1))
 x <- seq(-2, 2, by = 0.2)
 y <- seq(-1, 1, by = 0.2)
 z <- outer (x, y, function(x, y) x^3 - 3*x -2*y^2)
 contour2D(x, y, z = z, col = jet.col(10))

# gradients in x- and y-direction (analytical)
 dX <- outer(x, y, function(x,y) 3*x^2 - 3)
 dY <- outer(x, y, function(x,y) -4*y)

 quiver2D(u = dX, v = dY, x = x, y = y, scale = 1, add = TRUE, by = 1)
 flowpath(u = dX, v = dY, x = x, y = y, startx = c(-2, 1.1), 
            starty = c(-1, -1), add = TRUE, arr.length = 0.5,
            col = "darkgreen", lwd = 3, numarr = 1)

## =======================================================================
##  EXAMPLE 3: 
## =======================================================================
 
 x <- y <- 1:20
 u <- outer (x, y, function (x, y) cos(2*pi*y/10))
 v <- outer (x, y, function (x, y) cos(2*pi*x/10))

 quiver2D(x = x, y = y, u = u, v = v, col = "grey")

# flowpaths using all combinations of x and y at edges
 flowpath(x = x, y = y, u = u, v = v, add = TRUE, 
          lwd = 2, col = "orange")

## =======================================================================
##  EXAMPLE 4: quiver of an array.. 
## =======================================================================
 
 x <- y <- 1:20
 u2 <- outer (x, y, function (x, y) sin(2*pi*y/10))
 v2 <- outer (x, y, function (x, y) sin(2*pi*x/10))

# merge u, u2 and v, v2 to create an "array"
 U <- array(dim = c(dim(u2), 2), data = c(u, u2))
 V <- array(dim = c(dim(v2), 2), data = c(v, v2))

 quiver2D(u = U, v = V, x = x, y = y, main = c("time 1", "time 2"))

# quiver over x and time, for a subset of y-values:
 quiver2D(u = U, v = V, x = x, y = 1:2, 
        margin = c(1, 3), main = paste("y ", y), 
        subset = y <= 4)

## Not run: 
 quiver2D(u = U, v = V, x = x, y = y, ask = TRUE, 
        mfrow = c(1, 1))

 quiver2D(u = U, v = V, x = x, y = 1:2, ask = TRUE, 
        margin = c(1, 3), main = paste("y ", y),
        mfrow = c(1, 1))


## End(Not run)

## =======================================================================
##  EXAMPLE 5: 
## =======================================================================
 par(mfrow = c(1, 1))

 image2D(x = 1:nrow(volcano), y = 1:ncol(volcano), 
       z = volcano, contour = TRUE)

# Assume these are streamfunctions, we calculate the velocity field as:
 dx <- dy <- 1
 v <-   (volcano[-1, ] - volcano[-nrow(volcano), ] )/dx
 u <- - (volcano[, -1] - volcano[ ,-ncol(volcano)] )/dy

 quiver2D(x = 1:nrow(u), y = 1:ncol(v), 
        u = u, v = v, add = TRUE, by = 3)
 
 flowpath(x = 1:nrow(u), y = 1:ncol(v), numarr = 10,
          u = u, v = v, add = TRUE, lwd = 2, col = "grey", 
          startx = 20, starty = 30)
 
## =======================================================================
##  EXAMPLE 6: boundary mask, images, contours
## =======================================================================
 par (mfrow = c(2, 2))
 
 mask <- volcano; mask[volcano < 120]  <- NA
 quiver2D(by = c(3, 2), u = u, v = v, mask = mask)

 quiver2D(by = c(3, 2), u = u, v = v,  
        image = list(z = mask, NAcol = "black"))

 quiver2D(by = c(4, 3), u = u, v = v,
        contour = list(z = volcano, lwd = 2))

 quiver2D(by = c(4, 3), u = u, v = v, 
        contour = list(z = volcano, col = "black"), 
        image = list(z = volcano, NAcol = "black"))

## =======================================================================
##  Same in rgl
## =======================================================================
## Not run: 
 quiver2Drgl(by = c(3, 2), u = u, v = v, mask = mask, NAcol = "black")

 quiver2Drgl(by = c(3, 2), u = u, v = v,  
        image = list(z = volcano, NAcol = "black"))

 quiver2Drgl(by = c(4, 3), u = u, v = v, scale = 2,
        contour = list(z = volcano, lwd = 2))

 quiver2Drgl(by = c(4, 3), u = u, v = v, 
        contour = list(z = volcano, col = "black"), 
        image = list(z = volcano, NAcol = "black"))
 cutrgl()
 uncutrgl()

## End(Not run)

## =============================================================================
## 2-D Data set SyltSurf
## =============================================================================

 par(mfrow = c(1, 1))
 with (Syltsurf,
   quiver2D(x = x, y = y, u = u[ , ,2], v = v[ , ,2], 
     xlim = c(5, 20), ylim = c(10, 25), by = 3, 
     main = paste(formatC(time[1]), " hr"), scale = 1.5, 
     image = list(z = depth, x = x, y = y, NAcol = "black", 
                  colkey = TRUE), 
     contour = list(z = depth, x = x, y = y, col = "black",
       drawlabels = FALSE)
     )
  )

## =============================================================================
## 2-D Data set SyltSurf, several time points
## =============================================================================

# now for an array (first and 4th time point only)
 ii <- c(1, 4)
 with (Syltsurf,
   quiver2D(x = x, y = y, u = u[ ,,ii], v = v[ ,,ii], 
     xlim = c(5, 20), ylim = c(10, 25), by = 4, 
     mask = list(z = depth, x = x, y = y, NAcol = "blue"),
     main = paste(formatC(time[ii]), " hr"), scale = 1.5,
     contour = list(z = depth, x = x, y = y, drawlabels = FALSE)
     )
  )



## =============================================================================
## Adding quivers ...
## =============================================================================
x <- 1:2
y <- 1:3
u <- matrix(1:6,2,3)
v <- matrix(6:1,2,3)
 par(mfrow = c(1, 1))

A <- quiver2D(x = x, y = y, u = u, v = v)
B <- quiver2D(x = x, y = y[-1], u = u[,-1], v = v[,-1], col = 2, add = TRUE)
C <- quiver2D(x = x, y = y[-3], u = u[,-3], v = v[,-3], col = 3, add = TRUE)

# restore parameter settings
 par(mfrow = pm)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.

> library(OceanView)
Loading required package: plot3D
Loading required package: plot3Drgl
Loading required package: rgl
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/OceanView/quiver.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Quiver and flow paths
> ### Title: Plots velocities as arrows or as trajectory plots.
> ### Aliases: quiver2D quiver2D.matrix quiver2D.array quiver2Drgl flowpath
> ### Keywords: hplot
> 
> ### ** Examples
> 
> ## =======================================================================
> ##  EXAMPLE 1: 
> ## =======================================================================
>  pm <- par("mfrow")
>  par(mfrow = c(2, 2))
> 
> # generate velocities
>  x  <- seq(-1, 1, by = 0.2)
>  y  <- seq(-1, 1, by = 0.2)
>  dx <- outer(x, y , function(x, y) -y)
>  dy <- outer(x, y , function(x, y) x)
> 
> # velocity plot, with legend
>  F <- quiver2D(u = dx, v = dy, x = x, y = y)
>  legend("topright", bg = "white", 
+    legend = paste("max = ", format(F$speed.max, digits = 2))) 
> 
> # different color for up/downward pointing arrows
>  quiver2D(u = dx, v = dy, x = x, y = y, colvar = dx > 0, 
+         col = c("red", "blue"), colkey = FALSE,
+         arr.max = 0.4, arr.min = 0.1)
> 
> # different scale
>  quiver2D(u = dx, v = dy, x = x, y = y, by = 2, scale = 2)
> 
> # three flow paths
>  flowpath(u = dx, v = dy, x = x, y = y, startx = 0.1, starty = 0.1)
>  flowpath(u = dx, v = dy, x = x, y = y, 
+           startx = c(0.9, -0.9), starty = c(0.0, 0.0), col = "red",
+           numarr = 2, add = TRUE)
> 
> ## =======================================================================
> ##  EXAMPLE 2: note: has changed in version 1.0.3 - uses contour2D!
> ## =======================================================================
>  par(mfrow = c(1, 1))
>  x <- seq(-2, 2, by = 0.2)
>  y <- seq(-1, 1, by = 0.2)
>  z <- outer (x, y, function(x, y) x^3 - 3*x -2*y^2)
>  contour2D(x, y, z = z, col = jet.col(10))
> 
> # gradients in x- and y-direction (analytical)
>  dX <- outer(x, y, function(x,y) 3*x^2 - 3)
>  dY <- outer(x, y, function(x,y) -4*y)
> 
>  quiver2D(u = dX, v = dY, x = x, y = y, scale = 1, add = TRUE, by = 1)
>  flowpath(u = dX, v = dY, x = x, y = y, startx = c(-2, 1.1), 
+             starty = c(-1, -1), add = TRUE, arr.length = 0.5,
+             col = "darkgreen", lwd = 3, numarr = 1)
> 
> ## =======================================================================
> ##  EXAMPLE 3: 
> ## =======================================================================
>  
>  x <- y <- 1:20
>  u <- outer (x, y, function (x, y) cos(2*pi*y/10))
>  v <- outer (x, y, function (x, y) cos(2*pi*x/10))
> 
>  quiver2D(x = x, y = y, u = u, v = v, col = "grey")
> 
> # flowpaths using all combinations of x and y at edges
>  flowpath(x = x, y = y, u = u, v = v, add = TRUE, 
+           lwd = 2, col = "orange")
> 
> ## =======================================================================
> ##  EXAMPLE 4: quiver of an array.. 
> ## =======================================================================
>  
>  x <- y <- 1:20
>  u2 <- outer (x, y, function (x, y) sin(2*pi*y/10))
>  v2 <- outer (x, y, function (x, y) sin(2*pi*x/10))
> 
> # merge u, u2 and v, v2 to create an "array"
>  U <- array(dim = c(dim(u2), 2), data = c(u, u2))
>  V <- array(dim = c(dim(v2), 2), data = c(v, v2))
> 
>  quiver2D(u = U, v = V, x = x, y = y, main = c("time 1", "time 2"))
> 
> # quiver over x and time, for a subset of y-values:
>  quiver2D(u = U, v = V, x = x, y = 1:2, 
+         margin = c(1, 3), main = paste("y ", y), 
+         subset = y <= 4)
> 
> ## Not run: 
> ##D  quiver2D(u = U, v = V, x = x, y = y, ask = TRUE, 
> ##D         mfrow = c(1, 1))
> ##D 
> ##D  quiver2D(u = U, v = V, x = x, y = 1:2, ask = TRUE, 
> ##D         margin = c(1, 3), main = paste("y ", y),
> ##D         mfrow = c(1, 1))
> ##D 
> ## End(Not run)
> 
> ## =======================================================================
> ##  EXAMPLE 5: 
> ## =======================================================================
>  par(mfrow = c(1, 1))
> 
>  image2D(x = 1:nrow(volcano), y = 1:ncol(volcano), 
+        z = volcano, contour = TRUE)
> 
> # Assume these are streamfunctions, we calculate the velocity field as:
>  dx <- dy <- 1
>  v <-   (volcano[-1, ] - volcano[-nrow(volcano), ] )/dx
>  u <- - (volcano[, -1] - volcano[ ,-ncol(volcano)] )/dy
> 
>  quiver2D(x = 1:nrow(u), y = 1:ncol(v), 
+         u = u, v = v, add = TRUE, by = 3)
>  
>  flowpath(x = 1:nrow(u), y = 1:ncol(v), numarr = 10,
+           u = u, v = v, add = TRUE, lwd = 2, col = "grey", 
+           startx = 20, starty = 30)
>  
> ## =======================================================================
> ##  EXAMPLE 6: boundary mask, images, contours
> ## =======================================================================
>  par (mfrow = c(2, 2))
>  
>  mask <- volcano; mask[volcano < 120]  <- NA
>  quiver2D(by = c(3, 2), u = u, v = v, mask = mask)
> 
>  quiver2D(by = c(3, 2), u = u, v = v,  
+         image = list(z = mask, NAcol = "black"))
> 
>  quiver2D(by = c(4, 3), u = u, v = v,
+         contour = list(z = volcano, lwd = 2))
> 
>  quiver2D(by = c(4, 3), u = u, v = v, 
+         contour = list(z = volcano, col = "black"), 
+         image = list(z = volcano, NAcol = "black"))
> 
> ## =======================================================================
> ##  Same in rgl
> ## =======================================================================
> ## Not run: 
> ##D  quiver2Drgl(by = c(3, 2), u = u, v = v, mask = mask, NAcol = "black")
> ##D 
> ##D  quiver2Drgl(by = c(3, 2), u = u, v = v,  
> ##D         image = list(z = volcano, NAcol = "black"))
> ##D 
> ##D  quiver2Drgl(by = c(4, 3), u = u, v = v, scale = 2,
> ##D         contour = list(z = volcano, lwd = 2))
> ##D 
> ##D  quiver2Drgl(by = c(4, 3), u = u, v = v, 
> ##D         contour = list(z = volcano, col = "black"), 
> ##D         image = list(z = volcano, NAcol = "black"))
> ##D  cutrgl()
> ##D  uncutrgl()
> ## End(Not run)
> 
> ## =============================================================================
> ## 2-D Data set SyltSurf
> ## =============================================================================
> 
>  par(mfrow = c(1, 1))
>  with (Syltsurf,
+    quiver2D(x = x, y = y, u = u[ , ,2], v = v[ , ,2], 
+      xlim = c(5, 20), ylim = c(10, 25), by = 3, 
+      main = paste(formatC(time[1]), " hr"), scale = 1.5, 
+      image = list(z = depth, x = x, y = y, NAcol = "black", 
+                   colkey = TRUE), 
+      contour = list(z = depth, x = x, y = y, col = "black",
+        drawlabels = FALSE)
+      )
+   )
> 
> ## =============================================================================
> ## 2-D Data set SyltSurf, several time points
> ## =============================================================================
> 
> # now for an array (first and 4th time point only)
>  ii <- c(1, 4)
>  with (Syltsurf,
+    quiver2D(x = x, y = y, u = u[ ,,ii], v = v[ ,,ii], 
+      xlim = c(5, 20), ylim = c(10, 25), by = 4, 
+      mask = list(z = depth, x = x, y = y, NAcol = "blue"),
+      main = paste(formatC(time[ii]), " hr"), scale = 1.5,
+      contour = list(z = depth, x = x, y = y, drawlabels = FALSE)
+      )
+   )
> 
> 
> 
> ## =============================================================================
> ## Adding quivers ...
> ## =============================================================================
> x <- 1:2
> y <- 1:3
> u <- matrix(1:6,2,3)
> v <- matrix(6:1,2,3)
>  par(mfrow = c(1, 1))
> 
> A <- quiver2D(x = x, y = y, u = u, v = v)
> B <- quiver2D(x = x, y = y[-1], u = u[,-1], v = v[,-1], col = 2, add = TRUE)
> C <- quiver2D(x = x, y = y[-3], u = u[,-3], v = v[,-3], col = 3, add = TRUE)
> 
> # restore parameter settings
>  par(mfrow = pm)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>