vector field visualisation R - r

Question

I have a big text file with a lot of rows. Every row corresponds to one vector.
This is the example of each row:
x y dx dy
99.421875 52.078125 0.653356799108 0.782479314511
First two columns are coordinates of the beggining of the vector. And two second columnes are coordinate increments (the end minus the start).
I need to make the picture of this vector field (all the vectors on one picture).
How could I do this?
Thank you

Answer 1

If there is a lot of data (the question says "big file"),
plotting the individual vectors may not give a very readable plot.
Here is another approach: the vector field describes a way of deforming something drawn on the plane;
apply it to a white noise image.
vector_field <- function(
f, # Function describing the vector field
xmin=0, xmax=1, ymin=0, ymax=1,
width=600, height=600,
iterations=50,
epsilon=.01,
trace=TRUE
) {
z <- matrix(runif(width*height),nr=height)
i_to_x <- function(i) xmin + i / width * (xmax - xmin)
j_to_y <- function(j) ymin + j / height * (ymax - ymin)
x_to_i <- function(x) pmin( width, pmax( 1, floor( (x-xmin)/(xmax-xmin) * width ) ) )
y_to_j <- function(y) pmin( height, pmax( 1, floor( (y-ymin)/(ymax-ymin) * height ) ) )
i <- col(z)
j <- row(z)
x <- i_to_x(i)
y <- j_to_y(j)
res <- z
for(k in 1:iterations) {
v <- matrix( f(x, y), nc=2 )
x <- x+.01*v[,1]
y <- y+.01*v[,2]
i <- x_to_i(x)
j <- y_to_j(y)
res <- res + z[cbind(i,j)]
if(trace) {
cat(k, "/", iterations, "\n", sep="")
dev.hold()
image(res)
dev.flush()
}
}
if(trace) {
dev.hold()
image(res>quantile(res,.6), col=0:1)
dev.flush()
}
res
}
# Sample data
van_der_Pol <- function(x,y, mu=1) c(y, mu * ( 1 - x^2 ) * y - x )
res <- vector_field(
van_der_Pol,
xmin=-3, xmax=3, ymin=-3, ymax=3,
width=800, height=800,
iterations=50,
epsilon=.01
)
image(-res)
You may want to apply some image processing to the result to make it more readable.
image(res > quantile(res,.6), col=0:1)
In your case, the vector field is not described by a function:
you can use the value of the nearest neighbour or some 2-dimensional interpolation
(e.g., from the akima package).

Answer 2

With ggplot2, you can do something like this :
library(grid)
df <- data.frame(x=runif(10),y=runif(10),dx=rnorm(10),dy=rnorm(10))
ggplot(data=df, aes(x=x, y=y)) + geom_segment(aes(xend=x+dx, yend=y+dy), arrow = arrow(length = unit(0.3,"cm")))
This is taken almost directly from the geom_segment help page.

Answer 3

OK, here's a base solution:
DF <- data.frame(x=rnorm(10),y=rnorm(10),dx=runif(10),dy=runif(10))
plot(NULL, type = "n", xlim=c(-3,3),ylim=c(-3,3))
arrows(DF[,1], DF[,2], DF[,1] + DF[,3], DF[,2] + DF[,4])

Answer 4

Here is a example from the R-Help of pracma-package.
library(pracma)
f <- function(x, y) x^2 - y^2
xx <- c(-1, 1); yy <- c(-1, 1)
vectorfield(f, xx, yy, scale = 0.1)
for (xs in seq(-1, 1, by = 0.25)) {
sol <- rk4(f, -1, 1, xs, 100)
lines(sol$x, sol$y, col="darkgreen")
}
You can use quiver also.
library(pracma)
xyRange <- seq(-1*pi,1*pi,0.2)
temp <- meshgrid(xyRange,xyRange)
u <- sin(temp$Y)
v <- cos(temp$X)
plot(range(xyRange),range(xyRange),type="n",xlab=expression(frac(d*Phi,dx)),ylab=expression(d*Phi/dy))
quiver(temp$X,temp$Y,u,v,scale=0.5,length=0.05,angle=1)