How to draw a custom made vector field in base R? - r

Question

I want to generate a graph that would show a "vector field" in a plot using base R.
This section of the script will generate a graph with different circles (varying only their radius to make the base of the vector field).
r = 100 # Set the maximum radius to make an empty plot
x = function(ang) r* cos(ang) # To draw circles
y = function(ang) r* sin(ang) # To draw circles
nb = seq(from = 0,to = (2*pi),length.out = 100) # To have a sequence to draw the circles
plot(x(nb),y(nb), # Empty plot
asp = 1,
type = "n",
bg = "black",
col = "black",
pch =21, main = "Circle",
ylab = "Y values",
xlab ="X values")
abline(h=0,v=0) # Draw axes
for (i in seq(0,100,by = 5)) { # Draw a series of circles
r = i
points(x(nb),y(nb),
type = "l",
lwd = 1.0,
lty = 3)
}
# DRAWING TE VECTORS ----------------------
by = 10 # Define a "resolution" to see better the circles (This value will be smaller to be more precise)
changex = seq(0,100, by =by) # For each circle draw a radius with this sequence
current = -1 # This is to "flip" the orientation of the vectors
mag = current* seq(100,0, by = current*by)
arrows(x0 = changex, y0 = 0, # Draw the vectors
x1 = changex, y1 = mag,
code = 2,
length=0.1,
angle=40)
The rest of the code tries to print the vectors when changing the angle in the graph:
xycircle <- function(ang,r) { # function to draw position on the circle
x = r*cos(ang)
y = r*sin(ang)
return(list(x,y))
}
pilist = c(#0,1/4*pi,#1/2*pi, # List of PI values to go around the circle
#pi, #3/4*pi,
#3/2*pi,
2*pi)
for (pip in 1:length(pilist)) { # Going around the circle
ang = pilist[pip] # extract 1 angle value to draw
abline(a=0,b=tan(ang), lty = 3, lwd = 3) # Get a line that will show the angle selected
r = seq(0,100, by = by) # List of radius
mag = current* seq(-100,-0, by = by) # Magnitude of the vectors
for (i in 1:length(r)) { # Draw vectors when the angle changes
arrows(x0 = xycircle(ang,r[i])[[1]], # Base position of the vector (tangent to the circle)
y0 = xycircle(ang,r[i])[[2]],
x1 = cos(atan2(r[i],mag[i])-ang)*sqrt(r[i]^2+mag[i]^2), # Position of the tip of the vector (x)
y1 = sin(atan2(r[i],mag[i])-ang)*sqrt(r[i]^2+mag[i]^2), # Position of the tip of the vector (y)
code = 2, # Change the arrow head
length = 0.1,
angle = 40)
}
}
As you can see, when I complete a full revolution, the vectors are not aligned with the original vectors (they should...).
But when I start to turn around the circle (say 1/4*pi), it's perfect.
How would it be possible to make the vectors "turn" around the circle (based on angles) to make them rotate around the circle so that the vectors are always perpendicular to the circles (like the last graph, but all angles).

Answer 1

Finally, I got it to work
# parameter list ----------------------------------------------------------
by = 10
current = -1
invert.speed = TRUE
circleefrom = 10
circleeto = 28
# See 1 circle from 3 (2 for 4, 3 for 5...)
resolution = 15 # Which is also the number of arrows
resolution.circles = 100
maxcurrent = 10
mincurrent = 0
# Define functions --------------------------------------------------------
# Make a list of radius to draw various circles
r = seq(from = circleefrom, to = circleeto,
length.out = resolution)
# Make a function that will allow to draw circles and extract the values from the x,y position
xycircle <- function(ang,r) {
x = r*cos(ang)
y = r*sin(ang)
return(list(x,y))
}
# Samples enough point for the circles (100 at least)
nb = seq(from = 0, # starts at 0
to = (2*pi), # Does a FULL revolution around the circle
length.out = resolution.circles)
# Plot circles ------------------------------------------------------------
# Create empty canva
plot(x = xycircle(nb,max(r))[[1]],
y = xycircle(nb,max(r))[[2]],
asp = 1,
type = "n",
bg = "black",
col = "black",
pch =21, main = "Rheotaxis experiment",
ylab = "Y values",
xlab ="X values")
# Draw the axes
abline(h = 0,
v = 0)
# This will draw the circles
dbcicle = NULL
for (i in seq(from = circleefrom, to = circleeto,
length.out = resolution)) {
points(x = xycircle(nb,i)[[1]],
y = xycircle(nb,i)[[2]],
col = "blue",
type = "l",
lwd = 1.0,
lty = 3)
tmp = as.data.frame.list(x = c(xycircle(nb,i),i), col.names = c("x","y","radius"))
dbcicle = rbind(dbcicle,tmp)
}
# Add a black center to the design
plotrix::draw.circle(0, 0, radius = circleefrom,
nv = 1000,
border = NULL,
col = "black", lty = 1, lwd = 1)
# Add circle at the contour
plotrix::draw.circle(0, 0, radius = circleeto,
nv = 1000,
border = NULL,
col = NA, lty = 1, lwd = 1)
# Current specification ---------------------------------------------------
# Create the simulated current
if(invert.speed) {
mag = current * seq(from = mincurrent,
to = maxcurrent,
length.out = resolution + 1)
} else {
mag = current * seq(from = maxcurrent,
to = mincurrent,
length.out = resolution + 1)
}
# mag = current * rep(16,11)
# Draw the vecotrs of current --------------------------------------------
# Get different angle values
pilist = seq(from = 1/2*pi,
to = 2*pi,
by = 1/2*pi)
pilist = seq(from = 0,
to = 2*pi,
length.out = resolution)
dbcicle2 = NULL
for (pip in 1:length(pilist)) {
ang = pilist[pip]
abline(a=0,b=tan(ang), lty = 3, lwd = 3)
for (i in 1:length(r)) {
arrows(x0 = xycircle(ang,r[i])[[1]],
y0 = xycircle(ang,r[i])[[2]],
x1 = xycircle(c(ang-atan2(mag[i],r[i])),sqrt(r[i]^2+mag[i]^2))[[1]],
y1 = xycircle(c(ang-atan2(mag[i],r[i])),sqrt(r[i]^2+mag[i]^2))[[2]],
col = "blue",
code = 2,
length = 0.1,
angle = 40)
tmp = as.data.frame.list(x = c(xycircle(ang,r[i]),r[i],-1*mag[i],ang+pi/2),
col.names = c("x","y","radius","magnitude","ang"))
dbcicle2 = rbind(dbcicle2,tmp)
}
}