如何在基础 R 中绘制自定义矢量场？

Question

我想生成一个图表，该图表将使用基础 R 在绘图中显示“矢量场”。

脚本的这一部分将生成一个带有不同圆的图形（仅改变它们的半径来构成矢量场的底）。

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)

其余代码在改变图形角度时尝试打印向量：

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)
}

}

如您所见，当我完成一整圈时，向量未与原始向量对齐（它们应该...）。

但是当我开始转圈时（比如 1/4*pi），就完美了。

如何使向量围绕圆“旋转”（基于角度）以使它们围绕圆旋转，以便向量始终垂直于圆（如上一张图，但所有角度） .

Answer 1

终于搞定了

# 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)
  }
}