修复插值极坐标轮廓绘图功能以使用当前R和（可能）使用ggplot
问题R interpolated polar contour plot显示了在R中生成插值极坐标图的一种很好的方法。我包括我正在使用的略微修改的版本：
PolarImageInterpolate <- function(
### Plotting data (in cartesian) - will be converted to polar space.
x, y, z,
### Plot component flags
contours=TRUE, # Add contours to the plotted surface
legend=TRUE, # Plot a surface data legend?
axes=TRUE, # Plot axes?
points=TRUE, # Plot individual data points
extrapolate=FALSE, # Should we extrapolate outside data points?
### Data splitting params for color scale and contours
col_breaks_source = 1, # Where to calculate the color brakes from (1=data,2=surface)
# If you know the levels, input directly (i.e. c(0,1))
col_levels = 10, # Number of color levels to use - must match length(col) if
#col specified separately
col = rev(heat.colors(col_levels)), # Colors to plot
# col = rev(heat.colors(col_levels)), # Colors to plot
contour_breaks_source = 1, # 1=z data, 2=calculated surface data
# If you know the levels, input directly (i.e. c(0,1))
contour_levels = col_levels+1, # One more contour break than col_levels (must be
# specified correctly if done manually
### Plotting params
outer.radius = ceiling(max(sqrt(x^2+y^2))),
circle.rads = pretty(c(0,outer.radius)), #Radius lines
spatial_res=1000, #Resolution of fitted surface
single_point_overlay=0, #Overlay "key" data point with square
#(0 = No, Other = number of pt)
### Fitting parameters
interp.type = 1, #1 = linear, 2 = Thin plate spline
lambda=0){ #Used only when interp.type = 2
minitics <- seq(-outer.radius, outer.radius, length.out = spatial_res)
# interpolate the data
if (interp.type ==1 ){
Interp <- akima:::interp(x = x, y = y, z = z,
extrap = extrapolate,
xo = minitics,
yo = minitics,
linear = FALSE)
Mat <- Interp[[3]]
}
else if (interp.type == 2){
library(fields)
grid.list = list(x=minitics,y=minitics)
t = Tps(cbind(x,y),z,lambda=lambda)
tmp = predict.surface(t,grid.list,extrap=extrapolate)
Mat = tmp$z
}
else {stop("interp.type value not valid")}
# mark cells outside circle as NA
markNA <- matrix(minitics, ncol = spatial_res, nrow = spatial_res)
Mat[!sqrt(markNA ^ 2 + t(markNA) ^ 2) < outer.radius] <- NA
### Set contour_breaks based on requested source
if ((length(contour_breaks_source == 1)) & (contour_breaks_source[1] == 1)){
contour_breaks = seq(min(z,na.rm=TRUE),max(z,na.rm=TRUE),
by=(max(z,na.rm=TRUE)-min(z,na.rm=TRUE))/(contour_levels-1))
}
else if ((length(contour_breaks_source == 1)) & (contour_breaks_source[1] == 2)){
contour_breaks = seq(min(Mat,na.rm=TRUE),max(Mat,na.rm=TRUE),
by=(max(Mat,na.rm=TRUE)-min(Mat,na.rm=TRUE))/(contour_levels-1))
}
else if ((length(contour_breaks_source) == 2) & (is.numeric(contour_breaks_source))){
contour_breaks = pretty(contour_breaks_source,n=contour_levels)
contour_breaks = seq(contour_breaks_source[1],contour_breaks_source[2],
by=(contour_breaks_source[2]-contour_breaks_source[1])/(contour_levels-1))
}
else {stop("Invalid selection for \"contour_breaks_source\"")}
### Set color breaks based on requested source
if ((length(col_breaks_source) == 1) & (col_breaks_source[1] == 1))
{zlim=c(min(z,na.rm=TRUE),max(z,na.rm=TRUE))}
else if ((length(col_breaks_source) == 1) & (col_breaks_source[1] == 2))
{zlim=c(min(Mat,na.rm=TRUE),max(Mat,na.rm=TRUE))}
else if ((length(col_breaks_source) == 2) & (is.numeric(col_breaks_source)))
{zlim=col_breaks_source}
else {stop("Invalid selection for \"col_breaks_source\"")}
# begin plot
Mat_plot = Mat
Mat_plot[which(Mat_plot<zlim[1])]=zlim[1]
Mat_plot[which(Mat_plot>zlim[2])]=zlim[2]
image(x = minitics, y = minitics, Mat_plot , useRaster = TRUE, asp = 1, axes = FALSE, xlab = "", ylab = "", zlim = zlim, col = col)
# add contours if desired
if (contours){
CL <- contourLines(x = minitics, y = minitics, Mat, levels = contour_breaks)
A <- lapply(CL, function(xy){
lines(xy$x, xy$y, col = gray(.2), lwd = .5)
})
}
# add interpolated point if desired
if (points){
points(x, y, pch = 21, bg ="blue")
}
# add overlay point (used for trained image marking) if desired
if (single_point_overlay!=0){
points(x[single_point_overlay],y[single_point_overlay],pch=0)
}
# add radial axes if desired
if (axes){
# internals for axis markup
RMat <- function(radians){
matrix(c(cos(radians), sin(radians), -sin(radians), cos(radians)), ncol = 2)
}
circle <- function(x, y, rad = 1, nvert = 500){
rads <- seq(0,2*pi,length.out = nvert)
xcoords <- cos(rads) * rad + x
ycoords <- sin(rads) * rad + y
cbind(xcoords, ycoords)
}
# draw circles
if (missing(circle.rads)){
circle.rads <- pretty(c(0,outer.radius))
}
for (i in circle.rads){
lines(circle(0, 0, i), col = "#66666650")
}
# put on radial spoke axes:
axis.rads <- c(0, pi / 6, pi / 3, pi / 2, 2 * pi / 3, 5 * pi / 6)
r.labs <- c(90, 60, 30, 0, 330, 300)
l.labs <- c(270, 240, 210, 180, 150, 120)
for (i in 1:length(axis.rads)){
endpoints <- zapsmall(c(RMat(axis.rads[i]) %*% matrix(c(1, 0, -1, 0) * outer.radius,ncol = 2)))
segments(endpoints[1], endpoints[2], endpoints[3], endpoints[4], col = "#66666650")
endpoints <- c(RMat(axis.rads[i]) %*% matrix(c(1.1, 0, -1.1, 0) * outer.radius, ncol = 2))
lab1 <- bquote(.(r.labs[i]) * degree)
lab2 <- bquote(.(l.labs[i]) * degree)
text(endpoints[1], endpoints[2], lab1, xpd = TRUE)
text(endpoints[3], endpoints[4], lab2, xpd = TRUE)
}
axis(2, pos = -1.25 * outer.radius, at = sort(union(circle.rads,-circle.rads)), labels = NA)
text( -1.26 * outer.radius, sort(union(circle.rads, -circle.rads)),sort(union(circle.rads, -circle.rads)), xpd = TRUE, pos = 2)
}
# add legend if desired
# this could be sloppy if there are lots of breaks, and that's why it's optional.
# another option would be to use fields:::image.plot(), using only the legend.
# There's an example for how to do so in its documentation
if (legend){
library(fields)
image.plot(legend.only=TRUE, smallplot=c(.78,.82,.1,.8), col=col, zlim=zlim)
# ylevs <- seq(-outer.radius, outer.radius, length = contour_levels+ 1)
# #ylevs <- seq(-outer.radius, outer.radius, length = length(contour_breaks))
# rect(1.2 * outer.radius, ylevs[1:(length(ylevs) - 1)], 1.3 * outer.radius, ylevs[2:length(ylevs)], col = col, border = NA, xpd = TRUE)
# rect(1.2 * outer.radius, min(ylevs), 1.3 * outer.radius, max(ylevs), border = "#66666650", xpd = TRUE)
# text(1.3 * outer.radius, ylevs[seq(1,length(ylevs),length.out=length(contour_breaks))],round(contour_breaks, 1), pos = 4, xpd = TRUE)
}
}
不幸的是，这个函数有一些错误：
a）即使采用纯粹的放射状图案，制作的图也会出现失真，其起源我不明白：
#example
r <- rep(seq(0.1, 0.9, len = 8), each = 8)
theta <- rep(seq(0, 7/4*pi, by = pi/4), times = 8)
x <- r*sin(theta)
y <- r*cos(theta)
z <- z <- rep(seq(0, 1, len = 8), each = 8)
PolarImageInterpolate(x, y, z)
为什么在300°和360°之间摇摆？ z函数在theta中保持不变，因此没有理由为什么会出现摆动。
b）4年后，一些已加载的软件包已被修改，并且至少有一项功能被破坏。设置interp.type = 2应使用薄板样条进行插值而不是基本线性插值，但它不起作用：
> PolarImageInterpolate(x, y, z, interp.type = 2)
Warning:
Grid searches over lambda (nugget and sill variances) with minima at the endpoints:
(GCV) Generalized Cross-Validation
minimum at right endpoint lambda = 9.493563e-06 (eff. df= 60.80002 )
predict.surface is now the function predictSurface
Error in image.default(x = minitics, y = minitics, Mat_plot, useRaster = TRUE, :
'z' must be a matrix
第一条消息是警告，并不担心我，但第二条消息实际上是一个错误，并阻止我使用薄板样条。你能帮我解决这两个问题吗？
另外，我想“升级”为使用ggplot2，所以如果你能给出答案，那就太好了。否则，在修复错误后，我会尝试询问一个特定的问题，该问题仅要求修改该函数，以便它使用ggplot2。
2 个答案:
答案 0 :(得分：1)
对于ggplot2解决方案，这是一个开始。 geom_raster允许插值，但不适用于极坐标。相反，您可以使用geom_tile，但在将值传递给ggplot之前，您可能需要自己进行插值。
重要提示：使用geom_raster时，您提供的示例数据会出错，我认为这是由值的间距引起的。这是一个有效的示例集（注意，使用this blog作为指南，虽然现在已经过时了）：
dat_grid <-
expand.grid(x = seq(0,350,10), y = 0:10)
dat_grid$density <- runif(nrow(dat_grid))
ggplot(dat_grid
, aes(x = x, y = y, fill = density)) +
geom_tile() +
coord_polar() +
scale_x_continuous(breaks = seq(0,360,90)) +
scale_fill_gradient2(low = "white"
, mid = "yellow"
, high = "red3"
, midpoint = 0.5)
如果您使用的是原始数据，则可以让ggplot为您完成工作。这是一个使用原始数据的示例。有许多手动修补的事情要做，但它至少是一个可选的起点：
polarData <-
data.frame(
theta = runif(10000, 0, 2*pi)
, r = log(abs(rnorm(10000, 0, 10)))
)
toCart <-
data.frame(
x = polarData$r * cos(polarData$theta)
, y = polarData$r * sin(polarData$theta)
)
axisLines <-
data.frame(
x = 0
, y = 0
, xend = max(polarData$r)*cos(seq(0, 2*pi, pi/4))
, yend = max(polarData$r)*sin(seq(0, 2*pi, pi/4))
, angle = paste(seq(0, 2, 1/4), "pi") )
ticks <-
data.frame(
label = pretty(c(0, max(polarData$r)) )[-1]
)
ggplot(toCart) +
# geom_point(aes(x = x, y = y)) +
stat_density_2d(aes(x = x, y = y
, fill = ..level..)
, geom = "polygon") +
scale_fill_gradient(low = "white"
, high = "red3") +
theme(axis.text = element_blank()
, axis.title = element_blank()
, axis.line = element_blank()
, axis.ticks = element_blank()) +
geom_segment(data = axisLines
, aes(x = x, y = y
, xend = xend
, yend = yend)) +
geom_label(data = axisLines
, aes(x = xend, y = yend, label = angle)) +
geom_label(data = ticks
, aes(x = 0, y = label, label = label))
答案 1 :(得分：0)
从另一篇文章中，我知道软件包predict.surface中的功能fields已被弃用，而interp.type = 2中的PolarImageInterpolate使用了该函数。而是引入了一个新的predictSurface函数，可在此处使用。
示例：
r <- rep(seq(0.1, 0.9, len = 8), each = 8)
theta <- rep(seq(0, 7/4*pi, by = pi/4), times = 8)
x <- r*sin(theta)
y <- r*cos(theta)
z <- z <- rep(seq(0, 1, len = 8), each = 8)
PolarImageInterpolate(x, y, z, interp.type = 2)
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