这是我解决您问题的尝试。目前它也在雪花之外绘制颜色。如果您可以确定点是在雪花内部还是外部，您应该可以删除df_fill 中的外部点。
在这里，我首先创建用于绘制多边形的data.frame。然后我为背景颜色创建data.frame。最后我使用ggplot2 来绘制数据。
# creating relevant data
data.koch <- function(k){
df <- data.frame(x = 0,
y = 0,
grp = 0)
plotkoch <- function(x1, y1, x2, y2, n, data){
if (n==1) {
x=c(x1,(2*x1+x2)/3,(x1+x2)/2-(y1-y2)*sqrt(3)/6,(2*x2+x1)/3,x2)
y=c(y1,(2*y1+y2)/3,(y1+y2)/2-(x2-x1)*sqrt(3)/6,(2*y2+y1)/3,y2)
df <- rbind(data, data.frame(x, y, grp=max(data$grp)+1))
}
if (n > 1){
df <- plotkoch(x1,y1,(2*x1+x2)/3,(2*y1+y2)/3,n-1, data = data)
df <- plotkoch((2*x1+x2)/3,(2*y1+y2)/3,(x1+x2)/2-(y1-y2)*sqrt(3)/6,(y1+y2)/2-(x2-x1) *sqrt(3)/6,n-1, data=df)
df <- plotkoch((x1+x2)/2-(y1-y2)*sqrt(3)/6,(y1+y2)/2-(x2-x1)*sqrt(3)/6,(2*x2+x1)/3,(2 *y2+y1)/3,n-1, data=df)
df <- plotkoch((2*x2+x1)/3,(2*y2+y1)/3,x2,y2,n-1, data=df)
}
return(df)
}
df <- plotkoch(0,0,1,0,k, data = df)
df <- plotkoch(0.5,sqrt(3)/2,0,0,k, data = df)
df <- plotkoch(1,0,0.5,sqrt(3)/2,k, data = df)
return(df)
}
# plotting functon
plot.koch <- function(k){
stopifnot(require(ggplot2))
if (is.data.frame(k)) df <- k
else df <- data.koch(k)
# filling data (CHANGE HERE TO GET ONLY INSIDE POINTS)
l <- 500
df_fill <- expand.grid(x=seq(0, 1, length=l),
y=seq(-sqrt(3)/6, sqrt(3)/2, length=l))
df_fill[, "z"] <- atan2(-df_fill[, "y"] + sqrt(3)/6, df_fill[, "x"] - 0.5) + pi/2
df_fill[df_fill[, "z"] < 0, "z"] <- df_fill[df_fill[, "z"] < 0, "z"] + 2*pi
# plotting
ggplot(df, aes(x, y, group=grp)) +
geom_raster(data = df_fill,
aes(fill=z, group=NULL),
hjust = 0,
vjust = 0,
linetype='blank') +
geom_path(data=df, size=1) +
scale_fill_gradientn(colours = rainbow(30), guide = 'none') +
scale_x_continuous(name = '', limits = c(0, 1), expand=c(0, 0)) +
scale_y_continuous(name = '', limits = c(-sqrt(3)/6,sqrt(3)/2), expand=c(0, 0)) +
coord_fixed() +
theme_bw() +
theme(axis.line = element_blank(),
panel.grid = element_blank(),
axis.ticks = element_blank(),
axis.text = element_blank())
}
#
p <- plot.koch(4)
print(p)