如何用R统计两条曲线边界间及两侧的观测点数量？

步骤1：整理边界曲线数据 #

首先需要把两条边界曲线的x值按升序排列，确保后续插值逻辑准确：

# 排序上边界（data_line1）的x和y
data_line1_sorted <- data_line1[order(data_line1$x), ]
# 排序下边界（data_line2）的x和y
data_line2_sorted <- data_line2[order(data_line2$x), ]

步骤2：为每个观测点插值对应边界的y值 #

使用approx()函数，根据观测点的x值，从排序后的边界曲线中插值得到对应位置的上边界y值和下边界y值：

# 插值得到每个观测点对应的上边界y值
data_dots$y_upper <- approx(data_line1_sorted$x, data_line1_sorted$y, xout = data_dots$x)$y
# 插值得到每个观测点对应的下边界y值
data_dots$y_lower <- approx(data_line2_sorted$x, data_line2_sorted$y, xout = data_dots$x)$y

步骤3：分类统计观测点 #

通过观测点的y值与插值得到的上下边界y值比较，标记每个点的类别，再统计各类别数量：

# 添加类别标记
data_dots$category <- case_when(
  data_dots$y > data_dots$y_upper ~ "高于上边界",
  data_dots$y < data_dots$y_lower ~ "低于下边界",
  TRUE ~ "位于边界之间"
)

# 统计各类别数量
count_result <- table(data_dots$category)
print(count_result)

完整可运行代码 #

library(dplyr)
library(ggplot2)

# 生成原始数据
data_line1 <- data.frame(line = "1", x = c(0, round(runif(18,0,10), 2), 10), y = round(runif(20,40,60), 2))
data_line2 <- data.frame(line = "2", x = c(0, round(runif(18,0,10), 2), 10), y = round(runif(20,0,39), 2))
data_dots <- data.frame(x = round(runif(200,0,10), 2), y = round(runif(100,0,60), 2))

# 排序边界数据
data_line1_sorted <- data_line1[order(data_line1$x), ]
data_line2_sorted <- data_line2[order(data_line2$x), ]

# 插值获取对应边界y值
data_dots$y_upper <- approx(data_line1_sorted$x, data_line1_sorted$y, xout = data_dots$x)$y
data_dots$y_lower <- approx(data_line2_sorted$x, data_line2_sorted$y, xout = data_dots$x)$y

# 分类并统计
data_dots$category <- case_when(
  data_dots$y > data_dots$y_upper ~ "高于上边界",
  data_dots$y < data_dots$y_lower ~ "低于下边界",
  TRUE ~ "位于边界之间"
)

count_result <- table(data_dots$category)
print(count_result)

# 可选：可视化分类结果
ggplot()+
  geom_line(data = data_line1_sorted, aes(x,y), color = "black")+
  geom_line(data = data_line2_sorted, aes(x,y), color = "red")+
  geom_point(data = data_dots, aes(x,y, color = category))+
  scale_color_manual(values = c("高于上边界" = "orange", "位于边界之间" = "deepskyblue", "低于下边界" = "green"))

补充说明 #

• approx()默认使用线性插值，适配连续边界曲线场景；如果边界是非线性的，可以指定method = "spline"进行样条插值。
• case_when()来自dplyr包，用于清晰的多条件判断，需提前加载该包。

内容的提问来源于stack exchange，提问作者tipofey