在R中找到交点

Question

我有2个向量:

set.seed(1)
x1 = rnorm(100,0,1)
x2 = rnorm(100,1,1)

我想将这些作为线条绘制,然后找到线条的交点,如果有多个交叉点,那么我想找到它们中的每一个.

我遇到过类似的问题,并尝试使用解决此问题spatstat,但我无法将包含两个矢量值的组合数据帧转换为psp object.

Answer 1

如果你真的只有两个随机的数字向量,你可以使用一种非常简单的技术来获得两者的交集.只需找到x1上面的所有点x2,然后在下一点下面找到它,反之亦然.这些是交叉点.然后只需使用相应的斜率来查找该段的截距.

set.seed(1)
x1=rnorm(100,0,1)
x2=rnorm(100,1,1)
# Find points where x1 is above x2.
above<-x1>x2
# Points always intersect when above=TRUE, then FALSE or reverse
intersect.points<-which(diff(above)!=0)
# Find the slopes for each line segment.
x1.slopes<-x1[intersect.points+1]-x1[intersect.points]
x2.slopes<-x2[intersect.points+1]-x2[intersect.points]
# Find the intersection for each segment.
x.points<-intersect.points + ((x2[intersect.points] - x1[intersect.points]) / (x1.slopes-x2.slopes))
y.points<-x1[intersect.points] + (x1.slopes*(x.points-intersect.points))
# Plot.
plot(x1,type='l')
lines(x2,type='l',col='red')
points(x.points,y.points,col='blue')

Answer 2

这是一个替代的段 - 段交叉代码,

# segment-segment intersection code
# http://paulbourke.net/geometry/pointlineplane/
ssi <- function(x1, x2, x3, x4, y1, y2, y3, y4){

  denom <- ((y4 - y3)*(x2 - x1) - (x4 - x3)*(y2 - y1))
  denom[abs(denom) < 1e-10] <- NA # parallel lines

  ua <- ((x4 - x3)*(y1 - y3) - (y4 - y3)*(x1 - x3)) / denom
  ub <- ((x2 - x1)*(y1 - y3) - (y2 - y1)*(x1 - x3)) / denom

  x <- x1 + ua * (x2 - x1)
  y <- y1 + ua * (y2 - y1)
  inside <- (ua >= 0) & (ua <= 1) & (ub >= 0) & (ub <= 1)
  data.frame(x = ifelse(inside, x, NA), 
             y = ifelse(inside, y, NA))

}
# do it with two polylines (xy dataframes)
ssi_polyline <- function(l1, l2){
  n1 <- nrow(l1)
  n2 <- nrow(l2)
  stopifnot(n1==n2)
  x1 <- l1[-n1,1] ; y1 <- l1[-n1,2] 
  x2 <- l1[-1L,1] ; y2 <- l1[-1L,2] 
  x3 <- l2[-n2,1] ; y3 <- l2[-n2,2] 
  x4 <- l2[-1L,1] ; y4 <- l2[-1L,2] 
  ssi(x1, x2, x3, x4, y1, y2, y3, y4)
}
# do it with all columns of a matrix
ssi_matrix <- function(x, m){
  # pairwise combinations
  cn <- combn(ncol(m), 2)
  test_pair <- function(i){
    l1 <- cbind(x, m[,cn[1,i]])
    l2 <- cbind(x, m[,cn[2,i]])
    pts <- ssi_polyline(l1, l2)
    pts[complete.cases(pts),]
  }
  ints <- lapply(seq_len(ncol(cn)), test_pair)
  do.call(rbind, ints)

}
# testing the above
y1 = rnorm(100,0,1)
y2 = rnorm(100,1,1)
m = cbind(y1, y2)
x = 1:100
matplot(x, m, t="l", lty=1)
points(ssi_matrix(x, m))

Answer 3

回复晚了，但这里是使用 SP 包和 RGEOS 的“空间”方法。这要求 x 和 y 都是数字（或可以转换为数字）。投影是任意的，但 epsg:4269 似乎效果很好：

library(sp)
library(rgeos)
# dummy x data
x1 = rnorm(100,0,1)
x2 = rnorm(100,1,1)

#dummy y data 
y1 <- seq(1, 100, 1)
y2 <- seq(1, 100, 1) 

# convert to a sp object (spatial lines)
l1 <- Line(matrix(c(x1, y1), nc = 2, byrow = F))
l2 <- Line(matrix(c(x2, y2), nc = 2, byrow = F))
ll1 <- Lines(list(l1), ID = "1")
ll2 <- Lines(list(l2), ID = "1")
sl1 <- SpatialLines(list(ll1), proj4string = CRS("+init=epsg:4269"))
sl2 <- SpatialLines(list(ll2), proj4string = CRS("+init=epsg:4269"))

# Calculate locations where spatial lines intersect
int.pts <- gIntersection(sl1, sl2, byid = TRUE)
int.coords <- int.pts@coords

# Plot line data and points of intersection
plot(x1, y1, type = "l")
lines(x2, y2, type = "l", col = "red")
points(int.coords[,1], int.coords[,2], pch = 20, col = "blue")