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如果中心不重叠，则保留重叠的椭圆

Ulises CT 1月前

以下代码用于创建主轴长度为 1400 米、侧轴长度为 1000 米的椭圆。每个椭圆都分配有一个 ID。library(sf)library(ggplot2)library(dplyr)# 坐标数据...

以下代码创建了主轴长 1400 米、侧轴长 1000 米的椭圆。每个椭圆都分配有一个 ID。

library(sf)
library(ggplot2)
library(dplyr)

# coordinate data
x <- c(611547.6411, 589547.6411, 611447.6411, 609847.6411, 606347.6411, 611447.6411, 613547.6411,642747.6411, 589647.6411, 606447.6411, 613547.6411, 640347.6411, 642847.6411, 612147.6411, 613847.6411, 640247.6411, 642947.6411, 584347.6411, 587747.6411, 606447.6411, 614247.6411, 640447.6411, 642747.6411, 584447.6411, 608647.6411, 612047.6411, 612747.6411,
       613847.6411, 643147.6411, 583147.6411, 608747.6411, 611847.6411, 609647.6411, 610047.6411, 613747.6411, 586247.6411, 588647.6411, 643147.6411, 584347.6411, 606447.6411, 610147.6411, 613347.6411, 614647.6411, 586047.6411, 587247.6411, 611547.6411, 640347.6411, 643147.6411, 587147.6411, 583047.6411, 608747.6411, 612047.6411, 613947.6411, 587647.6411, 588547.6411, 586847.6411, 611247.6411, 643247.6411, 587247.6411, 590347.6411, 582947.6411, 608947.6411, 611847.6411, 613447.6411, 614647.6411, 585147.6411, 587647.6411, 588547.6411, 586947.6411, 611247.6411, 643047.6411, 587147.6411, 583947.6411, 587747.6411, 608547.6411, 611747.6411, 614047.6411, 585247.6411, 586247.6411, 588447.6411, 589147.6411, 611347.6411, 642447.6411, 586947.6411, 585847.6411, 587747.6411, 581447.6411, 612447.6411, 611947.6411, 600547.6411,
       612047.6411, 610347.6411, 614147.6411, 582847.6411, 588547.6411, 589247.6411, 611247.6411, 638147.6411, 640547.6411, 642947.6411, 587047.6411, 585947.6411, 587647.6411, 600447.6411, 611347.6411, 612347.6411, 610347.6411, 587747.6411, 579747.6411, 583847.6411, 586847.6411, 588447.6411, 589347.6411, 643347.6411, 589347.6411, 586947.6411, 588247.6411, 588847.6411, 585847.6411, 590847.6411, 589447.6411, 590947.6411, 581347.6411, 611847.6411, 600647.6411, 610347.6411, 615947.6411, 613947.6411, 586347.6411, 579647.6411, 584047.6411, 586347.6411, 587747.6411, 587947.6411, 586547.6411, 587647.6411, 614047.6411, 643047.6411, 587947.6411, 585747.6411, 584947.6411, 600547.6411, 611947.6411, 606847.6411, 600847.6411, 612847.6411, 615747.6411, 620747.6411, 614047.6411, 632947.6411, 588147.6411, 579747.6411, 582747.6411)

y <- c(5272140.5728, 5271740.5728, 5271640.5728, 5267440.5728, 5271540.5728, 5272040.5728, 5272340.5728, 5268540.5728, 5271240.5728, 5271640.5728, 5272140.5728, 5272240.5728, 5272240.5728, 5277940.5728, 5278040.5728, 5278040.5728, 5266940.5728, 5267040.5728, 5267440.5728, 5268140.5728, 5268640.5728, 5271140.5728, 5271740.5728, 5271740.5728, 5271940.5728, 5272140.5728, 5272240.5728, 5272040.5728, 5272140.5728, 5272140.5728, 5272140.5728, 5272240.5728, 5272340.5728, 5277240.5728, 5278040.5728, 5268540.5728, 5271240.5728, 5271340.5728, 5272240.5728, 5271940.5728, 5271940.5728, 5272040.5728, 5272040.5728, 5272040.5728, 5272040.5728, 5272040.5728, 5272140.5728, 5272140.5728,
       5272140.5728, 5272240.5728, 5272240.5728, 5277240.5728, 5278040.5728, 5278140.5728, 5278140.5728, 5265540.5728, 5266840.5728, 5266940.5728, 5267040.5728, 5268540.5728, 5272240.5728, 5272340.5728, 5272040.5728, 5272040.5728, 5277340.5728, 5278140.5728, 5278140.5728, 5265640.5728, 5266840.5728, 5267240.5728, 5268440.5728, 5271540.5728, 5272140.5728, 5271840.5728, 5271940.5728, 5271940.5728, 5271940.5728, 5272040.5728, 5272040.5728, 5272140.5728, 5272140.5728, 5272140.5728, 5272340.5728, 5277140.5728, 5277240.5728, 5277340.5728, 5277740.5728, 5277740.5728, 5278040.5728, 5278140.5728, 5278140.5728, 5278240.5728, 5278240.5728, 5264940.5728, 5265040.5728, 5265140.5728, 5266740.5728, 5266840.5728, 5266940.5728, 5267040.5728, 5267140.5728, 5267340.5728, 5267440.5728, 5268340.5728,
       5271240.5728, 5271840.5728, 5271940.5728, 5272040.5728, 5272040.5728, 5272340.5728, 5271840.5728, 5271840.5728, 5272140.5728, 5272140.5728, 5272240.5728, 5272240.5728, 5272340.5728, 5274340.5728, 5274440.5728, 5274640.5728, 5285140.5728, 5285240.5728, 5277340.5728, 5277540.5728, 5277840.5728, 5278040.5728, 5278040.5728, 5278140.5728, 5278140.5728, 5265540.5728, 5265640.5728, 5266740.5728, 5266740.5728, 5266940.5728, 5268340.5728, 5268440.5728, 5271440.5728, 5271540.5728, 5271540.5728, 5271740.5728, 5272040.5728, 5272340.5728, 5271740.5728, 5272240.5728, 5272240.5728, 5274540.5728, 5275040.5728, 5275340.5728, 5284840.5728, 5284940.5728, 5284940.5728, 5285040.5728, 5285040.5728)

# create data frame
coordinates.df <- data.frame(x = x, y = y)

# add ID column
coordinates.df$ID <- 1:nrow(coordinates.df)
coordinates.df <- coordinates.df[c(3,1:2)]

# convert data frame to sf object
coordinates.sf <- st_as_sf(coordinates.df, coords = c("x", "y"), crs = 25832)

# function for creating ellipses
create_ellipse <- function(center, a = 1400, b = 1000, angle = 225, n = 100) {
  angle_rad <- angle * pi / 180
  angles <- seq(0, 2 * pi, length.out = n)
  ellipse_coords <- cbind(a * cos(angles), b * sin(angles))
  rotation_matrix <- matrix(c(cos(angle_rad), -sin(angle_rad), 
                              sin(angle_rad),  cos(angle_rad)), 
                            nrow = 2)
  rotated_ellipse <- as.matrix(ellipse_coords) %*% rotation_matrix
  x_center <- center[1]
  y_center <- center[2]
  rotated_ellipse <- rotated_ellipse + matrix(c(x_center, y_center), nrow = n, ncol = 2, byrow = TRUE)
  rotated_ellipse <- rbind(rotated_ellipse, rotated_ellipse[1, ])
  st_polygon(list(rotated_ellipse))
}

# create ellipses
ellipses <- st_coordinates(coordinates.sf) %>%
  apply(1, function(p) create_ellipse(p)) %>%
  st_sfc(crs = st_crs(coordinates.sf))

# convert ellipses into sf objects
ellipses.sf <- st_sf(geometry = ellipses)

# plot
ggplot() +
  geom_sf(data = coordinates.sf, color = "black", size = 2) +
  geom_sf(data = ellipses.sf, fill = "blue", alpha = 0.2) +
  theme_minimal() +
  labs(x = "Easting", y = "Northing")

最终结果如下：

很明显，椭圆是重叠的。只要椭圆的中心不重叠，重叠是可以的。我希望这些图有助于更清楚地说明：

在第一种情况下，上椭圆不与下椭圆的中心重叠，这是可以的。在这种情况下，两个椭圆都应该保留。在第二种情况下，上椭圆与下椭圆（包括其中心）重叠，这是不行的。在这些情况下，应该删除 ID 较高的椭圆，只 留下 ID 较低的椭圆 。完全不接触的单个椭圆当然也应该保留。

有人知道如何实现这个吗？

如果有任何问题或不确定性，请随时发表评论。

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Cody Gray - on strike 1月前 0 只看Ta

引用 2楼

如果在带有绿色对勾的图中，ID6 被旋转，使得它与 ID4 的中心重叠，但 ID4 不与 ID6 的中心重叠（或反之亦然），会怎样？
Alex_ban 1月前 0 只看Ta

引用 3楼

此情况下不允许旋转，所有椭圆必须具有相同的方向。一般情况下，如果一个中心重叠，则需要删除 ID 较大的椭圆。
user2384330 1月前 0 只看Ta

引用 4楼
我认为这就是你想要的。我 data.table 出于习惯使用，但可以适应 dplyr 或作为基础。本质上，这只是使用， sf::st_intersects() 但在我看来，它变成了更可用的东西。
```
library(data.table)

# intersects
i <- sf::st_intersects(coordinates.sf, ellipses.sf)
i <- as.matrix(i)
rownames(i) <- seq_len(nrow(i))
colnames(i) <- seq_len(ncol(i))
i <- i |>
    as.data.frame.table(stringsAsFactors = FALSE) |>
    data.table::as.data.table() |>
    data.table::setnames(c("I1", "I2", "Intersect")) |>
    _[Intersect == TRUE] |>
    _[, c("I1", "I2") := lapply(.SD, as.integer), .SDcols = c("I1", "I2")] |>
    _[order(I1, I2)]

# remove identity
i <- i[I1 != I2]

# ensure that I2 > I1
# if 1 intersects 3 then 3 intersects 1
# this makes sure that only polygon 3 is removed, keeping polygon 1
i <- i[I2 > I1]

# now subset ellipses
ellipses.sf.subset <- ellipses.sf[!seq_len(nrow(ellipses.sf)) %in% i$I2, ]

# plot
ggplot() +
    geom_sf(data = coordinates.sf, color = "black", size = 2) +
    geom_sf(data = ellipses.sf.subset, fill = "blue", alpha = 0.2) +
    theme_minimal() +
    labs(x = "Easting", y = "Northing")
```
用来 mapview::mapview 验证红色圈出的可疑内容。

编辑

经过进一步调查，发现这不太可行。 i[I2 > I1] 删除了一些不应该删除的省略号。我知道这太简单了……如果一个省略号被之前应该删除的省略号删除，则它会失败。代码现在变得更加糟糕（并且可能会被彻底清理），但我相信这会产生实际的期望结果。
```
# ensure that I2 > I1
# if 1 intersects 3 then 3 intersects 1
# this makes sure that only polygon 3 is removed, keeping 1
rm <- c()
for (ix in unique(i$I1)) {
    x <- i[I1 == ix & I2 > I1 & !I1 %in% rm, I2]
    x <- x[!x %in% rm]
    if (length(x) > 0) {
        rm <- c(rm, x)
    }
}

# now subset ellipses
ellipses.sf.subset <- ellipses.sf[!seq_len(nrow(ellipses.sf)) %in% rm, ]
```
这里的红色圆圈表示第一种方法中不应该删除但是却删除了的椭圆。