r - 将多个不等式绘制为平面

Question

我想绘制多个平面，每个平面都是一个不等式。在绘制完所有平面后，我想将它们组合起来，并为这些线内的区域着色。绘制大量 3D 线条并为内部区域着色的图像 - 这就是我想要做的。

我的数据如下所示:

df <- structure(list(z = c(0, 0.06518, 0.08429, -0.01659, 0, 0.06808, 
0.12383, -1, -0.01662, 0.28782, 0, -0.09539, 0.04255, 0.09539, 
-0.13361, -0.28782, -0.14468, -0.19239, 0.10642), x = c(1, 0.02197, 
0.03503, -0.02494, 0, 0.04138, 0.17992, 0, -0.02482, 0.1122, 
0, 0.01511, 0.0011, -0.01511, -0.06699, -0.1122, -0.06876, 0.12078, 
0.10201), y = c(0, 0.08735, 0.09927, 0.03876, -1, 0.22114, -0.00152, 
0, 0.03811, -0.07335, 0, -0.03025, 0.07681, 0.03025, -0.23922, 
0.07335, -0.25362, -0.09879, 0.05804), value = c(5801L, 135L, 
162L, 109L, 4250L, 655L, 983L, 4500L, 108L, 1594L, 4400L, 540L, 
147L, 323L, 899L, 1023L, 938L, 1627L, 327L)), .Names = c("z", 
"x", "y", "value"), class = "data.frame", row.names = c(NA, -19L
))

每一行代表一个如下形式的方程:z + x + y < value 。 x是水平值，y是垂直的且 z是深度。 z 可解为:-x - y + value > z。

坐标系的限制是:

x <- z <- seq(-6000, 6000, by = 1)
y <- seq(-4000, 4000, by = 1)

所以，我想从每一行画一个平面。然后我想组合所有这些平面，并填写行内的值。结果应该看起来像一个多面不等的骰子。或者是一颗切工丑陋的钻石。

我一直在玩rgl和persp功能，但我不知道从哪里开始。我愿意接受其他软件推荐。

引用 persp3d 中的示例之一:

x <- seq(-6000, 6000, by = 1)
z <- x 
y <- seq(-4000, 4000, by = 1)

f <- function(x, y) <- { r <- -x - y + value > z } # stuck here, can you handle an inequality here?
z <- outer(x, y, f)
open3d()
bg3d("white")
material3d(col = "black")
persp3d(x, y, z, col = "lightblue",
        xlab = "X", ylab = "Y", zlab = "z")

我认识到这是相当大的限制。如果有助于减少它们，请随意，或者增加 sequence(..., by = ) 。

Answer 1

通过利用一些矩阵乘法，您可以节省大量计算时间。

library(dplyr)
library(geometry)
library(rgl)

# define point grid
r <- 50   # resolution
grid <- expand.grid(
  x = seq(-6000, 6000, by = r),
  y = seq(-4000, 4000, by = r),
  z = seq(-6000, 6000, by = r))  # data.table::CJ(x,y,z) if speed is a factor

# get points satisfying every inequality
toPlot <- df %>% 
  select(x, y, z) %>% 
  data.matrix %>% 
  `%*%`(t(grid)) %>%
  `<`(df$value) %>% 
  apply(2, all)

## Alternative way to get points (saves time avoiding apply)
toPlot2 <-
  colSums(data.matrix(df[, c('x', 'y', 'z')]) %*% t(grid) < df$value) == nrow(df)

由于您不需要内部，因此将点减少到凸包，然后仅绘制曲面。

# get convex hull, print volume
gridPoints <- grid[toPlot, ]
hull <- convhulln(gridPoints, "FA")
hull$vol
#> 285767854167

# plot (option 1: colors as in picture)
apply(hull$hull, 1, function(i) gridPoints[i, ]) %>% 
  lapply(rgl.triangles, alpha = .8, color = gray.colors(5))

## plot (option 2: extract triangles first - much faster avoiding apply)
triangles <- gridPoints[c(t(hull$hull)), ]
rgl.triangles(triangles, alpha=0.8, color=gray.colors(3))

<小时/>

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