R中曲面下体积的计算方法

Question

我正在尝试计算 R 中 3d 曲面下的体积。

我的数据，dat，看起来像：

          0.003     0.019     0.083      0.25       0.5         1
0     1.0000000 0.8884265 0.8603268 0.7719994 0.7443621 0.6571405
0.111 0.6909722 0.6775000 0.6443750 0.6243750 0.5914730 0.5698242
0.25  0.5847205 0.6022367 0.5572917 0.5432991 0.5170673 0.4835819
0.429 0.5210938 0.5139063 0.4995312 0.4864062 0.4648636 0.4163698
0.667 0.4363103 0.4526562 0.4321859 0.4027519 0.4046011 0.3661616
1     0.3958333 0.4167468 0.3964428 0.3810459 0.3486328 0.3487930

其中 x = rownames(dat)、y = colnames(dat) 和 z = dat。

我看过 here, here, and ，但似乎无法弄清楚如何将这些答案应用到我的用例中。

这是我的数据的可重现版本：

dat = structure(c(1,0.690972222222222,0.584720477386935,0.52109375,0.436310279187817,0.395833333333333,0.888426507537688,0.6775,0.602236675126904,0.51390625,0.45265625,0.416746794871795,0.860326776649746, 0.644375, 0.557291666666667,0.49953125,0.432185913705584,0.396442819148936,0.771999378109453,0.624375,0.543299129353234,0.48640625,0.402751865671642,0.381045854271357,0.744362113402062,0.591472989949749,0.517067307692308,0.464863578680203,0.404601130653266,0.3486328125,0.657140544041451,0.56982421875,0.483581852791878,0.41636981865285,0.366161616161616,0.348792989417989),.Dim = c(6L, 6L), .Dimnames = list(c("0","0.111","0.25","0.429","0.667","1"),c("0.003","0.019","0.083","0.25","0.5","1")))

Answer 1

您可以使用您链接的答案中提供的 getVolume() 函数，前提是您的矩阵采用必需的数据帧格式。

下面是制作该数据框的一些代码：

df <- expand.grid(x = as.numeric(rownames(dat)), y = as.numeric(colnames(dat)))
df$z = as.vector(dat)

然后定义函数并应用：

library(geometry)

getVolume=function(df) {
  #find triangular tesselation of (x,y) grid
  res=delaunayn(as.matrix(df[,-3]),full=TRUE,options="Qz")
  #calulates sum of truncated prism volumes
  sum(mapply(function(triPoints,A) A/3*sum(df[triPoints,"z"]),
             split.data.frame(res$tri,seq_along(res$areas)),
             res$areas))
}

getVolume(df)

[1] 0.4714882

R中曲面下体积的计算方法

Method for calculating volume under a surface in R

r

surface

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