r - Sampling values from an isosurface using misc3d

Question

Background

I want to sample values from an isosurface, calculated with the marching squares algorithm from the misc3d package in R. In essence, the problem is as follows: I have a simulation that takes three parameters and outputs a single value. I want to reverse the process: I would like to input the outcome and obtain possible combinations of parameters.

Approach

I have used the marching squares algorithm in the computeCountour3d function from the misc3d package. As I understood it correctly, it outputs a data frame in which every three rows represent the vertices of a triangular plane. In this plane, all the parameter combinations should lead to the same output (=level), right?

library(tidyverse)
library(misc3d)

# Create a dataset (the mean() is used for simplicity)
data <- expand_grid(x = seq(1, 51, 10), y = seq(0, -2, -0.5), z = seq(0, -3, -1)) %>%
  rowwise() %>% mutate(value = mean(c(x, y, z)))

data

#>        x     y     z  value
#>  1     1   0       0  0.333
#>  2     1   0      -1  0    
#>  3     1   0      -2 -0.333
#>  4     1   0      -3 -0.667
#>  5     1  -0.5     0  0.167
#>  6     1  -0.5    -1 -0.167

# Turn dataframe into an 3d array
value <- data$value
data <- data[order( data$x, data$y, data$z),]
dimensions <- c(length(unique(data$x)), length(unique(data$y)), length(unique(data$z)))

v <- array(data = value, dim=dimensions)

# Create subarrays that map indices back 
# to the original data
vX <- array( data=data$x, dim=dimensions )
vY <- array( data=data$y, dim=dimensions )
vZ <- array( data=data$z, dim=dimensions )

# Calculate isosurface, with level = 3
isosurface <-computeContour3d(vol = v,
                              maxvol = max(v), 
                              level = 3) %>%
  as.data.frame() %>%
  rowwise() %>% 
  
  # Map the indices of the output the original x,y,z values
  mutate(x = vX[V1, V2, V3], 
         y = vY[V1, V2, V3], 
         z = vZ[V1, V2, V3]) %>%
  ungroup()
 
isosurface
#>       V1    V2    V3     x     y     z
#>  1   3    1.2   2       11  -0.5    -3
#>  2   3    1     1.95     1  -2      -1
#>  3   2.8  1     2       11  -1       0
#> # … with 180 more rows

Question

How do you translate this dataframe of vertices to a set of parameter values that lead to a similar output? Are there functions to do so?

Answer 1

等待大神答复