使用 n 维生成 3D 笛卡尔曲面坐标

Question

我已经实现了一些代码来使用指定尺寸生成 3D 笛卡尔坐标表面。然而，这是相当缓慢且非常低效的实现方式。有人可以帮助我提供一种需要更少迭代次数的更好方法吗？

library(rgl)
density <- 1

#test data 5 x 10 x 15 box
a <- seq(from = 1, to = 5, by = density)
b <- seq(from = 1, to = 10, by = density)
c <- seq(from = 1, to = 15, by = density)

#length of each dimension
aL <- length(a)
bL <- length(b)
cL <- length(c)

#data.frame to store 3D box
test = data.frame()

#calculate the indices for the nested for loop
inner <- bL * cL
outer <- aL * bL * cL
tracker <- 1:inner
tracker <- c(tracker, (outer - (inner) + 1):outer)
for(x in 1:(aL-2)) {
    for(i in 1:bL) {
        if(i == 1 || i == bL) {
            tracker <- c(tracker, (inner+1):(inner+cL))
        } else {
            tracker <- c(tracker, inner + 1)
            tracker <- c(tracker, inner + cL)
        }
        inner <- inner + cL
    }
}

#loops over all possible combinations and uses only the indices above
iter <- 1
for(x in a) {
    for(y in b) {
        for(z in c) {
            if(any(iter == tracker)) {
                test <- rbind(test, data.frame(x = x, y = y, z = z))
            }
            iter <- iter + 1
        }
    }
}

points3d(test)

Answer 1

虽然有机会通过 pre-allocating 向量和数据框来加快速度，但您是否考虑过分别生成表面的六个面，然后将它们粘在一起？

expand.grid 函数让这一切变得简单：

faces_xy <- expand.grid(x = a, y = b, z = c(min(c), max(c)))
faces_xz <- expand.grid(x = a, y = c(min(b), max(b)), z = c)
faces_yz <- expand.grid(x = c(min(a), max(a)), y = b, z = c)
surface <- unique(rbind(faces_xy, faces_xz, faces_yz))

每个 faces_ 变量都包含指定平面上的两个面。调用unique是为了消除面共享边上的重复点。

我没有进行任何基准测试，也没有费心去分析每种方法的复杂性，但我希望这会快得多。

使用 n 维生成 3D 笛卡尔曲面坐标

Generate 3D Cartesian Surface Coordinates using n dimensions

r

cartesian-coordinates