我正在使用R编程语言。
下面是一个3D钟形曲线（高斯分布）：

library(plotly)
library(mvtnorm)  

mu <- c(0, 0)  
Sigma <- matrix(c(1, 0, 0, 1), nrow=2)  

x <- seq(-5, 5, length.out = 50)
y <- seq(-5, 5, length.out = 50)
grid <- expand.grid(x=x, y=y)

grid$z <- apply(grid, 1, function(x) dmvnorm(x, mean=mu, sigma=Sigma))

fig <- plot_ly(data = grid, x = ~x, y = ~y, z = ~z, type = 'scatter3d', mode = 'lines',
               line = list(color = '#0066FF', width = 2)) %>%
    layout(title = "3D Normal Distribution Wireframe Plot",
           scene = list(xaxis = list(title = "X",
                                     gridcolor = 'rgb(255, 255, 255)',
                                     zerolinecolor = 'rgb(255, 255, 255)',
                                     showbackground = TRUE,
                                     backgroundcolor = 'rgb(230, 230,230)'),
                        yaxis = list(title = "Y",
                                     gridcolor = 'rgb(255, 255, 255)',
                                     zerolinecolor = 'rgb(255, 255, 255)',
                                     showbackground = TRUE,
                                     backgroundcolor = 'rgb(230, 230,230)'),
                        zaxis = list(title = "Z",
                                     gridcolor = 'rgb(255, 255, 255)',
                                     zerolinecolor = 'rgb(255, 255, 255)',
                                     showbackground = TRUE,
                                     backgroundcolor = 'rgb(230, 230,230)')),
           showlegend = FALSE)

fig

字符串
x1c 0d1x的数据

**我的问题：**我想用x，y范围（-1到1）之间的许多红点填充这个图的内部。

我试着用下面的代码来做这件事：生成随机点，计算每个随机点的z值，然后把这些点放在图上：

points <- data.frame(x = runif(100, -1, 1), y = runif(100, -1, 1))
points$z <- apply(points, 1, function(x) dmvnorm(x, mean=mu, sigma=Sigma))

fig <- fig %>%
    add_trace(data = points, x = ~x, y = ~y, z = ~z, type = 'scatter3d', mode = 'markers',
              marker = list(color = 'red', size = 2))

fig <- fig %>%
    layout(title = "3D Normal Distribution Wireframe Plot",
           scene = list(xaxis = list(title = "X",
                                     gridcolor = 'rgb(255, 255, 255)',
                                     zerolinecolor = 'rgb(255, 255, 255)',
                                     showbackground = TRUE,
                                     backgroundcolor = 'rgb(230, 230,230)'),
                        yaxis = list(title = "Y",
                                     gridcolor = 'rgb(255, 255, 255)',
                                     zerolinecolor = 'rgb(255, 255, 255)',
                                     showbackground = TRUE,
                                     backgroundcolor = 'rgb(230, 230,230)'),
                        zaxis = list(title = "Z",
                                     gridcolor = 'rgb(255, 255, 255)',
                                     zerolinecolor = 'rgb(255, 255, 255)',
                                     showbackground = TRUE,
                                     backgroundcolor = 'rgb(230, 230,230)')),
           showlegend = FALSE)

fig

型

的

但是点出现在图的表面上-我希望点出现在图的内部。有什么方法可以解决这个问题吗？

谢谢你，谢谢