将曲面叠加到 3d 点

Question

假设我有一个 3D 点云表示为：

arv = data.frame(axis_x = rnorm(n=300, mean=-0.20, sd=1.01),
             axis_y = rnorm(n=300, mean=-0.45, sd=0.97),
             elevation = rnorm(n=300, mean=-813.2, sd=13.89))

我还有一个抛物面模型：

model = lm(formula = elevation ~ (axis_x + axis_y)^2 + I(axis_x^2) + I(axis_y^2), data = arv)

有没有办法在 3D 图中将两者（点和模型）一起绘制？

Answer 1

这可以通过persp() 和trans3d 完成。为了提高清晰度，它有助于用线将观察值连接到函数的 3d 表面：

# data
arv = data.frame(axis_x = rnorm(n=300, mean=-0.20, sd=1.01),
             axis_y = rnorm(n=300, mean=-0.45, sd=0.97),
             elevation = rnorm(n=300, mean=-813.2, sd=13.89))
# fit             
model = lm(formula = elevation ~ (axis_x + axis_y)^2 + I(axis_x^2) + I(axis_y^2), data = arv)

# grid for plotting function
x <- seq(min(arv$axis_x), max(arv$axis_x), length.out = 20)
y <- seq(min(arv$axis_y), max(arv$axis_y), length.out = 20)

# function for predicted surface from model
f <- function(x, y) { cbind(1,x,y,x^2,y^2,x*y) %*% coef(model) }

# predicted values in form that persp() can use
z <- outer(x, y, f)

# 3d plot of surface with persp()
ele_3d <- persp(x=x,y=y,z=z, theta=40, phi=15, zlim=c(min(arv$elevation), max(arv$elevation)) )

# transform observed values into 2d space
elevation_points <- trans3d(arv$axis_x, arv$axis_y, arv$elevation, pmat=ele_3d)

# plot observed values
points(elevation_points)

# add dotted lines from surface to observed values
fit_vals <- trans3d(arv$axis_x, arv$axis_y, fitted(model), pmat = ele_3d)
segments(fit_vals$x, fit_vals$y, elevation_points$x, elevation_points$y, lty = 3)

另一种选择是在格中使用带有wireframe() 的面板函数。见this post。