Surfaceplot with non-complete grid - r

Question

I want a surface plot, but my grid is incomplete. I searched, but without success. How can I make the following work:
x = c(10L, 20L, 30L, 40L, 50L, 60L, 70L, 80L, 90L, 100L, 30L, 40L,
50L, 60L, 70L, 80L, 90L, 100L, 50L, 60L, 70L, 80L, 90L, 100L,
70L, 80L, 90L, 100L, 90L, 100L)
y = c(10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 20L, 20L,
20L, 20L, 20L, 20L, 20L, 20L, 30L, 30L, 30L, 30L, 30L, 30L,
40L, 40L, 40L, 40L, 50L, 50L)
z = c(6.093955007, 44.329214443, 149.103755156, 351.517349974,
726.51174655, 1191.039562104, 1980.245204702, 2783.308022984,
6974.563519067, 5149.396230019, 142.236259009, 321.170609648,
684.959503897, 1121.475597135, 1878.334840961, 2683.116309688,
4159.60732066, 5294.774284119, 687.430547359, 1119.765405426,
1876.57337196, 2685.951176024, 3945.696884503, 5152.986796572,
1870.78724464, 2677.744176903, 3951.928931107, 5160.295960254,
3957.503273558, 5147.237754092)
# OK but not a surface plot
scatterplot3d::scatterplot3d(x, y, z,
color = "blue", pch = 19,
type = "h",
main = "",
xlab = "x",
ylab = "y",
zlab = "z",
angle = 35,
grid = FALSE)
# Not working:
M <- plot3D::mesh(x, y, z)
R <- with (M, sqrt(x^2 + y^2 +z^2))
p <- sin(2*R)/(R+1e-3)
plot3D::slice3D(x, y, z, colvar = p,
xs = 0, ys = c(-4, 0, 4), zs = NULL)
plot3D::isosurf3D(x, y, z, colvar = p, level = 0, col = "red")

Answer 1

For this kind of problem I can recommend the deldir-package which does "Delaunay triangulation and Dirichlet tessellation". From this you calculate the spacial triangles that give the surface plot.
The rgl-package gives the possibility to add the triangles to your scatterplot. And even better - the resulting plot is animated, so you can rotate and zoom for better overview.
x = c(10L, 20L, 30L, 40L, 50L, 60L, 70L, 80L, 90L, 100L, 30L, 40L,
50L, 60L, 70L, 80L, 90L, 100L, 50L, 60L, 70L, 80L, 90L, 100L,
70L, 80L, 90L, 100L, 90L, 100L)
y = c(10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 20L, 20L,
20L, 20L, 20L, 20L, 20L, 20L, 30L, 30L, 30L, 30L, 30L, 30L,
40L, 40L, 40L, 40L, 50L, 50L)
z = c(6.093955007, 44.329214443, 149.103755156, 351.517349974,
726.51174655, 1191.039562104, 1980.245204702, 2783.308022984,
6974.563519067, 5149.396230019, 142.236259009, 321.170609648,
684.959503897, 1121.475597135, 1878.334840961, 2683.116309688,
4159.60732066, 5294.774284119, 687.430547359, 1119.765405426,
1876.57337196, 2685.951176024, 3945.696884503, 5152.986796572,
1870.78724464, 2677.744176903, 3951.928931107, 5160.295960254,
3957.503273558, 5147.237754092)
# create spacial triangles
del <- deldir::deldir(x, y, z = z)
triangs <- do.call(rbind, triang.list(del))
# create plot
rgl::plot3d(x, y, z, size = 5, xlab = "my_x", ylab = "my_y", zlab = "my_z", col = "red")
rgl::triangles3d(triangs[, c("x", "y", "z")], col = "gray")
I hope this helps.

Answer 2

This is more of a hint than a complete answer:
library(plotly)
plot_ly(z = ~volcano) %>% add_surface()
is a nice way to do this kind of plots. So for your example:
x <- c(10L, 20L, 30L, 40L, 50L, 60L, 70L, 80L, 90L, 100L, 30L, 40L,
50L, 60L, 70L, 80L, 90L, 100L, 50L, 60L, 70L, 80L, 90L, 100L,
70L, 80L, 90L, 100L, 90L, 100L)
y <- c(10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 20L, 20L,
20L, 20L, 20L, 20L, 20L, 20L, 30L, 30L, 30L, 30L, 30L, 30L,
40L, 40L, 40L, 40L, 50L, 50L)
z <- c(6.093955007, 44.329214443, 149.103755156, 351.517349974,
726.51174655, 1191.039562104, 1980.245204702, 2783.308022984,
6974.563519067, 5149.396230019, 142.236259009, 321.170609648,
684.959503897, 1121.475597135, 1878.334840961, 2683.116309688,
4159.60732066, 5294.774284119, 687.430547359, 1119.765405426,
1876.57337196, 2685.951176024, 3945.696884503, 5152.986796572,
1870.78724464, 2677.744176903, 3951.928931107, 5160.295960254,
3957.503273558, 5147.237754092)
library(plotly)
m <- matrix(c(x,y,z), nrow = 3)
plot_ly(z = ~m) %>% add_surface()
produces
..this is a first step, but there's still some issues with the scaling of the x-axis. I think key to the solution is to set up the whole (sparse) matrix and then plot it.
x <- c(10L, 20L, 30L, 40L, 50L, 60L, 70L, 80L, 90L, 100L, 30L, 40L,
50L, 60L, 70L, 80L, 90L, 100L, 50L, 60L, 70L, 80L, 90L, 100L,
70L, 80L, 90L, 100L, 90L, 100L)
y <- c(10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 20L, 20L,
20L, 20L, 20L, 20L, 20L, 20L, 30L, 30L, 30L, 30L, 30L, 30L,
40L, 40L, 40L, 40L, 50L, 50L)
z <- c(6.093955007, 44.329214443, 149.103755156, 351.517349974,
726.51174655, 1191.039562104, 1980.245204702, 2783.308022984,
6974.563519067, 5149.396230019, 142.236259009, 321.170609648,
684.959503897, 1121.475597135, 1878.334840961, 2683.116309688,
4159.60732066, 5294.774284119, 687.430547359, 1119.765405426,
1876.57337196, 2685.951176024, 3945.696884503, 5152.986796572,
1870.78724464, 2677.744176903, 3951.928931107, 5160.295960254,
3957.503273558, 5147.237754092)
xx <- 1:100L
yy <- 1:100L
zz <- matrix(0, nrow = 100, ncol = 100)
for (i in 1:length(x)){
zz[x[i], y[i]] <- z[i]
}
library(plotly)
plot_ly(z = ~zz) %>% add_surface()
produces
which is basically what your data supposes..
Hope I can figure that out as well.
And hope this helps.