How to draw ellipsoid with plotly

Question

Are there any way to plot a surface like ellipsoid with plotly 3D?

Currently only surfaces of the form z=f(x,y) are discussed in the docs. There is also Mesh 3D, but I found no examples for it. It seem to be possible to make a triangulation of ellipsoid manually and then use Mesh to get ellipsoid, but it looks a bit difficult for me. Are there any better way to do it?

Answer 1

Okay, it is easier than I thought. There is alphahull option that asks plotly to calculate the corresponding triangulation automatically.

from plotly.offline import iplot, init_notebook_mode
from plotly.graph_objs import Mesh3d
import numpy as np

# some math: generate points on the surface of the ellipsoid

phi = np.linspace(0, 2*pi)
theta = np.linspace(-pi/2, pi/2)
phi, theta=np.meshgrid(phi, theta)

x = np.cos(theta) * np.sin(phi) * 3
y = np.cos(theta) * np.cos(phi) * 2
z = np.sin(theta)

# to use with Jupyter notebook

init_notebook_mode()

iplot([Mesh3d({
                'x': x.flatten(), 
                'y': y.flatten(), 
                'z': z.flatten(), 
                'alphahull': 0
})])

And this is R version:

library(pracma)
theta <- seq(-pi/2, pi/2, by=0.1)
phi <- seq(0, 2*pi, by=0.1)
mgrd <- meshgrid(phi, theta)
phi <- mgrd$X
theta <-  mgrd$Y
x <- cos(theta) * cos(phi) * 3
dim(x) <- NULL
y <- cos(theta) * sin(phi) * 2
dim(y) <- NULL
z <- sin(theta) * scale
dim(z) <- NULL

ell <- cbind(x, y, z)

ell <- setNames(ell, c('x', 'y', 'z'))

library(plotly)
p <- plot_ly(as.data.frame(ell), x=x, y=y, z=z, type='mesh3d', alphahull = 0)

p %>% layout(scene = list(aspectmode = 'data'))

---

EDIT: it is also possible to use type='surface' to produce parametric plots: in this case one have to provide two-dimensional x and y.

library(plotly)
library(pracma)
mgrd <- meshgrid(seq(-pi, pi, length.out = 100), seq(-pi/2, pi/2, length.out = 100))
U <- mgrd$X
V <- mgrd$Y
frame <- list(x=cos(V)*cos(U)*3, y=cos(V)*sin(U)*2, z=sin(V))
plot_ly(frame, type='surface', x=x, y=y, z=z, showlegend=F, showscale=F,
        colorscale=list(list(0, 'blue'), list(1, 'blue')))

Answer 2

Assuming the ellipsoid is given by the equation (X-c)'A(X-c) = r.

library(Rvcg)
sphr <- vcgSphere()
library(rgl)
ell <- scale3d(transform3d(sphr, chol(A)), r, r, r)
vs <- ell$vb[1:3,] + c
idx <- ell$it - 1
library(plotly)
p <- plot_ly(type="mesh3d",
  x = vs[1,], y = vs[2,], z = vs[3,],
  i = idx[1,], j = idx[2,], k = idx[3,],
  opacity = 0.3) 

Answer 3

Why not solve for z in this equation grabbed from the Mathematic item on ellipsoids:

require(plotly)
a=5; b=7; c=9
x=rep(seq(-10,10,by=1), each=21)
y=rep( seq(-10,10,by=1), times=21)
z <- c^2*sqrt(1-x^2/a^2-y^2/b^2)
#Warning message:
#In sqrt(1 - x^2/a^2 - y^2/b^2) : NaNs produced

 plot_ly(z = matrix(z,21,21), type = "surface")