I want to plot a 3-dimensional cylinder.
the parametric equations will be like this:
x= r*cos(u)
y=r*sin(u)
z=v
with $u \in [0, 2 \pi] $ and $v \in [0, h]$
I am able to create a sphere with GLMakie with this code:
using GLMakie
n = 20
θ = [0;(0.5:n-0.5)/n;1]
φ = [(0:2n-2)*2/(2n-1);2]
x = [cospi(φ)*sinpi(θ) for θ in θ, φ in φ]
y = [sinpi(φ)*sinpi(θ) for θ in θ, φ in φ]
z = [cospi(θ) for θ in θ, φ in φ]
surface(x, y, z)
but when I try to make a cylinder it fails:
using GLMakie
GLMakie.activate!()
set_theme!(backgroundcolor = :white)
# A cylinder of radius r, and height h, having z-axis as symmetry axis
# it is a stack of circles of radius r
r = 5
h = 3
n = 50
θ = LinRange(0, 2pi, 100)
#θ = [0;(0.5:n-0.5)/n;2π]
v = [0;(1:n)/n;h]
x = [r*cos(θ) for θ in θ]
y = [r*sin(θ) for θ in θ]
z = [v for v in v]
surface(x, y, z)
can anyone help me?
Thanks
Edited: (still need help for perfecting the plot)
I am now able to plot a cylinder, but it is still hollow on the top and at the bottom, here is the code:
using Plots
plotlyjs()
# If x, y, z are vectors then it won't generate a surface
# for a parameterized surface x,y,z should be matrices:
# Check for: typeof(X), typeof(Y), typeof(Z)
r = 5
h = 3
m, n =200, 150
u = range(0, 2pi, length=n)
v = range(0, h, length=m)
us = ones(m)*u'
vs = v*ones(n)'
#Surface parameterization
X = r*cos.(us)
Y = r*sin.(us)
Z = vs
Plots.surface(X, Y, Z, size=(600,600), cbar=:none, legend=false)
All of the surface you specify has radius of 5, so the interior of the ends is not filled in. You could additionally draw a disc at each end, though.
Related
I want to plot 3D HeatMap for 3D function f(x,y,z).
For 2D function f(x,y), I know the below code works.
using Plots
x = 1:L # coordinate range
y = 1:L
F = Float64[f(ix,iy) for ix in x, iy in y]' #convert f(x,y) to an array
plot(F,st=:heatmap,color= cgrad(:blues))
plot!(xlabel="x",ylabel="y",aspect_ratio=:equal)
plot!(xlims=(1,L),ylims=(1,L))
For 3D function, where should I change?
using Plots
x = 1:L # coordinate range
y = 1:L
z = 1:L
F = Float64[f(ix,iy,iz) for ix in x, iy in y,iz in z] #convert f(x,y,z) to an array
plot(F,st=:heatmap,color = cgrad(:blues),alpha=0.1)
plot!(xlabel="x",ylabel="y",zlabel="z",aspect_ratio=:equal)
plot!(xlims=(1,L),ylims=(1,L),zlims=(1,L))
This code passes, but something is wrong.
color = cgrad(:blues),alpha=0.1,xlabel="x",ylabel="y" are not reflected.
In addition, the figure does not seem to be f(x,y,z). For example, f(x,y,z) = x^2 + y^2 +z^2 gives a spherical gradation, but the result is not.
The above approach is slow for more data points. However, I think you don't want heatmaps as the heatmaps in the previous link are just projections from 2D into 3D planes.
I think you need something like this.
See code here.
https://lazarusa.github.io/BeautifulMakie/surfWireLines/volume/
See image
And for convenience also here:
using GLMakie
let
x = 1:10
y = 1:10
z = 1:10
f(x,y,z) = x^2 + y^2 + z^2
vol = [f(ix,iy,iz) for ix in x, iy in y, iz in z]
fig, ax, _ = volume(x, y, z, vol, colormap = :plasma,colorrange = (minimum(vol), maximum(vol)),
figure = (; resolution = (800,800)),
axis=(; type=Axis3, perspectiveness = 0.5, azimuth = 7.19, elevation = 0.57,
aspect = (1,1,1)))
fig
end
3D HeatMap by Makie.jl
I don't know how to plot 3D HeatMap by Plots.jl yet, but I found the another way by Makie.jl : https://lazarusa.github.io/BeautifulMakie/surfWireLines/RGBcube/ .
With the help of this sample code, I got the following code.
using GLMakie, GeometryBasics, Colors
positions = vec([(i, j, k) for i=1:L,j=1:L,k=1:L]) #3D coordinate
F = zeros(Float64,length(positions)
for i = 1:length(positions) #convert f(x,y,z) to an array
x = positions[i][1]
y = positions[i][2]
z = positions[i][3]
F[i] = f(x,y,z)
end
fig, ax = mesh(HyperRectangle(Vec3f0(positions[1]...),Vec3f0(0.8)), color = RGBA(0,0,F[1],0.5), transparency = false) #HyperRectangle(::position,::length),color=(::red,::green,::blue,::alpha)
wireframe!(ax,HyperRectangle(Vec3f0(positions[1]...), Vec3f0(0.8)), linewidth = 0.1, overdraw = false)
for i in 2:length(positions)
mesh!(ax, HyperRectangle(Vec3f0(positions[i]...), Vec3f0(0.8)), color = RGBA(0,0,F[i],0.5))
wireframe!(ax, HyperRectangle(Vec3f0(positions[i]...), Vec3f0(0.8)), linewidth = 0.1, overdraw = false)
end
fig
Is it possible to reproduce this graph using the Julia Plots Package?
Plotting using gnuplot
x = y = -15:0.4:15
f1 = (x,y) -> #. sin(sqrt(x*x+y*y))/sqrt(x*x+y*y)
surf(x, y, f1, w = :p, marker = "dot", Axes(hidden3d = :on))
Not exactly the same, but you can plot a surface with surface:
using Plots
x = y = -15:0.4:15
f(x,y) = sin(sqrt(x^2+y^2))/sqrt(x^2+y^2)
surface(x, y, f)
which will give
or a wireframe
wireframe(x, y, f)
will give
But if you really want a 3D scatter, then you need to create the mesh by hand and rearrange the data into vectors I think, like
X = [x for x in x for y in y]
Y = [y for x in x for y in y]
scatter3d(X, Y, f.(X,Y))
I have been trying to generate random values so that I can construct a circle.
The values of x and y are expected to satisfy the following equation
x^2 + y^2 = 1
Here is the code that I used.
par(type = "s")
x <- runif(1000, min = -1, max = 1)
y <- sqrt(1 - x^2)
z <- NULL
z$x <- x
z$y <- y
z <- as.data.frame(z)
plot.new()
plot(z$x, z$y, type = "p")
plot.window(xlim = c(-10,10), ylim = c(-10,10), asp = 1)
But the graph I get is not quite what I expected it to be.
The graph resembles an upper half of an ellipse rather than a semicircle
Why are there no values for y where y < 0
Please find the plot here.
I am also interested in finding out, how to generate random values for x, y, z, a; where x^2 + y^2 + z^2 + a^2 = 10
Maybe you missed #thelatemail's comment:
png()
plot(z$x, z$y, type = "p", asp=1)
dev.off()
The reason passing asp=1 to plot.window would fail(if it were called first, and this is what you might have tried) is that plot itself calls plot.window again, and in the process reacquires the default values. You can see that in the code of plot.default:
> plot.default
function (x, y = NULL, type = "p", xlim = NULL, ylim = NULL,
log = "", main = NULL, sub = NULL, xlab = NULL, ylab = NULL,
ann = par("ann"), axes = TRUE, frame.plot = axes, panel.first = NULL,
panel.last = NULL, asp = NA, ...)
{
localAxis <- function(..., col, bg, pch, cex, lty, lwd) Axis(...)
localBox <- function(..., col, bg, pch, cex, lty, lwd) box(...)
localWindow <- function(..., col, bg, pch, cex, lty, lwd) plot.window(...)
#.... omitted the rest of the R code.
(Calling plot.window after that plot call should not be expected to have any favorable effect.)
The problem is within this part of your code:
x <- runif(1000, min = -1, max = 1)
y <- sqrt(1 - x^2)enter code here
This problem arises from interpreting two distinct mathematical entities as the same (functions and equations are two different things). A function f takes an input x, and returns a single output f(x). Equations don't have this limitation, so if you are encoding this equation as a function, you will lose half the points in the circle, you will generate all the points in the upper semicircle.
Since the circle equation has two y outputs for any x value you can just generate two pairs of coordinates for each point generated by your uniform distribution like this:
x1 = runif(1000, min = -1, max = 1)
x2 = x1
y1 = sqrt(1 - x1^2)
y2 = (-1)*y1
x = c(x1,x2)
y = c(y1,y2)
plot(x,y, asp=1)
As John Coleman recommended in his comment, i'd prefer using parametric/polar coordinates instead. Generate angles in radians between 0 and 2pi and then calculate the appropriate x and y positions using the generated angle and the radius you want.
radius = 1
theta = runif(1000, min = 0, max = 2*pi)
x = radius * cos(theta)
y = radius * sin(theta)
plot(x,y, asp=1)
For the last part of your question, for each value of a variable, you'd have to work out all the possible tuples that solve the equation, and if z and a are also variables, it may not be possible to represent it solely on a 2-dimensional graph.
I am looking to use the R plotly library to create a 3d surface plot of x,y,z coordinate data, similar to what is shown at the link below:
https://plot.ly/r/3d-surface-plots/
It appears that the plot_ly function requires the z coordinates to be in a matrix of dimensions x * y, as seen in datasets::volcano, used in the linked example. I'd appreciate some guidance on how to construct this matrix. Here is my sample x,y coordinate data:
## x coordinates
xSeq = seq(0, 1, .01)
## y coordinates
ySeq = seq(0, 1, .01)
## list with x, y coordinates
exmplList = list(x = xSeq, y = ySeq)
The z coordinates would be calculated via a formula from the x,y pairs (example formula used here is x + y). I've played around with something like:
exmplList = within(exmplList, z <- matrix(x + y, nrow = length(xSeq), ncol = length(ySeq)))
But that doesn't accomplish the pair combinations that I am trying to achieve.
Plotly surface needs a matrix so you could simply use this bit directly:
z = matrix(xSeq + ySeq, nrow = length(xSeq), ncol = length(ySeq))
Instead of doing a list. So, by running the following code:
## x coordinates
xSeq = seq(0, 1, 0.01)
## y coordinates
ySeq = seq(0, 1, 0.01)
## list with x, y coordinates
z = matrix(xSeq + ySeq, nrow = length(xSeq), ncol = length(ySeq))
fig = plot_ly(z = ~z) %>% add_surface()
fig
One obtains the following plot:
You might need to click and rotate a bit to see the plane. Hope it helps, cheers.
Is it possible to plot a plane, given the equation
x^2 + y^2 - 1.6z^2 + 1 = 0
with R?
It should look like this:
(Image source: https://commons.wikimedia.org/wiki/File:Zweischaliges_Hyperboloid.png)
What I've tried
library(rgl)
x = -20:20
xs = rep(x, 40)
y = -20:20
ys = rep(y, each=40)
z = (-(-1-x^2-y^2)/1.6)^0.5
plot3d(x=xs, y=ys, z=z)
This does plot the upper part, but I would like to see the lower part, too. Also, the plot doesn't look nice.
Answering the question I posed in my comment and providing what I think is a complete answer using rgl
library(rgl)
# define +ve function and plot it
zfun <- function(x,y) (-(-1-x^2-y^2)/1.6)^0.5
persp3d(zfun, c(-20,20), c(-20,20), n = 101)
# define x-y grid for second surface
xyvec <- seq(-20, 20, length.out = 101)
# calculate surface as -ve function and plot it
zmat <- -outer(xyvec, xyvec, zfun)
surface3d(xyvec, xyvec, zmat)