How does one create a cube with Julia and Makie? - julia

Question

The following Julia program uses Makie to create the image shown below, a "cube with holes." However, I would like to eliminate the holes, and also make the cube nearer the shape of an actual cube, with only slightly rounded corners and edges. I've tried changing the exponent to values other than ^2 and also passing the range directly to the volume! function, to no avail. Examples of the types of cubes desired can be found in three-rounded-box images at CodeSandbox.
using Makie, GLMakie
fig = Figure()
range = LinRange(-1, 1, 100) # 100-element LinRange{Float64, Int64}
cube = [ (x.^2 + y.^2 + z.^2) for x = range, y = range, z = range ] # 100×100×100 Array{Float64, 3}
ax = Axis3( fig[1,1], aspect = :data, azimuth = 1.17 * pi, viewmode = :fit, title = "Cube" )
volume!( cube, algorithm = :iso, isorange = 0.05, isovalue = 1.7 )
fig

Answer 1

Like this?
using Makie, GLMakie
fig = Figure()
range = LinRange(-1, 1, 100) # 100-element LinRange{Float64, Int64}
cube = [ (abs.(x).^10 + abs.(y).^10 + abs.(z).^10) for x = range, y = range, z = range ] # 100×100×100 Array{Float64, 3}
ax = Axis3( fig[1,1], aspect = :data, azimuth = 1.17 * pi, viewmode = :fit, title = "Cube" )
volume!( cube, algorithm = :iso, isorange = 0.05, isovalue = 1 )
fig
Or you can use a parametric surface, a supershape:
using Makie, GLMakie
function r(phi; a, b, m, n1, n2, n3)
return 1 / (abs(cos(m*phi/4)/a)^n2 + (abs(sin(m*phi/4)/b)^n3))^(1/n1)
end
phi = (-pi/2):0.01:(pi/2)
theta = (-pi):0.01:(pi)
x = [
r(theta; a=1, b=1, m=4, n1=10, n2=10, n3=10) * cos(theta) *
r(phi; a=1, b=1, m=4, n1=10, n2=10, n3=10) * cos(phi)
for phi in phi, theta in theta
]
y = [
r(theta; a=1, b=1, m=4, n1=10, n2=10, n3=10) * sin(theta) *
r(phi; a=1, b=1, m=4, n1=10, n2=10, n3=10) * cos(phi)
for phi in phi, theta in theta
]
z = [
r(phi; a=1, b=1, m=4, n1=10, n2=10, n3=10) * sin(phi)
for phi in phi, theta in theta
]
fig, _ = surface(x, y, z)
fig
Better to use a function:
function r(phi; a, b, m, n1, n2, n3)
return 1 / (abs(cos(m*phi/4)/a)^n2 + (abs(sin(m*phi/4)/b)^n3))^(1/n1)
end
function supershape(p1, p2)
phi = (-pi/2):0.01:(pi/2)
theta = (-pi):0.01:(pi)
x = [
r(theta; a=p1.a, b=p1.b, m=p1.m, n1=p1.n1, n2=p1.n2, n3=p1.n3) * cos(theta) *
r(phi; a=p2.a, b=p2.b, m=p2.m, n1=p2.n1, n2=p2.n2, n3=p2.n3) * cos(phi)
for phi in phi, theta in theta
]
y = [
r(theta; a=p1.a, b=p1.b, m=p1.m, n1=p1.n1, n2=p1.n2, n3=p1.n3) * sin(theta) *
r(phi; a=p2.a, b=p2.b, m=p2.m, n1=p2.n1, n2=p2.n2, n3=p2.n3) * cos(phi)
for phi in phi, theta in theta
]
z = [
r(phi; a=p2.a, b=p2.b, m=p2.m, n1=p2.n1, n2=p2.n2, n3=p2.n3) * sin(phi)
for phi in phi, theta in theta
]
return (x = x, y = y, z = z)
end
params1 = (a=1, b=1, m=4, n1=10, n2=10, n3=10)
params2 = params1
x, y, z = supershape(params1, params2)
fig, _ = surface(x, y, z)
EDIT
The rendering is not nice with surface. It's better to do a mesh:
function parametricMesh(f, umin, umax, vmin, vmax, nu, nv)
u_ = LinRange(umin, umax, nu)
v_ = LinRange(vmin, vmax, nv)
vertices = Array{Float64}(undef, nu*nv, 3)
triangles = Array{Int64}(undef, 2*(nu-1)*(nv-1), 3)
k = 1
for i in 1:nv
v = v_[i]
for j in 1:nu
vertices[k,:] = f(u_[j], v)
k = k+1
end
end
k = 1
for i in 1:(nv-1)
for j in 1:(nu-1)
a = (i-1) * nu + j
b = (i-1) * nu + j + 1
c = i*nu + j + 1
d = i*nu + j
triangles[2*(k-1)+1,:] = [b, a, d]
triangles[2*k,:] = [c, b, d]
k = k+1
end
end
return (vertices = vertices, triangles = triangles)
end
function r(phi; a, b, m, n1, n2, n3)
return 1 / (abs(cos(m*phi/4)/a)^n2 + (abs(sin(m*phi/4)/b)^n3))^(1/n1)
end
p1 = (a=1, b=1, m=4, n1=10, n2=10, n3=10)
p2 = p1
function f(phi, theta)
x = r(theta; a=p1.a, b=p1.b, m=p1.m, n1=p1.n1, n2=p1.n2, n3=p1.n3) * cos(theta) *
r(phi; a=p2.a, b=p2.b, m=p2.m, n1=p2.n1, n2=p2.n2, n3=p2.n3) * cos(phi)
y = r(theta; a=p1.a, b=p1.b, m=p1.m, n1=p1.n1, n2=p1.n2, n3=p1.n3) * sin(theta) *
r(phi; a=p2.a, b=p2.b, m=p2.m, n1=p2.n1, n2=p2.n2, n3=p2.n3) * cos(phi)
z = r(phi; a=p2.a, b=p2.b, m=p2.m, n1=p2.n1, n2=p2.n2, n3=p2.n3) * sin(phi)
return [x, y, z]
end
vertices, triangles = parametricMesh(f, -pi/2, pi/2, -pi, pi, 50, 50)
mesh(vertices, triangles, color = "yellow")