using PlotlyJS
f(r,θ) = (r^2)*cos(θ)*sin(2*θ)/1.5

r = range(0, 1, 50)
θ = range(0, 2*pi, 100)
z= [f(s, t)  for t  in θ, s in r]
x = cos.(θ) * r' #outer product;
y = sin.(θ) * r'
h=-1.4  #project the surface onto the plane z=h
a= 1.15 # the disk radius around which the angles are placed 

pl = Plot(surface(x=x, y=y, z=z, coloraxis="coloraxis"), 
          Layout(width=500, height=500, font_size=11,
                 coloraxis=attr(colorscale=colors.matter, 
                                colorbar_thickness=23,
                                colorbar_len=0.75),
                 scene=attr(zaxis_range=[h-0.1, 0.8],
                            camera_eye=attr(x=1.6, y=1.6, z=1))))
#project the surface onto the plane z=h and draw the initial surface height as a heatmap  on this plane  
addtraces!(pl, surface(x=x, y=y, z= h*ones(size(x)), surfacecolor=z, 
           coloraxis="coloraxis"))
t = range(0, 7pi/4, 8)
txt= [k*45 for k in 0:7]
relayout!(pl, scene_annotations =[
        attr(showarrow=false,
            x=a*cos(s),
            y=a*sin(s),
            z=h,
            text=txt[k],
            font_size=10
            ) for (k, s) in enumerate(t)])
display(pl)