Make 3d Python plot as beautiful as Matlab

Question

Note: This is not a conversion question. It is meant to see if Python has the capability to produce 3D plot like Matlab.

I have created a Matlab plot as follows:

I tried to plot it using Python but I could not get it as good as Matlab. Is there any packages that can plot the above as good as the original one? If it is please convert my code to a Python version. Here is my Matlab code.

set(groot,'defaultAxesTickLabelInterpreter','latex');  
set(groot,'defaulttextinterpreter','latex');
set(groot,'defaultLegendInterpreter','latex');
x0=0;
y0=0;
width=3000;
height=2000;
set(gcf,'position',[x0,y0,width,height])
[X,Y] = meshgrid(-1:.01:1);
a = 3;
b = 2;
Z = a*X.^2 + b*Y.^2;
subplot(1,3,1)
s = surf(X,Y,Z,'FaceColor','r', 'FaceAlpha',0.5, 'EdgeColor','none');
s.EdgeColor = 'none';
xlabel('$x_1$','Interpreter','latex','FontSize', 15)
ylabel('$x_2$','Interpreter','latex','FontSize', 15)
zlabel('$f(\mathbf{x};\mathbf{\theta})$','Interpreter','latex','FontSize', 15)
legend({'$f([x_1, x_2]^\top; [\theta_1=3,\theta_2=2]^\top)=3x_1^2+2x_2^2$'},'interpreter','latex','FontSize', 10)
subplot(1,3,2)
Z2 = a*X.^2 ;
s2 = surf(X,Y,Z2,'FaceColor','b', 'FaceAlpha',0.5, 'EdgeColor','none');
s2.EdgeColor = 'none';
xlabel('$x_1$','Interpreter','latex','FontSize', 15)
ylabel('$x_2$','Interpreter','latex','FontSize', 15)
zlabel('$f(\mathbf{x};\mathbf{\theta})$','Interpreter','latex','FontSize', 15)
legend({'$f([x_1, x_2]^\top; [\theta_1=3,\theta_2=0]^\top)=3x_1^2$'},'interpreter','latex','FontSize', 10)
subplot(1,3,3)
s3 = surf(X,Y,Z,'FaceColor','r', 'FaceAlpha',0.5, 'EdgeColor','none');
s3.EdgeColor = 'none';
hold
s4 = surf(X,Y,Z2,'FaceColor','b', 'FaceAlpha',0.5, 'EdgeColor','none');
s4.EdgeColor = 'none';
xlabel('$x_1$','Interpreter','latex','FontSize', 15)
ylabel('$x_2$','Interpreter','latex','FontSize', 15)
zlabel('$f(\mathbf{x};\mathbf{\theta})$','Interpreter','latex','FontSize', 15)
legend({'$f(\mathbf{x};\mathbf{\theta})=3x_1^2+2x_2^2$', '$f(\mathbf{x};\mathbf{\theta})=3x_1^2$'},'interpreter','latex','FontSize', 10)

Answer 1

Yes.

numpy + plotly is an effective Matlab replacement - you may recognize some of the code :). As a benefit, the plots render as html, which means they are highly portable, save as a single file, and can be embedded in a webpage. There may be small details that are different (I don't know the current status of latex axis labels), but, provided you have python, numpy and plotly installed, the following is a good replacement of your first plot:

import plotly.graph_objects as go
import numpy as np

x = np.arange(-1,1,.01)
y = np.arange(-1,1,.01)
X,Y = np.meshgrid(x,y)
a = 3
b = 2
Z = a*X**2 + b*Y**2

fig = go.Figure(
    data=[go.Surface(z=Z, x=x, y=y, colorscale="Reds", opacity=0.5)])
fig.update_layout(
    title='My title', 
    autosize=False,
    width=500, 
    height=500,
    margin=dict(l=65, r=50, b=65, t=90), 
    scene_aspectmode='cube'
)
fig.show()

Notice that the go-to plotting package in python is Matplotlib. IMO, it inherited all the worst parts of Matlab's plotting and none of the good (performant rendering). Plotly superior from a performance (esp 3D rendering), interactivity, and API standpoint.