VPDEMO: Surface plots of function f(x,y) on the rectangular domain in Jupyter Vpython

[Michal Kaukič]

Maybe this is of interest for someone...

I need to make such plots for students in my Calculus course.
Below is an example, based on Rag demo (needs numpy and autograd package for automatic differentiation installed):

from vpython import vertex, vector, quad, scene, color
import autograd.numpy as np
from autograd import grad

scene.width = scene.height = 600
scene.scale = (1,1,0.4)

def plot_fxy(fxy,xydom,nx=50,ny=50,color=color.green):
    xmi,xma,ymi,yma=xydom
    xx = np.linspace(xmi,xma,nx+1)
    yy = np.linspace(ymi,yma,ny+1)
    fdx, fdy = grad(fxy,0), grad(fxy,1)
    verts = np.zeros((ny+1,nx+1),dtype=object)

    for yi,y in enumerate(yy):
        for xi,x in enumerate(xx):
            verts[yi,xi] = vertex(pos=vector(x,y,fxy(x,y)), normal=vector(-fdx(x,y),-fdy(x,y),1),
                                          shininess= 0,color=color)

    for yi in range(ny):
        for xi in range(nx):
            quad(v0=verts[yi,xi], v1=verts[yi,xi+1], v2=verts[yi+1,xi+1], v3=verts[yi+1,xi])

# ---------------------------------- example function and plot -------------------------------------------------

mex_hat = lambda x,y:  np.sin(1-x**2-y**2)/((x**2+y**2)+1)
plot_fxy(mex_hat,[-2,2,-2,2],40,50)

[Bruce Sherwood]

Thanks for the quite beautiful Jupyter VPython plot. I confess that I thought that Rag was some math package that I was unfamiliar with, but now I understand you were referring to the Rug demo. I'm intrigued that your program is as short as it is. I'm using Anaconda, and numpy was already installed, but I did have to install autograd.

[Bruce Sherwood]

You should delete the statement "scene.scale = (1,1,0.4)" which has no effect; it just addes a tuple to the scene object but is never referenced. Jupyter VPython does have "scene.range", with a scalar value.

[Michal Kaukič]

Hi, Bruce,

    I am glad that You liked the demo. Yes, Rag is Rug demo :-)  Thanks for advice with range. I have no previous knowledge  of VPython, but Jupyter version, I think, is the big step in the right direction. I will use it, following new releases closely. 

Dňa nedeľa, 17. apríla 2016 6:43:50 UTC+2 Bruce Sherwood napísal(-a):

[Henri Girard]

Hi Michal,
Would you share more graphs or tutorial about it ?
It's very interesting
Best regards
Hg

[Michal Kaukič]

Hi, Henri,

I have only Jupyter notebooks made with 2D graphics (matplotlib,
bokeh) and interactivity by means of ipywidgets. The material covered
- Laplace and z-transforms, solving differential and difference
equations, stability of continuous and discrete linear systems,...
You can contact me by mail, I will send You that material as .ipynb or
by jupyterhub running on my website feelmath.eu.

For 3D in Calculus 2 (functions of several variables) I used
IPython and mayavi2.
If the development of vpython-jupyter permits (needed features
available) I will transform some of the Python scripts to Jupyter
notebooks.

Michal

[Henri Girard]

Very interesting I use jupyter notebook for many kernels (vpython (ivisual) sage, etc... If you can send me then at ipynb it's great.
henri.girard_at_gmail.com
Best regards
Henri

Le samedi 16 avril 2016 18:02:21 UTC+2, Michal Kaukič a écrit :