Plot gradient vector in ContourPlot

  • #1
Lambda96
203
71
TL;DR Summary
Plot gradient vector in ContourPlot
Hi,

I have made the following ContourPlot in mathematica and now I wanted to ##\vec{r}_1= \left(\begin{array}{c} -1 \\ 1 \end{array}\right)##, ##\vec{r}_2= \left(\begin{array}{c} 0 \\ \sqrt{2} \end{array}\right)## and ##\vec{r}_3= \left(\begin{array}{c} 1 \\ 1 \end{array}\right)## insert the gradient into the ContourPlot.

Bildschirmfoto 2023-12-11 um 15.33.19.png


Is this possible and if so, how?
 
Physics news on Phys.org
  • #3
Thank you Orodruin for your help 👍

Since I want to have the vectors at certain points in the ContourPlot, I used ListVectorPlot[{{x1,y1},{vx1,vy1}},...}].

Unfortunately, Mathematica then plots a vector field

Bildschirmfoto 2023-12-12 um 12.35.57.png
 
  • #4
Check out the VectorPoints option
 

FAQ: Plot gradient vector in ContourPlot

How do I plot a gradient vector field on a ContourPlot?

To plot a gradient vector field on a ContourPlot, you can use the `quiver` function in combination with `contour`. First, calculate the gradient of your function, then use `quiver` to plot the vectors and `contour` to plot the contours. For example, in Python with matplotlib, you might use:

import numpy as npimport matplotlib.pyplot as pltx = np.linspace(-5, 5, 100)y = np.linspace(-5, 5, 100)X, Y = np.meshgrid(x, y)Z = X**2 + Y**2 # Example function# Calculate gradientsU, V = np.gradient(Z)# Plot contour and gradientplt.contour(X, Y, Z)plt.quiver(X, Y, U, V)plt.show()

How can I adjust the density of the gradient vectors in the plot?

You can adjust the density of the gradient vectors by changing the step size in your meshgrid or by using the `quiver` function's `scale` parameter. For instance, to reduce the density, you can create a coarser grid:

x = np.linspace(-5, 5, 20) # Fewer pointsy = np.linspace(-5, 5, 20)X, Y = np.meshgrid(x, y)Z = X**2 + Y**2U, V = np.gradient(Z)plt.contour(X, Y, Z)plt.quiver(X, Y, U, V)plt.show()

How can I normalize the gradient vectors for better visualization?

To normalize the gradient vectors, you can divide each vector by its magnitude. This ensures that all vectors have the same length, making the direction of the gradient more apparent:

magnitude = np.sqrt(U**2 + V**2)U_normalized = U / magnitudeV_normalized = V / magnitudeplt.contour(X, Y, Z)plt.quiver(X, Y, U_normalized, V_normalized)plt.show()

Can I color the gradient vectors based on their magnitude?

Yes, you can color the gradient vectors based on their magnitude by passing a color array to the `quiver` function using the `C` parameter. Here's how you can do it:

magnitude = np.sqrt(U**2 + V**2)plt.contour(X, Y, Z)plt.quiver(X, Y, U, V, magnitude)plt.colorbar

Similar threads

Plotting the trajectory of a particle in polar coordinates
Replies
6
Views
935
Calculate E and B fields when given A
Replies
5
Views
129
Two point masses, where is the force zero?
Replies
19
Views
2K
Model for a Qubit system using the Hamiltonion Operator
Replies
6
Views
1K
Mathematica Mathematica Plot Real Portion (Contour Plot)
Replies
5
Views
2K
Mathematica Solving equation and plotting issue with Mathematica
Replies
2
Views
699
Slope of a mountain ridge (Gradient)
Replies
5
Views
1K
Perform suitable gauge transformations
Replies
3
Views
1K
Inner product between velocity and acceleration is zero (parametric)
Replies
6
Views
893
Rotation of macroscopic magnetization = average (Magnetization current density)
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top