In this lecture, we'll cover the following:

• How to build a function that draws the local $x$, $y$ and $z$ axes on every element,
• How to position those axes at the centroid of each element and extract the direction vectors from the rotation matrix,
• How to optionally label each axis with text and tie the new plotting function into our existing figure.

We start with a quick clean-up. At the end of the previous lecture, we left out a small step: converting our list of elements into a NumPy array. We add that step in so that array operations like subtracting one from every entry will work as expected. With that fixed, we move on to the main task of the lecture, which is plotting the local reference frame on each element so that we can visually verify the rotation matrices we built. We define a new function called draw_all_axes that takes our figure, the rotation matrices, the nodes, the elements, an axis scale, and a Boolean flag controlling whether or not to display text labels on the axes.

Inside the function, we set up a small dictionary that ties each axis name $(x, y, z)$ to the corresponding row index in the rotation matrix and to a colour (red, green and blue). For every element, we calculate its centroid as the origin of the local frame, extract the relevant rotation matrix, and then iterate through each axis to plot a short line from the centroid in the direction of that axis. We use Plotly's scatter3d for the lines, optionally add text labels at the ends, and finally return the modified figure. When we re-plot the mesh and overlay the axes, we can see that the x-axis aligns with the first edge of every element, the z-axis is normal to the surface, and the y-axis sits mutually perpendicular to both, exactly as we expect.

Next up

In the next lecture, we will identify which nodes and degrees of freedom are restrained on our shell.