Results

 I spent quite a bit of time last week trying to produce a sphere with a

point on it on Geogebra. I wanted the point to move with the sphere. Went

back to Desmos, with which I had graphing experience. Threw my pride

to the wind and asked Gemini to show me how to do this. With a little help

from Copilot, who told me to instantiate the sphere on the last line, got what 

I wanted. Generative AI is the cat's meow...

                                                                  

https://www.desmos.com/3d/jryz8gda7l

In effect, Gemini told me what my mistake was on Geogebra: I was using the sphere 

tool rather defining the sphere I wanted!!

                                                   *     *     *

Below, upping the apparent size of the sphere with the + button:

                                                                   

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Meta Ai:

                                                                          

How does Desmos actually render 3D objects like this sphere?

Desmos primarily focuses on 2D graphing, but it can represent 3D objects using some clever techniques. Here’s how Desmos typically renders 3D objects like your sphere:

2D Projections:

Desmos uses mathematical projections to show a 3D shape on a 2D screen. For a sphere, it calculates the 2D "shadow" or outline that a 3D object would cast from a certain viewpoint, similar to how a camera takes a picture of it.

Parameterized Surfaces or Slices:

Instead of rendering a full 3D solid, Desmos often plots many 2D curves or slices that approximate the 3D shape. For a sphere, you might see various circles corresponding to different cross-sections of the sphere at different heights (zz-values).

Shading and Color:

To give the illusion of depth, Desmos may use shading or color gradients on these curves or regions to imply which parts are closer or further away based on light source assumptions.

Web Technology (WebGL or SVG):

Under the hood, Desmos uses modern web graphics technologies like SVG (Scalable Vector Graphics) or WebGL. These allow it to draw smooth curves and shapes dynamically and interactively, although full 3D rendering (like rotating objects freely) is limited compared to dedicated 3D software.

In short, Desmos creates convincing 3D visuals through 2D projections and careful plotting of curves rather than real 3D modeling. This approach balances visual clarity and interactive speed in the browser.

If you want true 3D rendering with rotation and lighting, software like GeoGebra 3D or specialized 3D tools would be better suited.