How do I project lines onto a canvas at runtime?

For starters, I asked this question a few years back for a game dev project, and never got a satisfactory answer. THe project got shelved and I moved on. Now I am working on a trig and calc visualizer as a dual project to teach my son programming and my daughter how to visualize trig and calc functions.

What I am trying to achieve is as follows:

-Create a 3d object with editable parameters to define its movement.
-Raycast from the tip of the object onto a object/canvas/etc
-Render the trail where the raycast collides with the object.
-Be able to reset the graphic between tests.

The first two I can manage, including getting the hit returns and locations. Being able to reset when the test ends is easy enough. It’s that third bit that is giving me fits.

I’d use render targets.