Make a line animation that is thicker at the start and thinner at the end?

At 00:40 to 00:42 of the following YouTube video, a line that is thicker at the start and thinner at the end is moving along a path, as if you move a fireball. This is a Blender tutorial channel, so this is probably made with Blender, but there is no tutorial for that part. https://www.youtube.com/watch?v=saxpjudV_88&t=40

How can I make it like a thinning line like the video above?

PS: This is the animation I made after learning from the accepted answer: https://i.sstatic.net/paLDr.jpg

You can do it with curve only or with mesh and Curve modifier:

- With curves only:

Create your line curve, create a second curve that will be your taper, make it flat with V > Vector, rotate it slightly on the Z axis in Edit mode, the rotation angle will give the thickness of your line, i.e. the difference between its minimum and maximum radius. Now choose this second curve as the Taper Object of your line:

If you enable the Map Taper option and play with Bevel Start and End values you'll be able to animate your line:

You need to play with both the Start and End values if you want the line to follow along the curve:

Settings at frame 0:

Settings at frame 20:

The file:

- With mesh and Curve modifier:

Put the cylinder at the same point as the curve's origin, and make sure that the curve's direction is good, if not, go in Edit mode and right click > Switch Direction:

Give your object a Curve modifier with the curve as Curve Object, then animate the cylinder along the X axis so that the mesh follows the curve.

• Thanks, but there is one big problem. Using the bevel method, the line is just growing like this imgur.com/iwES1A0 , not moving like the YouTube video youtube.com/watch?v=saxpjudV_88&t=40 . Also, pressing v had no effect on my Blender. It would be helpful if you explain how to adjust the "taping" (thin/thickness control) in more details (how to make thicker/thinner). Commented Oct 20, 2020 at 9:02
• Animating both Bevel Start/End does not give me the move effect I need, because the moving line's end did not get any thinner. Commented Oct 20, 2020 at 9:04
• I've edited my answer, does it answer? Commented Oct 20, 2020 at 9:43
• Yeah, after inspecting your example file and some trial-and-error, I could achieve the same effect in a new Blender file. Commented Oct 20, 2020 at 22:43