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I want to use blender to draw a cycloid animation. I know the function, but is it possible to render the motion path of a vertex of a circle like the following video?

https://www.youtube.com/watch?v=x0Z9OeJbRy4

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  • $\begingroup$ From your answers, I find an easy way to finish this task. I put the method here. $\endgroup$ – pdcxs Mar 3 at 6:19
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You can use dynamic paint, but as far as I know, this will alias a bit.

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So I propose to use Animation Nodes instead. For 2.8 you can find an experimental version here.

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The principle is to create a Bezier curve, set it to 2D, bevel it a bit and use it in Animation Nodes.

enter image description here

Calculation steps:

  • Take the moving sphere, its location and append it to the spline so that it is reinjected in the curve (bottom line of the nodes).
  • The used spline (top part of the nodes) is either an empty one (at frame 1, so that the curve starts to be empty) or the current spline of the curve as it is.

Few words about the cycloide itself.

If you add a simple deform (bend mode) to a subdivided segment, this will make a circle:

enter image description here

If we add an empty as axis origin, then moving the empty will make the obtained circle to rotate.

To make this rotation visible, add another empty (below with a sphere shape), and make the 3 first vertices of the segment parent of this empty.

Now the empty will move and rotate following the segment made circular thanks to the simple deform modifier:

enter image description here

The "drawing sphere above" is simply parented to this sphere empty.

(the file contains also the Dynamic Paint setting, using vertex color, it is on the hidden plane)

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Two other tips more than Answers ... (thanks Lemon for Cycloid :) )

Particles

Scene Properties > Gravity off, Particles Properties > Velocity > Normal zero). To keep all particles you can enable Render > Extra > Dead or increase Emision > Life Time.

enter image description here

I just could not figure out, how to dense particles, they are appears on frame step, increase Sub-Steps didn't helped ... hm


Btrace

Addon that can create path from moving objects (particles etc.)

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In this case, it dint work on lemon's cycloid (probably because driving object by Empty?), but worked on object Follow path. So it depence what exactly you would need to follow.

enter image description here

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