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Generating volumetrail from moving points?

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I have a set of points that define a shape.

Untitled-1.jpg.6117941eb2c5df809c5a76c072044bee.jpg

 

I wan to turn that into a velocity field that I can advect points through.

I have a basic setup, but I can't figure out how to bend the red lines along the curved particle generated line.

vel_trail.gif.d8b14c285f30c3d1373bd8ec081dfccf.gif

ap_particle_sphere_arcs.hiplc

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