How to Match Points Between Two Helical Polyline

I have two Polylines that are helical and based on elliptical footprints. In order to place Adaptive Components I need Points on both Polylines. I can divide the outer one equally, giving me the first list of points, but as the inner one has a different incline and overall length I cannot simply divide it equally as well.

I have thought about using the Curve.NormalAtParameter from the outer points to find a perpendicular to the tangent … but the inner points will be a different Z value. I thought about using something that gives me intersections, but since the helix revolves further than 360° I would receive multiple values …

Any suggestions how to find a corresponding point on the inner Helix that lies on the outer Points “Normal” but with a different Z value so that it lies on the inner Helix?

It’s all part of a bigger plan:

Just first impressions, but about the intersection solution : I think you can try to develop it, and then, even if you get an output with multiple point, just extract for each point on the outer helix the intersection that is at minimal distance from the initial point (the one on the outer helix).

Another idea I guess would be to divide the inner helix using something like Curve.PointAtParameter (and you could extract the parameter value you need from the Curve.ParameterAtPoint using your outer helix and the points you already placed). (edit : i guess Curve.ParameterAtSegmentLength could also help).

Thank you, @mellouze

The solution was indeed in the idea of looking to define the points by intersections. Quite simple actually, by using rectangle with limited height and depth (which are currently manual inputs, but which can be easily adopted to be formula driven) I was able to “map” the points onto the inner helix.

For anyone coming across this post later, below my current working solution:

@philipp_lammers Wouldn’t Geometry.ClosestPointTo work for you?

helix-20180802.dyn (32.2 KB)

@Vikram_Subbaiah, that might work. Though I am not sure if in the steeper parts of the inner polyline the XY offset is smaller than the Z offset. Wouldn’t that distort the results?

Hello Phillipp,

One way you could approach this is with a Plane Intersection as shown below:

This will be less nodes than your intersection solution as the plane is infinite in size

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