I know there must be an elegant solution I’m just not thinking of here: Given: two points A and B and a line C, I’m looking to find: the point X on line C, where line AXB has the minimum distance of any possible point on C. I realize that if line C is co-planar with A and B, then X can be thought…

[image] Joseph_Oster: Find the closest point on C for both A and B, then find the midpoint between them? almost, but it seems that using the weighted average do works (using point distance to line as weight), haven’t tested deeply. [2020-08-26 16_46_21-Window] weighted average.gh (6.0 KB)

BRAVO!!! I was wondering about a weighted average but wasn’t sure how to do it. From what I can tell, your solution works fine on both the planar and non-planar cases. I LOVE a simple solution! Very nice.

Still, i feel like i “cheated”. Is like, pencil on paper, comparing a guy that finds the tangent of a circle by drawing another circle and finding the intersection, and another guy that measure distance and diameter and calculate the position of the tangent point. The latter is so uncool! Geometri…

It does look like it’s correct, so the question is why? Since this all comes down to vector algebra there must be a derivation. Nice work!

Ha ha! Now that I’ve gone over it again I see how I “inspired” you. Once you look at the unfolding into one plane, it’s obvious that its the weighted average along the line. It also avoids the nastiness that @Joseph_Oster mentioned about curve direction.

Even though it seems to work fine in your code (when you didn’t reparameterize your Line?), this issue of assuming that a ‘t’ value corresponds to distance has been bothering me all day. So I wrote a slightly different method that applies the weighted average to the magnitude of a Vector 2Pt that m…

Wow, and wow… I got pulled into a bunch of work stuff all day and just got back to look at all this. You guys rock! First, Ethan, once again elegant geometric solution in the 3D version of your method --and of course it makes total sense that you just reflect each point in the line on the plane fo…

Hey Joseph, I’m still playing catch up here --but are you talking about the ‘t’ value input for the “Evaluate Curve” component in Riccardo’s Definition? I don’t think its accurate to say that he is using distance as a ‘t’ value here --the way I’m reading Riccardo’s definition, the value he is feed…

[image] Walt-D: I’m still playing catch up here --but are you talking about the ‘t’ value input for the “Evaluate Curve” component in Ethan’s Definition? I am referring to Riccardo’s definition ( @maje90 ), where the weighted average is used as a ‘t’ input value to Evaluate Curve, corresponding…

[image] Joseph_Oster: this issue of assuming that a ‘t’ value corresponds to distance has been bothering me all day What issue? A pure “Line” object (not “linear curve”) is like already reparametrized: t=0 means start, t=1 means end… And, as a line have a direct proportion between parameter…

[image] maje90: A pure “Line” object (not “linear curve”) is like already reparametrized: t=0 means start, t=1 means end… I didn’t know that. Another special GH feature… But I’ve only been playing with Grasshopper for ~6 years so I still have a lot to learn. [t_lines]

Point on line closest to two points outside that line

Grasshopper

akilli (Ethan Gross) August 27, 2020, 5:57pm 33

The equations for rolling contact are not that difficult, the real messiness is in calculating the teeth profiles for gearing.

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Point on line closest to two points outside that line

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