New locations of points on a new shaped curve

Hi, I am trying something in grasshopper and Python, but my knowledge doesn’t go so far to know how to do it till now.

As picture shown above, the 1st diagram is showing the original curve (black line) with several inner control points. The dash line is offset from center line (Red line) on both sides with equal distance. Odd points are on center line, even points are on dash line. The 2nd diagram is showing the new shaped curve. Unchanged parameters are 1. Distance between dash line and center line. 2. The length of curves between odd points respectively. 3. Odd points stay on center line as well as even points stay on dash line. Based on such constraints and conditions, I am trying to figure out the relation between the new location of points and the new shaped center line via grasshopper or Python.

Thank you so much for any help!

When the points on the base curve are evenly spaced(?), these curve lengths won’t be identical except when the base curve is a straight line. Adjusting the points on the base curve to satisfy this constraint is beyond my pay grade.

If the two lines are equal you can use offset curves and horizontal frames (divide) than use flow to project the diagram from curve 1 to 2 (15.5 KB)

Hi, Joseph. Thank you for your reply. The points on base cure are not evenly space. What I am trying to do is staying the distance from even points to center line respectively the same, the length of curve between even points the same, even if those points would move along the center line and dash lines respectively. One of the examples in the reality is a rope (center line showing red) is passing through several holes (odd points) located on the center line of a piece of wave-shaped steel sheet, and this surface (steel sheet) would be placed in a space (between dash lines) that limits its shape. Based on this, when I change the shape of the rope (center line), the steel sheet would adjust its shape, but the length of steel sheet, the length of each part of steel sheet between adjacent holes (odd points) are changeless and the shape of steel sheet is still a smooth and continue curve from top view. I am not sure about that I explain it clearly or not, but thank you so much though.

Thank you, Seghier. But the method you offer is not what I need. Because I need the wave-shaped curve stay in smooth and continue, and the length of curve, not the straight distance between points, is changeless.

You can develop the method , and where you see that straight distance between points ?

Sorry, I didn’t see you attached a gh file. I thought the distance showing in the picture is between points. I tried to open the gh file, but it said there is a unrecognized objects called Curve Middle, I don’t have it and I cannot even found it in Food4Rhino. Thanks

Maybe you use Rhino V5, it is availabel in V6

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I can explain all day why I should be rich but that doesn’t make it so.

Use Evaluate Length set to 0.5 in Rhino 5 to substitute.

Or ‘Crv | Analysis | Point On Curve’ with the default value of 0.50 (‘1/2 (mid)’)

@seghierkhaled’s code also uses this: