Tangential arc with change in direction and plane

What’s the simplest/”most elegant” way to create a curve that tangentially blends two straight lines in different directions and planes?

“Curve > Arc > Tangent to Curves” seems to only blend with one line asymptotically and intersect other line at an acute angle.

I was able to blend at both ends only as follows but there must be a better way?:

  1. Generate two tangent curves between the lines, each starting at opposite ends.
  2. Create two 3D planes and trim to get intersecting edge curve for desired pipe to smoothly blend change in “elevation” and “direction.”

The first surface was generated from 2 intersections of curves and straight lines and 2 projected intersections of the two straight lines.

The second surface was created from the two arcs as edge curves.

(Had to be careful creating first surface since “Tangent to Curves” command moves the end tangential intersection based on position of start intersection).

Drawing and file are attached.


George (Version 5.0)

Pipe asymptotic in two planes

Rhino techsptasymptotic.3dm (212.1 KB)

Would the BlendCrv command (BlendCrv | Rhino 3-D modeling) work for you here? Seem to create an elegant curve for me (although I had to split the lines where the blended curved starts):

If this doesn’t work for you I might have some grasshopper solutions that would do this.

Henry, BlendCrv works beautifully. The key is your hint to split curves to be blended. Associate at McNeel Support didn’t mention that. I was trying to blend at intersections and got wild curves that did not do the trick. Apologies for not acknowledging sooner. Still new at Discourse protocol, had enabled notifications and thought I would get “push” email message. Thanks, George

Hello - the curves to be blended do not need to be split. You can move the blend curve to any location along the input curves.


Pascal, Thanks for further guidance. Of the three blends, “Quick” and “Arc” seem to blend from ends of curves. For my design purpose I like to project straight lines to establish the outer bounds for the blend. “Adjustable curve” appears to generate one asymptotic blend and acute angle intersect at other end. So, to get asymptotic blend at both ends, within my bounded region, with a comfortable “radius”, the intermediate inset split points on both lines seem to do the trick. BTW – Is there a Discourse option to provide a “push” email when there is a response? Thanks, George

Pascal, I missed that! Thanks for pointing it out. George, it’s a command line option to pick the start of the blend (either end of curve or pick point). Makes it even easier to use (I think I have grasshopper brain which may be why I missed it):

Hello - well, that is that but you also can drag the curve end to anyplace you like. while in the command, no matter where it starts out.