Rhino7 idea new primitive type - perfect curve transition/blend euler spiral in 3d

Serengeti (Rhino WIP)
1

Hi,

I think this function would be super cool.

BlendCrv could offer perfect blend between two curves matching start and end curvatures of blended curves BUT the resulting curve would have curvature linearly changing along its length → perfectly smooth transition between two curves in 3d space (perfect in the elegancy). It is called euler spiral or clothoid and is not trivial to describe mathematically. I dont know if euler spiral is defined only in 2D space but in 3D should have the same properties.

What do you think? Is it a easy thing to implement?

Sorry for my kids drawing :smiley:

image
image1370×729 486 KB

2 Likes
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challenge to big brains out here. i cannot stop thinking about perfect transition curve between any two curves in 3d space. only contraints for the transition curve would be as follows which would guarantee its fully defined and only one solution exists: 1 curve is the shortest possible meeting other contraint 2 curve respects start and end tangency and curvature 3 curvature along curve length changes linearly from start to end.

what would be the method to find such curve?

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