Component:interpolate t curve

if i know 3 points, and the curvature of the start and end points,how can I get the tangent vector at these two points, and use the three points with "interpolate t curve" to construct a curve.

Replies to This Discussion

Permalink Reply by Nick on November 26, 2013 at 10:40am

This might help.

http://tutorial.math.lamar.edu/Classes/CalcIII/TangentNormalVectors...

Permalink Reply by David Rutten on November 26, 2013 at 11:54am

Yeah it's quite tricky to reverse engineer a tangent vector to match a certain curvature. There's code deep in Rhino that solves these cases but none of that has been exposed as Grasshopper components and probably not even as RhinoCommon methods.

Some approaches spring to mind:

Use Galapagos.
Generate N curves from clearly too little curvature to too much, measure the curvature for all of them, interpolate a curve through the curvature data, intersect with a line that represents the target curvature, find the X coordinate and then create a new tangent vector with a length matching that X. Very involved, lots of work, lots of complexity.
Write a script that binary-searches for the ideal tangent vector, this will probably be quite fast, though if you have to do it for both ends of a curve then it will be much harder if there aren't enough control-points in between.

David Rutten

david@mcneel.com

Permalink Reply by qiushi on November 26, 2013 at 12:14pm