I am trying to model a 4th order 2-D (planar) equation (that also has a square root term) but I want to use only a few (6±) control vertices and preferably with a single span (although maybe I need to consider 2 or 3 spans). 6 points should enable a 5th order curve which should be more than adequate to get an exact match (although the square root term may upend that assessment). In any event, I can calculate (exactly) any CV’s position, tangents, and higher-order derivatives at any and all locations along the curve’s span.

The Grasshopper “tancurve” NURBS interpolation component takes in the position and tangents at each CV, and by adjusting the spacing of the control vertices so they are closer where the curvature is tighter, the curve is still not close to being exact, and the curvature graphs are not as well behaved as I would like to see. The attached screen shot shows different results I am seeing (yellow being the “exact” curve and the green curve getting closest (using the interpolate(t) component). The red one that is closest to yellow uses a mysterious “blend” parameter that can move different parts of the curve around for better localized fit, but setting the “blend” term is still a mystery.

- So, is there a component that also takes in the higher order derivatives?
- Is there an alternate/better approach to doing this?