Curve Osculating Planes

This guide demonstrates how to calculate osculating planes.

Problem

Is it possible to calculate the osculating plane at point $P$ on a given curve with the methods provided by RhinoScript?

Solution

Yes. There are a number of methods included in RhinoScript that can be used to calculate a curve’s osculating plane, such as CurveClosestPoint, CurveTangent, CurveCurvature, and CurveEvaluate. In this example, we will use the CurveEvaluate function to calculate the 2nd derivative of a curve at a parameter…

Function CurveOsculatingPlane(crv, t)
CurveOsculatingPlane = Null ' default return value
If Not Rhino.IsCurveLinear(crv) Then
Dim rc : rc = Rhino.CurveEvaluate(crv, t, 2)
If IsArray(rc) Then
CurveOsculatingPlane = Rhino.PlaneFromFrame(rc(0), rc(1), rc(2))
End If
End If
End Function


The following is an example of how you might use this function…

Sub TestCurveOsculatingPlane
Dim segs : segs = 10
Dim crv : crv = Rhino.GetObject("Select non-linear curve", 4)
If Not IsNull(crv) Then
Dim pts : pts = Rhino.DivideCurve(crv, segs)
If IsArray(pts) Then
Dim i, t, p
For i = 0 To UBound(pts)
t = Rhino.CurveClosestPoint(crv, pts(i))
p = CurveOsculatingPlane(crv, t)