Developer: RhinoScript
Summary: Demonstrates how to evaluate the torsion of a curve.

How determine the torsion of a curve at a parameter using RhinoScript?

The torsion of a curve measures how sharply it is twisting. It is analogous to curvature in two dimensions. The following example function calculates the torsion of a curve at a parameters:

 '''
 ''' Description
 '''   Evaluate the torsion of a curve.
 ''' Parameters
 '''   crv - a string that identifies the curve to evaluate
 '''   t   - a parameter of the curve within its domain
 ''' Returns
 '''   The torsion if successful.
 '''   Null if the torsion is undefined at the parameter.
 '''
 Function EvaluateTorsion(crv, t)
 
   ' Local variables
   Dim data, d1xd2, numer, denom
 
   ' Default return value
   EvaluateTorsion = Null
 
   ' Calculate the torsion
   data = Rhino.CurveEvaluate(crv, t, 3)
   If IsArray(data) And UBound(data) = 3 Then
     d1xd2 = Rhino.VectorCrossProduct(data(1), data(2))
     numer = Rhino.VectorDotProduct(d1xd2, data(3))
     denom = Rhino.VectorDotProduct(d1xd2, d1xd2)
     If denom > 0 Then
       EvaluateTorsion = numer / denom
     End If
   End If
 
 End Function

The following example script demonstates how you might use the above function:

 Sub TestTorsionOnCurve()
 
   ' Local variables  
   Dim crv, pt, t, tor
 
   ' Select curve to evaluate
   crv = Rhino.GetObject("Select curve to evaluate", 4, True)
   If IsNull(crv) Then Exit Sub
 
   ' Get point on curve to evalaute  
   pt = Rhino.GetPointOnCurve(crv, "Point to evaluate")
   If Not IsArray(pt) Then Exit Sub
 
   ' Get parameter of the point on a curve that is closest to pt    
   t = Rhino.CurveClosestPoint(crv, pt)
   If IsNull(t) Then Exit Sub
 
   ' Evaluate the torsion of the curve at t.    
   tor = EvaluateTorsion(crv, t)
   If IsNull(tor) Then
     Rhino.Print "Torsion at curve parameter " & CStr(t) & " is undefined"
   Else
     Rhino.Print "Torsion at curve parameter " & CStr(t) & " is " & CStr(tor)
   End If
 
 End Sub