Normal at position t1 of a space curve 3D

Rhino Developer
1

Hello,
I would like to know if I can use the Rhino.Geometry.Curve.DerivativeAt method to calculate the normal vector (according to the definition in the attached diagram or (Frenet–Serret formulas - Wikipedia)) with the derivative in seconds at position t1 of a space curve 3D:

v_normal = Curve.DerivativeAt(t1, 2)

definition_repere_Frenet
definition_repere_Frenet720×644 96.6 KB

1 Like
2

Hello
I can be wrong but I think this is better
https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.curve/perpendicularframeat

3

Hello,
Thank you very much, but I am looking for the normal of a space curve and not of a plane.

4

whats a space curve

5

Hello
the plane contains the vectors. It contains the Tangent (Z axis) and the Normal vector (surely X axis)!

6

I think he/she means 3D curve.

7

Hi @msgatrong,

Perhaps this?

import Rhino
import scriptcontext as sc

def test_curve_normal():
    go = Rhino.Input.Custom.GetObject()
    go.GeometryFilter = Rhino.DocObjects.ObjectType.Curve
    go.SubObjectSelect = False
    go.Get()
    if go.CommandResult() != Rhino.Commands.Result.Success:
        return
    
    objref = go.Object(0)
    curve, t = objref.CurveParameter()
    if not curve:
        return
    
    point = curve.PointAt(t)
    print("Point: {0}".format(point.ToString()))
    
    tangent = curve.TangentAt(t)
    print("Tangent: {0}".format(tangent.ToString()))
    
    kappa = curve.CurvatureAt(t)
    print("Curvature: {0}".format(kappa.ToString()))
    
    # The normal to the curve at a particular point is the line
    # perpendicular to the tangent at this point.
    normal = Rhino.Geometry.Vector3d.CrossProduct(tangent, kappa)
    normal.Unitize()
    print("Normal: {0}".format(normal.ToString()))
    
if __name__ == "__main__":
    test_curve_normal()

– Dale

8

Thank you very much, if the curvature vector of Rhino is defined as in the equation 2.20 of this reference
2.2 Principal normal and curvature), the kappa vector=curve.CurvatureAt(t) in your proposal is the normal vertor. We do not need to calculate the vector product.

Best regards,

image
image1531×161 5.91 KB

9

Hello,
Yes, It concerns the 3D curve with double curvatures. The 2D curve has only one curvature.