Question

How can I compute the radius of curvature of a curve object at a selected location?

Answer

The following example code demonstrates how to compute the radius of curvature of a ON_Curve object. This example uses a a combination of ON_Curve::TangentAt and ON_Curve::CurvatureAt. But, we could have also used ON_Curve::EvCurvature. See opennurbs_curve.h for details on these functions.

  CRhinoCommand::result CCommandTest::RunCommand( const CRhinoCommandContext& context )
  {
    CRhinoGetObject go;
    go.SetCommandPrompt( L"Select curve for curvature measurement" );
    go.SetGeometryFilter( CRhinoGetObject::curve_object );
    go.GetObjects( 1, 1 );
    if( go.CommandResult() != success )
      return go.CommandResult();


    const ON_Curve* crv = go.Object(0).Curve();
    if( 0 == crv )
      return failure;


    CRhinoGetPoint gp;
    gp.SetCommandPrompt( L"Select point on curve for curvature measurement" );
    gp.Constrain( *crv );
    gp.GetPoint();
    if( gp.CommandResult() != success )
      return gp.CommandResult();


    ON_3dPoint pt = gp.Point();


    double t = 0.0;
    if( !crv->GetClosestPoint(pt, &t) )
    {
      RhinoApp().Print( L"Failed to compute radius of curvature.\n" );
      return failure;
    }


    ON_3dVector tangent = crv->TangentAt( t );
    if( tangent.IsTiny() )
    {
      RhinoApp().Print( L"Failed to compute radius of curvature. Curve may have stacked control points.\n" );
      return failure;
    }


    ON_3dVector curvature = crv->CurvatureAt( t );
    const double k = curvature.Length();
    if( k < ON_SQRT_EPSILON )
    {
      RhinoApp().Print( L"Radius of curvature: infinite.\n" );
      return failure;
    }


    ON_3dVector radius_vector = curvature / (k * k); 
    ON_Circle circle;
    if ( !circle.Create(pt, tangent, pt + 2.0 * radius_vector) )
    {
      RhinoApp().Print( L"Failed to compute radius of curvature.\n" );
      return failure;
    }


    context.m_doc.AddCurveObject( circle );
    context.m_doc.AddPointObject( pt );
    context.m_doc.Redraw();


    ON_wString wRadius;
    RhinoFormatNumber( circle.Radius(), wRadius );
    RhinoApp().Print( L"Radius of curvature: %s.\n", wRadius );


    return success;
  }