Create Principal Curvature Curves
Windows only

by Dale Fugier (Last updated:  Wednesday, December 5, 2018)

Problem

You are looking for a way to create Principal Curvature lines starting with points on a surface. There is an ON_EvPrincipalCurvatures function, it’s not clear how it should be used.

Solution

Before using ON_EvPrincipalCurvatures, you will need to calculate the second derivative of the surface that the test location. Then, it is just a matter of creating up some curves based on the results.

Sample

The following is an example of how you might write such a command.

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

  const CRhinoObject* obj = go.Object(0).Object();
  const ON_BrepFace* face = go.Object(0).Face();
  if (nullptr == obj || nullptr == face)
    return CRhinoCommand::failure;

  CRhinoGetPoint gp;
  gp.SetCommandPrompt(L"Select point on surface");
  gp.Constrain(*face, obj->Attributes().m_wire_density);
  gp.GetPoint();
  if (gp.CommandResult() != CRhinoCommand::success)
    return gp.CommandResult();

  double s = 0.0, t = 0.0;
  const ON_Surface* srf = gp.PointOnSurface(&s, &t);
  if (nullptr == srf)
    return CRhinoCommand::failure;

  ON_3dPoint P;
  ON_3dVector Ds, Dt, Dss, Dst, Dtt;
  if (!srf->Ev2Der(s, t, P, Ds, Dt, Dss, Dst, Dtt))
    return CRhinoCommand::failure; // failed to evaluate derivatives

  ON_3dVector N;
  if (!srf->EvNormal(s, t, N))
    return CRhinoCommand::failure; // failed to evaluate normal

  double gauss = 0.0, mean = 0.0, k[2] = { 0.0, 0.0 };
  ON_3dVector K[2];
  if (!ON_EvPrincipalCurvatures(Ds, Dt, Dss, Dst, Dtt, N, &gauss, &mean, &k[0], &k[1], K[0], K[1]))
    return CRhinoCommand::failure; // failed to evaluate principal curvatures

  for (int i = 0; i < 2; i++)
  {
    if (fabs(k[i]) <= 1.0e-4 || fabs(k[i]) >= 1.0e4)
    {
      // just draw a line as curvature is huge/tiny
      ON_Line line(P - K[i] * 5.0, P + K[i] * 5.0);
      context.m_doc.AddCurveObject(line);
    }
    else
    {
      double r = 1.0 / k[i];
      ON_3dPoint center = P + r * N;
      ON_3dPoint start = center - r * K[i];
      ON_3dPoint end = center + r * K[i];
      ON_Arc arc(start, P, end);
      context.m_doc.AddCurveObject(arc);
    }
  }
  context.m_doc.Redraw();

  return CRhinoCommand::success;
}