Summary: Demonstrates how to analytically solve for gaussian, mean and principal curvatures and principal directions on a surface.

The following sample code demonstrates analytically solve for gaussian, mean and principal curvatures and principal directions on a surface.

 
public override IRhinoCommand.result RunCommand(IRhinoCommandContext context)
{
  // Select surface to evaluate
  MRhinoGetObject go = new MRhinoGetObject();
  go.SetCommandPrompt("Select surface for curvature measurement");
  go.SetGeometryFilter(IRhinoGetObject.GEOMETRY_TYPE_FILTER.surface_object);
  go.GetObjects(1, 1);
  if (go.CommandResult() != IRhinoCommand.result.success)
    return go.CommandResult();
 
  // Validate selection
  MRhinoObjRef objref = go.Object(0);
  IOnSurface srf = objref.Surface();
  if (srf == null)
    return IRhinoCommand.result.failure;
 
  // Select surface to evaluate
  MRhinoGetPoint gp = new MRhinoGetPoint();
  gp.SetCommandPrompt("Select point on surface for curvature measurement");
  gp.Constrain(srf);
  gp.GetPoint();
  if (gp.CommandResult() != IRhinoCommand.result.success)
    return gp.CommandResult();
 
  // Calculate closest point on surface to test point
  double s = 0.0, t = 0.0;
  if (!srf.GetClosestPoint(gp.Point(), ref s, ref t))
    return IRhinoCommand.result.failure;
 
  // Calculate the second derivative of the surface at s,t
  On3dPoint P = new On3dPoint();
  On3dVector Ds = new On3dVector();
  On3dVector Dt = new On3dVector();
  On3dVector Dss = new On3dVector();
  On3dVector Dst = new On3dVector();
  On3dVector Dtt = new On3dVector();
  if (!srf.Ev2Der(s, t, ref P, ref Ds, ref Dt, ref Dss, ref Dst, ref Dtt))
    return IRhinoCommand.result.failure;
 
  // Calculate normal to surface at s,t
  On3dVector N = new On3dVector();
  if (!srf.EvNormal(s, t, ref N))
    return IRhinoCommand.result.failure;
 
  // Calculate the surface prinicpal curvatures
  double gauss = 0.0, mean = 0.0;
  double k0 = 0.0, k1 = 0.0;
  On3dVector K0 = new On3dVector();
  On3dVector K1 = new On3dVector();
  if (!OnUtil.ON_EvPrincipalCurvatures(Ds, Dt, Dss, Dst, Dtt, N, ref gauss, ref mean, ref k0, ref k1, ref K0, ref K1))
    return IRhinoCommand.result.failure;
 
  // Print the results
  RhUtil.RhinoApp().Print(string.Format("Surface curvature evaluation at parameter: ({0}, {1})\n", s, t));
  RhUtil.RhinoApp().Print(string.Format("  3-D Point: ({0}, {1}, {2})\n", P.x, P.y, P.z));
  RhUtil.RhinoApp().Print(string.Format("  3-D Normal: ({0}, {1}, {2})\n", N.x, N.y, N.z));
  RhUtil.RhinoApp().Print(string.Format("  Maximum principal curvature: {0} ({1}, {2}, {3})\n", k0, K0.x, K0.y, K0.z));
  RhUtil.RhinoApp().Print(string.Format("  Minimum principal curvature: {0} ({1}, {2}, {3})\n", k1, K1.x, K1.y, K1.z));
  RhUtil.RhinoApp().Print(string.Format("  Gaussian curvature: {0}\n", gauss));
  RhUtil.RhinoApp().Print(string.Format("  Mean curvature: {0}\n", mean));
 
  return IRhinoCommand.result.success;
}