/// <summary>
        /// Get knot multiplicity.
        /// </summary>
        /// <param name="knots"></param>
        /// <param name="index">Index of knot to query.</param>
        /// <param name="tolerance"></param>
        /// <param name="average"></param>
        /// <param name="strict"></param>
        /// <returns>The multiplicity (valence) of the knot.</returns>
        public static int KnotMultiplicity(NurbsSurfaceKnotList knots, int index, double tolerance, out double average, out bool strict)
        {
            var i     = index;
            var value = knots[i++];

            average = value;

            strict = true;
            while (i < knots.Count && SurfaceKnotEqualTo(value, knots[i], tolerance, out var s))
            {
                strict  &= s;
                average += knots[i];
                i++;
            }

            var multiplicity = i - index;

            if (strict)
            {
                average = knots[index];
            }
            else
            {
                average /= multiplicity;
            }

            return(multiplicity);
        }
        static bool ToKinkedSpans(NurbsSurfaceKnotList knots, int degree, out List <double> kinks, double knotTolerance = KnotTolerance)
        {
            kinks = default;

            for (int k = degree; k < knots.Count - degree;)
            {
                var multiplicity = KnotMultiplicity(knots, k, knotTolerance, out var _, out var strict);

                if (multiplicity > degree)
                {
                    if (kinks is null)
                    {
                        kinks = new List <double>();
                    }
                    kinks.Add(knots[k]);
                }

                if (!strict)
                {
                    var excess = multiplicity - knots.KnotMultiplicity(k);

                    // Correct multiplicity in case more than degree knots are snapped here
                    multiplicity = Math.Min(multiplicity, degree);

                    // Insert new knot multiplicity
                    knots.InsertKnot(knots[k], multiplicity);

                    // Remove old knots that do not overlap knots[k]
                    if (excess > 0)
                    {
                        knots.RemoveKnots(k + multiplicity, k + multiplicity + excess);
                    }
                }

                k += multiplicity;
            }

            for (int k = degree; k < knots.Count - degree;)
            {
                var m = KnotMultiplicity(knots, k, knotTolerance, out var a, out var s);
                global::System.Diagnostics.Debug.Assert(m <= degree);
                k += m;
            }

            return(!(kinks is null));
        }
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        public static double[] ToHost(NurbsSurfaceKnotList list)
        {
            var count = list.Count;
            var knots = new double[count + 2];

            int j = 0, k = 0;

            while (j < count)
            {
                knots[++k] = list[j++];
            }

            knots[0]         = knots[1];
            knots[count + 1] = knots[count];

            return(knots);
        }
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        public static List <double> ConvertRhinoKnotList(NurbsSurfaceKnotList knotList)
        {
            List <double> knots = new List <double>();

            try
            {
                foreach (double knot in knotList)
                {
                    knots.Add(knot);
                }
            }
            catch (Exception ex)
            {
                string message = ex.Message;
            }
            return(knots);
        }
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        public static global::Topologic.Face ToTopologic(this Rhino.Geometry.NurbsSurface nurbsSurface)
        {
            if (nurbsSurface == null)
            {
                return(null);
            }

            int  uDegree     = nurbsSurface.Degree(0);
            int  vDegree     = nurbsSurface.Degree(1);
            bool isUPeriodic = nurbsSurface.IsPeriodic(0);
            bool isVPeriodic = nurbsSurface.IsPeriodic(1);
            bool isRational  = nurbsSurface.IsRational;
            NurbsSurfaceKnotList ghUKnots = nurbsSurface.KnotsU;
            List <double>        uKnots   = ghUKnots.ToList();

            NurbsSurfaceKnotList ghVKnots = nurbsSurface.KnotsV;
            List <double>        vKnots   = ghVKnots.ToList();

            // OCCT-compatible
            uKnots.Insert(0, uKnots[0]);
            uKnots.Add(uKnots.Last());
            vKnots.Insert(0, vKnots[0]);
            vKnots.Add(vKnots.Last());

            NurbsSurfacePointList  ghControlPoints = nurbsSurface.Points;
            List <IList <Vertex> > controlPoints   = new List <IList <Vertex> >();
            List <IList <double> > weights         = new List <IList <double> >();

            for (int i = 0; i < ghControlPoints.CountU; ++i)
            {
                List <Vertex> controlPoints1D = new List <Vertex>();
                List <double> weights1D       = new List <double>();
                for (int j = 0; j < ghControlPoints.CountV; ++j)
                {
                    ControlPoint ghControlPoint = ghControlPoints.GetControlPoint(i, j);
                    controlPoints1D.Add(ghControlPoint.Location.ToTopologic());
                    weights1D.Add(ghControlPoint.Weight);
                }
                controlPoints.Add(controlPoints1D);
                weights.Add(weights1D);
            }

            return(global::Topologic.Face.ByNurbsParameters(controlPoints, weights, uKnots, vKnots, isRational, isUPeriodic, isVPeriodic, uDegree, vDegree));
        }
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        static internal IList <double> ToHost(this NurbsSurfaceKnotList knotList)
        {
            var knotListCount = knotList.Count;

            if (knotListCount > 0)
            {
                var knots = new List <double>(knotListCount + 2);

                knots.Add(knotList[0]);
                foreach (var k in knotList)
                {
                    knots.Add(k);
                }
                knots.Add(knotList[knotListCount - 1]);

                return(knots);
            }

            return(new List <double>());
        }
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        private Face ByNurbsSurface(Rhino.Geometry.NurbsSurface ghNurbsSurface)
        {
            int  uDegree     = ghNurbsSurface.Degree(0);
            int  vDegree     = ghNurbsSurface.Degree(1);
            bool isUClosed   = ghNurbsSurface.IsClosed(0);
            bool isVClosed   = ghNurbsSurface.IsClosed(1);
            bool isUPeriodic = ghNurbsSurface.IsPeriodic(0);
            bool isVPeriodic = ghNurbsSurface.IsPeriodic(1);
            bool isRational  = ghNurbsSurface.IsRational;
            NurbsSurfaceKnotList ghUKnots = ghNurbsSurface.KnotsU;
            List <double>        uKnots   = ghUKnots.ToList();

            NurbsSurfaceKnotList ghVKnots = ghNurbsSurface.KnotsV;
            List <double>        vKnots   = ghVKnots.ToList();

            // OCCT-compatible
            uKnots.Insert(0, uKnots[0]);
            uKnots.Add(uKnots.Last());
            vKnots.Insert(0, vKnots[0]);
            vKnots.Add(vKnots.Last());

            NurbsSurfacePointList           ghControlPoints = ghNurbsSurface.Points;
            List <List <Topologic.Vertex> > controlPoints   = new List <List <Topologic.Vertex> >();
            List <List <double> >           weights         = new List <List <double> >();

            for (int i = 0; i < ghControlPoints.CountU; ++i)
            {
                List <Topologic.Vertex> controlPoints1D = new List <Topologic.Vertex>();
                List <double>           weights1D       = new List <double>();
                for (int j = 0; j < ghControlPoints.CountV; ++j)
                {
                    ControlPoint ghControlPoint = ghControlPoints.GetControlPoint(i, j);
                    controlPoints1D.Add(ByPoint(ghControlPoint.Location));
                    weights1D.Add(ghControlPoint.Weight);
                }
                controlPoints.Add(controlPoints1D);
                weights.Add(weights1D);
            }

            return(Topologic.Face.ByNurbsParameters(controlPoints, weights, uKnots, vKnots, isRational, isUPeriodic, isVPeriodic, uDegree, vDegree));
        }
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        //public static IEnumerable<NXOpen.BRepBuilderEdgeGeometry> ToHost(BrepEdge edge)
        //{
        //    var edgeCurve = edge.EdgeCurve.Trim(edge.Domain);

        //    if (edge.ProxyCurveIsReversed)
        //        edgeCurve.Reverse();

        //    switch (edgeCurve)
        //    {
        //        case LineCurve line:
        //            yield return NXOpen.BRepBuilderEdgeGeometry.Create(ToHost(line));
        //            yield break;
        //        case ArcCurve arc:
        //            yield return NXOpen.BRepBuilderEdgeGeometry.Create(ToHost(arc));
        //            yield break;
        //        case NurbsCurve nurbs:
        //            yield return NXOpen.BRepBuilderEdgeGeometry.Create(ToHost(nurbs));
        //            yield break;
        //        default:
        //            Debug.Fail($"{edgeCurve} is not supported as a Solid Edge");
        //            yield break;
        //    }
        //}

        public static double[] ToHost(NurbsSurfaceKnotList list)
        {
            //list.CreateUniformKnots(1.0);

            var count = list.Count;
            var knots = new double[count + 2];

            var minValue = list.First();
            var maxValue = list.Last();

            var range = maxValue - minValue;

            int j = 0, k = 0;

            while (j < count)
            {
                knots[++k] = (list[j++] - minValue) / range;
            }

            knots[0]         = knots[1];
            knots[count + 1] = knots[count];

            return(knots);
        }
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        //public static Parasite_BrepSurface ToParasiteType(this DB.Face face, bool untrimmed = false)
        //{
        //    var surface = face.ToRhinoSurface();
        //    if (surface is null)
        //        return null;

        //    var brep = Brep.CreateFromSurface(surface);
        //    if (brep is null)
        //        return null;


        //    if (untrimmed)
        //        return brep;

        //    var loops = face.GetEdgesAsCurveLoops().ToRhino().ToArray();



        //    try { return brep.TrimFaces(loops); }
        //    finally { brep.Dispose(); }
        //}


        //public static Parasite_BrepSolid ToParasiteType(DB.Solid solid)
        //{
        //    return solid.Faces.
        //           Cast<DB.Face>().
        //           Select(x => x.ToRhino()).
        //           ToArray().
        //           JoinAndMerge(Revit.VertexTolerance);
        //}


        #endregion


        #region NURBS SURFACE

        public static Parasite_NurbsSurface ToParasiteType(Rhino.Geometry.NurbsSurface nurbsSurface, Dictionary <string, string> properties = null)
        {
            Parasite_NurbsSurface parasite_NurbsSurface = null;

            if (!nurbsSurface.IsValid)
            {
                throw new ParasiteArgumentException("Please enter a valid Rhino Nurbs Surface");
            }

            else
            {
                if (nurbsSurface.IsSphere())
                {
                    throw new ParasiteNotImplementedExceptions("There is still no support for Rhino NURBS Spheres");
                }

                else if (nurbsSurface.IsTorus())
                {
                    throw new ParasiteNotImplementedExceptions("There is still no support for Rhino NURBS Torus");
                }

                else
                {
                    NurbsSurfaceKnotList  rhinoKnotsU = nurbsSurface.KnotsU;
                    NurbsSurfaceKnotList  rhinoKnotsV = nurbsSurface.KnotsV;
                    NurbsSurfacePointList cp          = nurbsSurface.Points;

                    double[]   knotsU  = new double[rhinoKnotsU.Count];
                    double[]   knotsV  = new double[rhinoKnotsV.Count];
                    double[][] weights = new double[cp.Count()][];

                    if (cp.Any((x) => !x.Location.IsValid))
                    {
                        throw new ParasiteArgumentException("The Rhino NURBS Surface had an invalid Control Point!");
                    }

                    Parasite_Point3d[][] vertices = new Parasite_Point3d[cp.Count()][];

                    for (int i = 0; i < rhinoKnotsU.Count; i++)
                    {
                        knotsU[i] = rhinoKnotsU[i];
                        knotsV[i] = rhinoKnotsV[i];
                    }


                    //for (int u = 0; u < cp.CountU; u++)
                    //{
                    //    for (int v = 0; v < cp.CountV; v++)
                    //    {
                    //        Point3d controlP = cp.GetControlPoint(u, v).Location;
                    //        double weight = cp.GetWeight(u, v);

                    //    }
                    //}



                    int count = -1;
                    foreach (var item in cp)
                    {
                        count++;
                        if (item.Weight <= 1e-11)
                        {
                            weights[count] = new double[] { 0.0 }
                        }
                        ;

                        weights[count]  = new double[] { item.Weight };
                        vertices[count] = new Parasite_Point3d[] { ToParasiteType(item.Location) };
                    }

                    parasite_NurbsSurface = new Parasite_NurbsSurface(vertices, knotsU, knotsV, weights, nurbsSurface.Degree(0), nurbsSurface.Degree(1));
                }
            }

            return(parasite_NurbsSurface);
        }

        #endregion

        #endregion
    }