Graph3D.cs

using System;
using System.Collections;
using System.Collections.Generic;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;
using System.Xml;
using SkiaSharp;
using Waher.Runtime.Inventory;
using Waher.Script.Abstraction.Elements;
using Waher.Script.Abstraction.Sets;
using Waher.Script.Exceptions;
using Waher.Script.Functions.Vectors;
using Waher.Script.Graphs;
using Waher.Script.Model;
using Waher.Script.Objects;
using Waher.Script.Objects.Matrices;
using Waher.Script.Objects.VectorSpaces;
using Waher.Script.Operators.Vectors;
using Waher.Script.Units;
 
namespace Waher.Script.Graphs3D
{
    public class Graph3D : Graph
    {
        private readonly LinkedList<IMatrix> x = new LinkedList<IMatrix>();
        private readonly LinkedList<IMatrix> y = new LinkedList<IMatrix>();
        private readonly LinkedList<IMatrix> z = new LinkedList<IMatrix>();
        private readonly LinkedList<Vector4[,]> normals = new LinkedList<Vector4[,]>();
        private readonly LinkedList<object[]> parameters = new LinkedList<object[]>();
        private readonly LinkedList<IPainter3D> painters = new LinkedList<IPainter3D>();
        private IElement minX, maxX;
        private IElement minY, maxY;
        private IElement minZ, maxZ;
        private Type axisTypeX;
        private Type axisTypeY;
        private Type axisTypeZ;
        private string title = string.Empty;
        private string labelX = string.Empty;
        private string labelY = string.Empty;
        private string labelZ = string.Empty;
        private double angle = 20;
        private double inclination = 30;
        private int overSampling = 2;
        private bool showXAxis = true;
        private bool showYAxis = true;
        private bool showZAxis = true;
        private bool showGrid = true;
        //private readonly bool showZeroX = false;
        //private readonly bool showZeroY = false;
        //private readonly bool showZeroZ = false;
 
        public Graph3D(Variables Variables)
            : this(Variables, null, null)
        {
        }
 
        public Graph3D(Variables Variables, int? DefaultWidth, int? DefaultHeight)
            : base(Variables, DefaultWidth, DefaultHeight)
        {
        }
 
        public Graph3D(GraphSettings Settings)
            : base(Settings)
        {
        }
 
        public Graph3D(Variables Variables, IMatrix X, IMatrix Y, IMatrix Z, Vector4[,] Normals, IPainter3D Painter,
            bool ShowZeroX, bool ShowZeroY, bool ShowZeroZ, ScriptNode Node, params object[] Parameters)
            : base(Variables)
        {
            int c = X.Columns;
            int d = X.Rows;
            IElement Zero;
 
            if (c != Y.Columns || d != Y.Rows || c != Z.Columns || d != Z.Rows)
                throw new ScriptException("X, Y and Z matrices must be of equal dimensions.");
 
            if (!(Normals is null) && (c != Normals.GetLength(0) || d != Normals.GetLength(1)))
                throw new ScriptException("Normal matrix must be of equal dimensions as axes.");
 
            //this.showZeroX = ShowZeroX;
            //this.showZeroY = ShowZeroY;
            //this.showZeroZ = ShowZeroZ;
 
            this.minX = Min.CalcMin(X, Node);
            this.maxX = Max.CalcMax(X, Node);
 
            if (ShowZeroX && c > 0 && this.minX.AssociatedSet is IAbelianGroup AG)
            {
                Zero = AG.AdditiveIdentity;
 
                this.minX = Min.CalcMin(new ObjectVector(this.minX, Zero), null);
                this.maxX = Max.CalcMax(new ObjectVector(this.maxX, Zero), null);
            }
 
            this.minY = Min.CalcMin(Y, Node);
            this.maxY = Max.CalcMax(Y, Node);
 
            if (ShowZeroY && c > 0 && this.minY.AssociatedSet is IAbelianGroup AG2)
            {
                Zero = AG2.AdditiveIdentity;
 
                this.minY = Min.CalcMin(new ObjectVector(this.minY, Zero), null);
                this.maxY = Max.CalcMax(new ObjectVector(this.maxY, Zero), null);
            }
 
            this.minZ = Min.CalcMin(Z, Node);
            this.maxZ = Max.CalcMax(Z, Node);
 
            if (ShowZeroZ && c > 0 && this.minZ.AssociatedSet is IAbelianGroup AG3)
            {
                Zero = AG3.AdditiveIdentity;
 
                this.minZ = Min.CalcMin(new ObjectVector(this.minZ, Zero), null);
                this.maxZ = Max.CalcMax(new ObjectVector(this.maxZ, Zero), null);
            }
 
            this.axisTypeX = X.GetType();
            this.axisTypeY = Y.GetType();
            this.axisTypeZ = Z.GetType();
 
            if (c > 0)
            {
                this.x.AddLast(X);
                this.y.AddLast(Y);
                this.z.AddLast(Z);
                this.normals.AddLast(Normals);
                this.painters.AddLast(Painter);
                this.parameters.AddLast(Parameters);
            }
        }
 
        public LinkedList<IMatrix> X => this.x;
 
        public LinkedList<IMatrix> Y => this.y;
 
        public LinkedList<IMatrix> Z => this.z;
 
        public LinkedList<Vector4[,]> Normals => this.normals;
 
        public LinkedList<object[]> Parameters => this.parameters;
 
        public IElement MinX => this.minX;
 
        public IElement MaxX => this.maxX;
 
        public IElement MinY => this.minY;
 
        public IElement MaxY => this.maxY;
 
        public IElement MinZ => this.minZ;
 
        public IElement MaxZ => this.maxZ;
 
        public string Title
        {
            get => this.title;
            set => this.title = value;
        }
 
        public string LabelX
        {
            get => this.labelX;
            set => this.labelX = value;
        }
 
        public string LabelY
        {
            get => this.labelY;
            set => this.labelY = value;
        }
 
        public string LabelZ
        {
            get => this.labelZ;
            set => this.labelZ = value;
        }
 
        public bool ShowXAxis
        {
            get => this.showXAxis;
            set => this.showXAxis = value;
        }
 
        public bool ShowYAxis
        {
            get => this.showYAxis;
            set => this.showYAxis = value;
        }
 
        public bool ShowZAxis
        {
            get => this.showZAxis;
            set => this.showZAxis = value;
        }
 
        public bool ShowGrid
        {
            get => this.showGrid;
            set => this.showGrid = value;
        }
 
        public double Angle
        {
            get => this.angle;
            set => this.angle = value;
        }
 
        public double Inclination
        {
            get => this.inclination;
            set => this.inclination = value;
        }
 
        public int Oversampling
        {
            get => this.overSampling;
            set
            {
                if (value < 1)
                    throw new ArgumentException("Must be a positive integer.", nameof(this.Oversampling));
 
                this.overSampling = value;
            }
        }
 
        public override ISemiGroupElement AddLeft(ISemiGroupElement Element)
        {
            return Element.AddRight(this);
        }
 
        public override ISemiGroupElement AddRight(ISemiGroupElement Element)
        {
            return this.AddRight(Element, false);
        }
 
        public override ISemiGroupElementWise AddLeftElementWise(ISemiGroupElementWise Element)
        {
            return Element.AddRightElementWise(this);
        }
 
        public override ISemiGroupElementWise AddRightElementWise(ISemiGroupElementWise Element)
        {
            return this.AddRight(Element, true) as ISemiGroupElementWise;
        }
 
        protected ISemiGroupElement AddRight(ISemiGroupElement Element, bool _)
        {
            if (this.x.First is null)
                return Element;
 
            if (!(Element is Graph3D G))
                return null;
 
            if (G.x.First is null)
                return this;
 
            Graph3D Result = new Graph3D(this.Settings)
            {
                axisTypeX = this.axisTypeX,
                axisTypeY = this.axisTypeY,
                axisTypeZ = this.axisTypeZ,
                title = this.title,
                labelX = this.labelX,
                labelY = this.labelY,
                labelZ = this.labelZ,
                SameScale = this.SameScale
            };
 
            foreach (IMatrix M in this.x)
                Result.x.AddLast(M);
 
            foreach (IMatrix M in this.y)
                Result.y.AddLast(M);
 
            foreach (IMatrix M in this.z)
                Result.z.AddLast(M);
 
            foreach (Vector4[,] M in this.normals)
                Result.normals.AddLast(M);
 
            foreach (IPainter3D Painter in this.painters)
                Result.painters.AddLast(Painter);
 
            foreach (object[] P in this.parameters)
                Result.parameters.AddLast(P);
 
            foreach (IMatrix M in G.x)
            {
                if (M.GetType() != this.axisTypeX)
                    throw new ScriptException("Incompatible types of series.");
 
                Result.x.AddLast(M);
            }
 
            foreach (IMatrix M in G.y)
            {
                if (M.GetType() != this.axisTypeY)
                    throw new ScriptException("Incompatible types of series.");
 
                Result.y.AddLast(M);
            }
 
            foreach (IMatrix M in G.z)
            {
                if (M.GetType() != this.axisTypeZ)
                    throw new ScriptException("Incompatible types of series.");
 
                Result.z.AddLast(M);
            }
 
            foreach (Vector4[,] M in G.normals)
                Result.normals.AddLast(M);
 
            foreach (IPainter3D Painter in G.painters)
                Result.painters.AddLast(Painter);
 
            foreach (object[] P in G.parameters)
                Result.parameters.AddLast(P);
 
            Result.minX = Min.CalcMin((IVector)VectorDefinition.Encapsulate(new IElement[] { this.minX, G.minX }, false, null), null);
            Result.maxX = Max.CalcMax((IVector)VectorDefinition.Encapsulate(new IElement[] { this.maxX, G.maxX }, false, null), null);
            Result.minY = Min.CalcMin((IVector)VectorDefinition.Encapsulate(new IElement[] { this.minY, G.minY }, false, null), null);
            Result.maxY = Max.CalcMax((IVector)VectorDefinition.Encapsulate(new IElement[] { this.maxY, G.maxY }, false, null), null);
            Result.minZ = Min.CalcMin((IVector)VectorDefinition.Encapsulate(new IElement[] { this.minZ, G.minZ }, false, null), null);
            Result.maxZ = Max.CalcMax((IVector)VectorDefinition.Encapsulate(new IElement[] { this.maxZ, G.maxZ }, false, null), null);
 
            Result.showXAxis |= G.showXAxis;
            Result.showYAxis |= G.showYAxis;
            Result.showZAxis |= G.showZAxis;
 
            return Result;
        }
 
        public override bool Equals(object obj)
        {
            if (!(obj is Graph3D G))
                return false;
 
            return (
                this.minX.Equals(G.minX) &&
                this.maxX.Equals(G.maxX) &&
                this.minY.Equals(G.minY) &&
                this.maxY.Equals(G.maxY) &&
                this.minZ.Equals(G.minZ) &&
                this.maxZ.Equals(G.maxZ) &&
                this.axisTypeX.Equals(G.axisTypeX) &&
                this.axisTypeY.Equals(G.axisTypeY) &&
                this.axisTypeZ.Equals(G.axisTypeZ) &&
                this.title.Equals(G.title) &&
                this.labelX.Equals(G.labelX) &&
                this.labelY.Equals(G.labelY) &&
                this.labelZ.Equals(G.labelZ) &&
                this.showXAxis.Equals(G.showXAxis) &&
                this.showYAxis.Equals(G.showYAxis) &&
                this.showZAxis.Equals(G.showZAxis) &&
                this.showGrid.Equals(G.showGrid) &&
                this.Equals(this.x.GetEnumerator(), G.x.GetEnumerator()) &&
                this.Equals(this.y.GetEnumerator(), G.y.GetEnumerator()) &&
                this.Equals(this.z.GetEnumerator(), G.z.GetEnumerator()) &&
                this.Equals(this.normals?.GetEnumerator(), G.normals?.GetEnumerator()) &&
                this.Equals(this.parameters.GetEnumerator(), G.parameters.GetEnumerator()) &&
                this.Equals(this.painters.GetEnumerator(), G.painters.GetEnumerator()));
        }
 
        private bool Equals(IEnumerator e1, IEnumerator e2)
        {
            if ((e1 is null) ^ (e2 is null))
                return false;
 
            if (e1 is null)
                return true;
 
            bool b1 = e1.MoveNext();
            bool b2 = e2.MoveNext();
 
            while (b1 && b2)
            {
                if (!e1.Current.Equals(e2.Current))
                    return false;
 
                b1 = e1.MoveNext();
                b2 = e2.MoveNext();
            }
 
            return !(b1 || b2);
        }
 
        public override int GetHashCode()
        {
            int Result = this.minX.GetHashCode();
            Result ^= Result << 5 ^ this.maxX.GetHashCode();
            Result ^= Result << 5 ^ this.minY.GetHashCode();
            Result ^= Result << 5 ^ this.maxY.GetHashCode();
            Result ^= Result << 5 ^ this.minZ.GetHashCode();
            Result ^= Result << 5 ^ this.maxZ.GetHashCode();
            Result ^= Result << 5 ^ this.axisTypeX.GetHashCode();
            Result ^= Result << 5 ^ this.axisTypeY.GetHashCode();
            Result ^= Result << 5 ^ this.axisTypeZ.GetHashCode();
            Result ^= Result << 5 ^ this.title.GetHashCode();
            Result ^= Result << 5 ^ this.labelX.GetHashCode();
            Result ^= Result << 5 ^ this.labelY.GetHashCode();
            Result ^= Result << 5 ^ this.labelZ.GetHashCode();
            Result ^= Result << 5 ^ this.showXAxis.GetHashCode();
            Result ^= Result << 5 ^ this.showYAxis.GetHashCode();
            Result ^= Result << 5 ^ this.showZAxis.GetHashCode();
            Result ^= Result << 5 ^ this.showGrid.GetHashCode();
 
            foreach (IElement E in this.x)
                Result ^= Result << 5 ^ E.GetHashCode();
 
            foreach (IElement E in this.y)
                Result ^= Result << 5 ^ E.GetHashCode();
 
            foreach (IElement E in this.z)
                Result ^= Result << 5 ^ E.GetHashCode();
 
            if (!(this.normals is null))
            {
                foreach (Vector4[,] Normals in this.normals)
                    Result ^= Result << 5 ^ Normals.GetHashCode();
            }
 
            foreach (object Obj in this.parameters)
                Result ^= Result << 5 ^ Obj.GetHashCode();
 
            foreach (IPainter3D Painter in this.painters)
                Result ^= Result << 5 ^ Painter.GetHashCode();
 
            return Result;
        }
 
        public override PixelInformation CreatePixels(GraphSettings Settings, out object[] States)
        {
            IVector XLabels = GetLabels(ref this.minX, ref this.maxX, this.x, Settings.ApproxNrLabelsX, out LabelType XLabelType);
            IVector YLabels = GetLabels(ref this.minY, ref this.maxY, this.y, Settings.ApproxNrLabelsY, out LabelType YLabelType);
            IVector ZLabels = GetLabels(ref this.minZ, ref this.maxZ, this.z, Settings.ApproxNrLabelsX, out LabelType ZLabelType);
 
            int OffsetX = -500;
            int OffsetY = -500;
            int OffsetZ = 1000;
            int Width = 1000;
            int Height = 1000;
            int Depth = 1000;
            float? OrigoX;
            float? OrigoY;
            float? OrigoZ;
 
            if (this.SameScale &&
                this.minX.AssociatedObjectValue is double MinX &&
                this.maxX.AssociatedObjectValue is double MaxX &&
                this.minY.AssociatedObjectValue is double MinY &&
                this.maxY.AssociatedObjectValue is double MaxY &&
                this.minZ.AssociatedObjectValue is double MinZ &&
                this.maxZ.AssociatedObjectValue is double MaxZ)
            {
                double DX = MaxX - MinX;
                double DY = MaxY - MinY;
                double DZ = MaxZ - MinZ;
                double SX = Width / (DX == 0 ? 1 : DX);
                double SY = Height / (DY == 0 ? 1 : DY);
                double SZ = Depth / (DZ == 0 ? 1 : DZ);
                double MinScale = Math.Min(SX, Math.Min(SY, SZ));
 
                if (SX == MinScale)
                {
                    int Height2 = (int)(Height * SX / SY + 0.5);
                    OffsetY += (Height - Height2) / 2;
                    Height = Height2;
 
                    int Depth2 = (int)(Depth * SX / SZ + 0.5);
                    OffsetZ += (Depth - Depth2) / 2;
                    Depth = Depth2;
                }
                else if (SY == MinScale)
                {
                    int Width2 = (int)(Width * SY / SX + 0.5);
                    OffsetX += (Width - Width2) / 2;
                    Width = Width2;
 
                    int Depth2 = (int)(Depth * SY / SZ + 0.5);
                    OffsetZ += (Depth - Depth2) / 2;
                    Depth = Depth2;
                }
                else
                {
                    int Width2 = (int)(Width * SZ / SX + 0.5);
                    OffsetX += (Width - Width2) / 2;
                    Width = Width2;
 
                    int Height2 = (int)(Height * SZ / SY + 0.5);
                    OffsetY += (Height - Height2) / 2;
                    Height = Height2;
                }
            }
 
            if (this.minX.AssociatedSet is IAbelianGroup AgX)
                OrigoX = (float)Scale(new ObjectVector(AgX.AdditiveIdentity), this.minX, this.maxX, OffsetX, Width, null)[0];
            else
                OrigoX = null;
 
            if (this.minY.AssociatedSet is IAbelianGroup AgY)
                OrigoY = (float)Scale(new ObjectVector(AgY.AdditiveIdentity), this.minY, this.maxY, OffsetY, Height, null)[0];
            else
                OrigoY = null;
 
            if (this.minZ.AssociatedSet is IAbelianGroup AgZ)
                OrigoZ = (float)Scale(new ObjectVector(AgZ.AdditiveIdentity), this.maxZ, this.minZ, OffsetZ, Depth, null)[0];
            else
                OrigoZ = null;
 
            float PlaneX = OrigoX ?? OffsetX;
            float PlaneY = OrigoY ?? OffsetY;
            float PlaneZ = OrigoZ ?? OffsetZ + Depth;
 
            DrawingVolume DrawingVolume = new DrawingVolume(this.minX, this.maxX,
                this.minY, this.maxY, this.minZ, this.maxZ, OffsetX, OffsetY, OffsetZ,
                Width, Height, Depth, OrigoX, OrigoY, OrigoZ);
 
            Dictionary<string, double> XLabelPositions = XLabelType == LabelType.String ? new Dictionary<string, double>() : null;
            Dictionary<string, double> YLabelPositions = YLabelType == LabelType.String ? new Dictionary<string, double>() : null;
            Dictionary<string, double> ZLabelPositions = ZLabelType == LabelType.String ? new Dictionary<string, double>() : null;
            double[] LabelXX = DrawingVolume.ScaleX(XLabels);
            double[] LabelYY = DrawingVolume.ScaleY(YLabels);
            double[] LabelZZ = DrawingVolume.ScaleZ(ZLabels);
            string[] XLabelStrings = LabelStrings(XLabels, XLabelType);
            string[] YLabelStrings = LabelStrings(YLabels, YLabelType);
            string[] ZLabelStrings = LabelStrings(ZLabels, ZLabelType);
            string s;
            int i;
 
            if (!(XLabelPositions is null))
            {
                i = 0;
 
                foreach (IElement Label in XLabels.ChildElements)
                {
                    s = XLabelStrings[i];
                    XLabelPositions[s] = LabelXX[i++];
                }
            }
 
            if (!(YLabelPositions is null))
            {
                i = 0;
 
                foreach (IElement Label in YLabels.ChildElements)
                {
                    s = YLabelStrings[i];
                    YLabelPositions[s] = LabelYY[i++];
                }
            }
 
            if (!(ZLabelPositions is null))
            {
                i = 0;
 
                foreach (IElement Label in ZLabels.ChildElements)
                {
                    s = ZLabelStrings[i];
                    ZLabelPositions[s] = LabelZZ[i++];
                }
            }
 
            DrawingVolume.XLabelPositions = XLabelPositions;
            DrawingVolume.YLabelPositions = YLabelPositions;
            DrawingVolume.ZLabelPositions = ZLabelPositions;
 
            Canvas3D Canvas = new Canvas3D(Settings, Settings.Width, Settings.Height, this.overSampling, Settings.BackgroundColor);
 
            Canvas.Perspective(Settings.Height / 2, 2000);
            Canvas.RotateX(-(float)this.inclination, new Vector3(0, 0, 1500));
            Canvas.RotateY((float)this.angle, new Vector3(0, 0, 1500));
 
            IEnumerator<IMatrix> ex = this.x.GetEnumerator();
            IEnumerator<IMatrix> ey = this.y.GetEnumerator();
            IEnumerator<IMatrix> ez = this.z.GetEnumerator();
            IEnumerator<Vector4[,]> eN = this.normals.GetEnumerator();
            IEnumerator<object[]> eParameters = this.parameters.GetEnumerator();
            IEnumerator<IPainter3D> ePainters = this.painters.GetEnumerator();
            Vector4[,] Points;
            Vector4[,] Normals;
            Vector4[,] PrevPoints = null;
            Vector4[,] PrevNormals = null;
            object[] PrevParameters = null;
            IPainter3D PrevPainter = null;
 
            while (ex.MoveNext() && ey.MoveNext() && ez.MoveNext() &&
                eN.MoveNext() && eParameters.MoveNext() && ePainters.MoveNext())
            {
                Points = DrawingVolume.Scale(ex.Current, ey.Current, ez.Current);
                Normals = eN.Current;
 
                if (!(PrevPainter is null) && ePainters.Current.GetType() == PrevPainter.GetType())
                    ePainters.Current.DrawGraph(Canvas, Points, Normals, eParameters.Current, PrevPoints, PrevNormals, PrevParameters, DrawingVolume);
                else
                    ePainters.Current.DrawGraph(Canvas, Points, Normals, eParameters.Current, null, null, null, DrawingVolume);
 
                PrevPoints = Points;
                PrevNormals = Normals;
                PrevParameters = eParameters.Current;
                PrevPainter = ePainters.Current;
            }
 
            Matrix4x4 M = Canvas.ModelTransformation;
            float LabelMargin = (float)Settings.LabelFontSize * 0.1f;
            float TextSize0 = (float)Settings.LabelFontSize * 5;
            float TextSize = this.CalcTextSize(LabelXX, TextSize0);
            SKSize Size;
            float f;
 
            i = 0;
 
            foreach (IElement Label in XLabels.ChildElements)
            {
                s = XLabelStrings[i];
                Size = Canvas.TextDimensions(s, Settings.FontName, TextSize);
 
                f = (float)LabelXX[i++];
 
                if (this.showGrid)
                {
                    if (Label.AssociatedObjectValue is double DLbl && DLbl == 0)
                    {
                        this.DrawPlaneLine(Canvas,
                            new Vector4(f, PlaneY, OffsetZ, 1),
                            new Vector4(f, PlaneY, OffsetZ + Depth, 1),
                            Settings.AxisColor, 3);
 
                        this.DrawPlaneLine(Canvas,
                            new Vector4(f, OffsetY, PlaneZ, 1),
                            new Vector4(f, OffsetY + Height, PlaneZ, 1),
                            Settings.AxisColor, 3);
                    }
                    else
                    {
                        this.DrawPlaneLine(Canvas,
                            new Vector4(f, PlaneY, OffsetZ, 1),
                            new Vector4(f, PlaneY, OffsetZ + Depth, 1),
                            Settings.GridColor, 3);
 
                        this.DrawPlaneLine(Canvas,
                            new Vector4(f, OffsetY, PlaneZ, 1),
                            new Vector4(f, OffsetY + Height, PlaneZ, 1),
                            Settings.GridColor, 3);
                    }
                }
 
                if (this.showXAxis)
                {
                    Canvas.Translate(f, PlaneY, OffsetZ);
                    Canvas.RotateY(-90);
                    Canvas.RotateX(90);
                    Canvas.Text(s,
                        new Vector4(-5 * LabelMargin - Size.Width, LabelMargin - Size.Height / 2, 0, 1),
                        Settings.FontName, TextSize, Settings.AxisColor);
                    Canvas.ModelTransformation = M;
                }
            }
 
            if (!string.IsNullOrEmpty(this.labelX))
            {
                Size = Canvas.TextDimensions(this.labelX, Settings.FontName, TextSize0 * 1.25f);
 
                Canvas.Translate(OffsetX + Width / 2, PlaneY, OffsetZ);
                Canvas.RotateX(90);
                Canvas.Text(this.labelX,
                    new Vector4(-Size.Width / 2, -2 * Size.Height, 0, 1),
                    Settings.FontName, TextSize0 * 1.25f, Settings.AxisColor);
                Canvas.ModelTransformation = M;
            }
 
            i = 0;
            TextSize = this.CalcTextSize(LabelZZ, TextSize0);
 
            foreach (IElement Label in ZLabels.ChildElements)
            {
                s = ZLabelStrings[i];
                Size = Canvas.TextDimensions(s, Settings.FontName, TextSize);
 
                f = (float)LabelZZ[i++];
 
                if (this.showGrid)
                {
                    if (Label.AssociatedObjectValue is double DLbl && DLbl == 0)
                    {
                        this.DrawPlaneLine(Canvas,
                            new Vector4(OffsetX, PlaneY, f, 1),
                            new Vector4(OffsetX + Width, PlaneY, f, 1),
                            Settings.AxisColor, 3);
 
                        this.DrawPlaneLine(Canvas,
                            new Vector4(PlaneX, OffsetY, f, 1),
                            new Vector4(PlaneX, OffsetY + Height, f, 1),
                            Settings.AxisColor, 3);
                    }
                    else
                    {
                        this.DrawPlaneLine(Canvas,
                            new Vector4(OffsetX, PlaneY, f, 1),
                            new Vector4(OffsetX + Width, PlaneY, f, 1),
                            Settings.GridColor, 3);
 
                        this.DrawPlaneLine(Canvas,
                            new Vector4(PlaneX, OffsetY, f, 1),
                            new Vector4(PlaneX, OffsetY + Height, f, 1),
                            Settings.GridColor, 3);
                    }
                }
 
                if (this.showZAxis)
                {
                    Canvas.Translate(OffsetX + Width, PlaneY, f);
                    Canvas.RotateX(90);
                    Canvas.Text(s,
                        new Vector4(5 * LabelMargin, LabelMargin - Size.Height / 2, 0, 1),
                        Settings.FontName, TextSize, Settings.AxisColor);
                    Canvas.ModelTransformation = M;
                }
            }
 
            if (!string.IsNullOrEmpty(this.labelZ))
            {
                Size = Canvas.TextDimensions(this.labelZ, Settings.FontName, TextSize0 * 1.25f);
 
                Canvas.Translate(OffsetX + Width, PlaneY, OffsetZ + Depth / 2);
                Canvas.RotateY(-90);
                Canvas.RotateX(90);
                Canvas.Text(this.labelZ,
                    new Vector4(-Size.Width / 2, -2 * Size.Height, 0, 1),
                    Settings.FontName, TextSize0 * 1.25f, Settings.AxisColor);
                Canvas.ModelTransformation = M;
            }
 
            i = 0;
            TextSize = this.CalcTextSize(LabelYY, TextSize0);
 
            foreach (IElement Label in YLabels.ChildElements)
            {
                s = YLabelStrings[i];
                Size = Canvas.TextDimensions(s, Settings.FontName, TextSize);
 
                f = (float)LabelYY[i++];
 
                if (this.showGrid)
                {
                    if (Label.AssociatedObjectValue is double DLbl && DLbl == 0)
                    {
                        this.DrawPlaneLine(Canvas,
                            new Vector4(PlaneX, f, OffsetZ, 1),
                            new Vector4(PlaneX, f, OffsetZ + Depth, 1),
                            Settings.AxisColor, 3);
 
                        this.DrawPlaneLine(Canvas,
                            new Vector4(OffsetX, f, PlaneZ, 1),
                            new Vector4(OffsetX + Width, f, PlaneZ, 1),
                            Settings.AxisColor, 3);
                    }
                    else
                    {
                        this.DrawPlaneLine(Canvas,
                            new Vector4(PlaneX, f, OffsetZ, 1),
                            new Vector4(PlaneX, f, OffsetZ + Depth, 1),
                            Settings.GridColor, 3);
 
                        this.DrawPlaneLine(Canvas,
                            new Vector4(OffsetX, f, PlaneZ, 1),
                            new Vector4(OffsetX + Width, f, PlaneZ, 1),
                            Settings.GridColor, 3);
                    }
                }
 
                if (this.showYAxis)
                {
                    Canvas.Translate(OffsetX, f, PlaneZ);
                    Canvas.Text(s,
                        new Vector4(-5 * LabelMargin - Size.Width, LabelMargin - Size.Height / 2, 0, 1),
                        Settings.FontName, TextSize, Settings.AxisColor);
                    Canvas.ModelTransformation = M;
                }
            }
 
            if (!string.IsNullOrEmpty(this.labelY))
            {
                Size = Canvas.TextDimensions(this.labelY, Settings.FontName, TextSize0 * 1.25f);
 
                Canvas.Translate(OffsetX, OffsetY + Height / 2, PlaneZ);
                Canvas.RotateZ(90);
                Canvas.Text(this.labelY,
                    new Vector4(-Size.Width / 2, 2 * Size.Height, 0, 1),
                    Settings.FontName, TextSize0 * 1.25f, Settings.AxisColor);
                Canvas.ModelTransformation = M;
            }
 
            if (!string.IsNullOrEmpty(this.title))
            {
                Size = Canvas.TextDimensions(this.title, Settings.FontName, TextSize0 * 1.5f);
 
                Canvas.Translate(OffsetX + Width / 2, OffsetY + Height, OffsetZ + Depth / 2);
                Canvas.Text(this.title,
                    new Vector4(-Size.Width / 2, Size.Height / 2, 0, 1),
                    Settings.FontName, TextSize0 * 1.5f, Settings.AxisColor);
                Canvas.ModelTransformation = M;
            }
 
            I3DShader AxisPlaneShader = ToShader(new SKColor(Settings.AxisColor.Red,
                Settings.AxisColor.Green, Settings.AxisColor.Blue, 32));
 
            this.DrawPlane(Canvas,
                new Vector4(OffsetX, OffsetY, PlaneZ, 1),
                new Vector4(OffsetX + Width, OffsetY, PlaneZ, 1),
                new Vector4(OffsetX + Width, OffsetY + Height, PlaneZ, 1),
                new Vector4(OffsetX, OffsetY + Height, PlaneZ, 1),
                AxisPlaneShader, true, 3);
 
            this.DrawPlane(Canvas,
                new Vector4(OffsetX, PlaneY, OffsetZ, 1),
                new Vector4(OffsetX + Width, PlaneY, OffsetZ, 1),
                new Vector4(OffsetX + Width, PlaneY, OffsetZ + Depth, 1),
                new Vector4(OffsetX, PlaneY, OffsetZ + Depth, 1),
                AxisPlaneShader, true, 3);
 
            this.DrawPlane(Canvas,
                new Vector4(PlaneX, OffsetY, OffsetZ, 1),
                new Vector4(PlaneX, OffsetY, OffsetZ + Depth, 1),
                new Vector4(PlaneX, OffsetY + Height, OffsetZ + Depth, 1),
                new Vector4(PlaneX, OffsetY + Height, OffsetZ, 1),
                AxisPlaneShader, true, 3);
 
            return Canvas.CreatePixels(Settings, out States);
        }
 
        private float CalcTextSize(double[] LabelPositions, float TextSize)
        {
            int i, c = LabelPositions.Length;
            float Diff;
 
            for (i = 1; i < c; i++)
            {
                Diff = (float)(Math.Abs(LabelPositions[i] - LabelPositions[i - 1]));
                if (Diff < TextSize)
                    TextSize = Diff;
            }
 
            return TextSize;
        }
 
        private void DrawPlaneLine(Canvas3D Canvas, Vector4 P0, Vector4 P1,
            SKColor Color, int Halvings)
        {
            if (Halvings == 0)
                Canvas.Line(P0, P1, Color);
            else
            {
                Halvings--;
 
                Vector4 Pm = (P0 + P1) / 2;
 
                this.DrawPlaneLine(Canvas, P0, Pm, Color, Halvings);
                this.DrawPlaneLine(Canvas, Pm, P1, Color, Halvings);
            }
        }
 
        private void DrawPlane(Canvas3D Canvas, Vector4 P0, Vector4 P1, Vector4 P2, Vector4 P3,
            I3DShader Shader, bool TwoSided, int Halvings)
        {
            if (Halvings == 0)
                Canvas.Polygon(new Vector4[] { P0, P1, P2, P3 }, Shader, TwoSided);
            else
            {
                Halvings--;
 
                Vector4 Pm = (P0 + P1 + P2 + P3) / 4;
                Vector4 P0p = (P3 + P0) / 2;
                Vector4 P1p = (P0 + P1) / 2;
                Vector4 P2p = (P1 + P2) / 2;
                Vector4 P3p = (P2 + P3) / 2;
 
                this.DrawPlane(Canvas, Pm, P2p, P2, P3p, Shader, TwoSided, Halvings);
                this.DrawPlane(Canvas, P1p, P1, P2p, Pm, Shader, TwoSided, Halvings);
                this.DrawPlane(Canvas, P3, P0p, Pm, P3p, Shader, TwoSided, Halvings);
                this.DrawPlane(Canvas, P0p, P0, P1p, Pm, Shader, TwoSided, Halvings);
            }
        }
 
        public static IVector GetLabels(ref IElement Min, ref IElement Max, IEnumerable<IMatrix> Series, int ApproxNrLabels, out LabelType LabelType)
        {
            if (Min.AssociatedObjectValue is double DMin &&
                Max.AssociatedObjectValue is double DMax)
            {
                LabelType = LabelType.Double;
                return new DoubleVector(GetLabels(DMin, DMax, ApproxNrLabels));
            }
            else if (Min.AssociatedObjectValue is DateTime DTMin &&
                Max.AssociatedObjectValue is DateTime DTMax)
            {
                return new DateTimeVector(GetLabels(DTMin, DTMax, ApproxNrLabels, out LabelType));
            }
            else if (Min.AssociatedObjectValue is IPhysicalQuantity PQMin && 
                Max.AssociatedObjectValue is IPhysicalQuantity PQMax)
            {
                LabelType = LabelType.PhysicalQuantity;
                return new ObjectVector(GetLabels(PQMin.ToPhysicalQuantity(), PQMax.ToPhysicalQuantity(), ApproxNrLabels));
            }
            else if (Min.AssociatedObjectValue is string && Max.AssociatedObjectValue is string)
            {
                Dictionary<string, bool> Indices = new Dictionary<string, bool>();
                List<IElement> Labels = new List<IElement>();
                string s;
 
                foreach (IMatrix Matrix in Series)
                {
                    foreach (IElement E in Matrix.ChildElements)
                    {
                        s = E.AssociatedObjectValue.ToString();
                        if (Indices.ContainsKey(s))
                            continue;
 
                        Labels.Add(E);
                        Indices[s] = true;
                    }
                }
 
                LabelType = LabelType.String;
 
                if (Labels.Count > 0)
                {
                    Min = Labels[0];
                    Max = Labels[Labels.Count - 1];
                }
 
                return new ObjectVector(Labels.ToArray());
            }
            else
            {
                SortedDictionary<string, bool> Labels = new SortedDictionary<string, bool>();
 
                foreach (IMatrix Matrix in Series)
                {
                    foreach (IElement E in Matrix.ChildElements)
                        Labels[E.AssociatedObjectValue.ToString()] = true;
                }
 
                string[] Labels2 = new string[Labels.Count];
                Labels.Keys.CopyTo(Labels2, 0);
 
                LabelType = LabelType.String;
                return new ObjectVector(Labels2);
            }
        }
 
        public static Vector4[,] Scale(IMatrix MatrixX, IMatrix MatrixY, IMatrix MatrixZ,
            IElement MinX, IElement MaxX, IElement MinY, IElement MaxY,
            IElement MinZ, IElement MaxZ, double OffsetX, double OffsetY, double OffsetZ,
            double Width, double Height, double Depth, Dictionary<string, double> XLabelPositions,
            Dictionary<string, double> YLabelPositions, Dictionary<string, double> ZLabelPositions)
        {
            int Columns = MatrixX.Columns;
            int Rows = MatrixX.Rows;
 
            if (MatrixY.Columns != Columns || MatrixY.Rows != Rows ||
                MatrixZ.Columns != Columns || MatrixZ.Rows != Rows)
            {
                throw new ScriptException("Dimension mismatch.");
            }
 
            double[,] X = Scale(MatrixX, MinX, MaxX, OffsetX, Width, XLabelPositions);
            double[,] Y = Scale(MatrixY, MinY, MaxY, OffsetY, Height, YLabelPositions);
            double[,] Z = Scale(MatrixZ, MinZ, MaxZ, OffsetZ, Depth, ZLabelPositions);
            int i, j;
            Vector4[,] Points = new Vector4[Columns, Rows];
 
            for (i = 0; i < Columns; i++)
            {
                for (j = 0; j < Rows; j++)
                    Points[i, j] = new Vector4((float)X[i, j], (float)Y[i, j], (float)Z[i, j], 1);
            }
 
            return Points;
        }
 
        public static double[,] Scale(IMatrix Matrix, IElement Min, IElement Max, double Offset,
            double Size, Dictionary<string, double> LabelPositions)
        {
            if (Matrix is DoubleMatrix DM)
            {
                if (!(Min.AssociatedObjectValue is double dMin) ||
                    !(Max.AssociatedObjectValue is double dMax))
                {
                    throw new ScriptException("Incompatible values.");
                }
 
                return Scale(DM.Values, dMin, dMax, Offset, Size);
            }
            else if (Matrix is ObjectMatrix OM)
            {
                IElement[,] Elements = OM.Values;
                IElement E;
                int c = OM.Columns;
                int r = OM.Rows;
                int i, j;
 
                if (Min.AssociatedObjectValue is IPhysicalQuantity PMinQ && 
                    Max.AssociatedObjectValue is IPhysicalQuantity PMaxQ)
                {
                    PhysicalQuantity MinQ = PMinQ.ToPhysicalQuantity();
                    PhysicalQuantity MaxQ = PMaxQ.ToPhysicalQuantity();
 
                    if (MinQ.Unit != MaxQ.Unit)
                    {
                        if (!Unit.TryConvert(MaxQ.Magnitude, MaxQ.Unit, MinQ.Unit, out double d))
                            throw new ScriptException("Incompatible units.");
 
                        MaxQ = new PhysicalQuantity(d, MinQ.Unit);
                    }
 
                    PhysicalQuantity[,] Matrix2 = new PhysicalQuantity[c, r];
                    IPhysicalQuantity Q;
 
                    for (i = 0; i < c; i++)
                    {
                        for (j = 0; j < r; j++)
                        {
                            E = Elements[i, j];
                            Q = E.AssociatedObjectValue as IPhysicalQuantity ?? throw new ScriptException("Incompatible values.");
                            Matrix2[i, j] = Q.ToPhysicalQuantity();
                        }
                    }
 
                    return Scale(Matrix2, MinQ.Magnitude, MaxQ.Magnitude, MinQ.Unit, Offset, Size);
                }
                else
                {
                    if (Min.AssociatedObjectValue is double MinD && 
                        Max.AssociatedObjectValue is double MaxD)
                    {
                        double[,] Matrix2 = new double[c, r];
                        DoubleNumber D;
 
                        for (i = 0; i < c; i++)
                        {
                            for (j = 0; j < r; j++)
                            {
                                E = Elements[i, j];
                                D = E as DoubleNumber ?? throw new ScriptException("Incompatible values.");
                                Matrix2[i, j] = D.Value;
                            }
                        }
 
                        return Scale(Matrix2, MinD, MaxD, Offset, Size);
                    }
                    else
                    {
                        if (Min.AssociatedObjectValue is DateTime MinDT && 
                            Max.AssociatedObjectValue is DateTime MaxDT)
                        {
                            DateTime[,] Matrix2 = new DateTime[c, r];
                            DateTimeValue DT;
 
                            for (i = 0; i < c; i++)
                            {
                                for (j = 0; j < r; j++)
                                {
                                    E = Elements[i, j];
                                    DT = E as DateTimeValue ?? throw new ScriptException("Incompatible values.");
                                    Matrix2[i, j] = DT.Value;
                                }
                            }
 
                            return Scale(Matrix2, MinDT, MaxDT, Offset, Size);
                        }
                        else
                            return Scale(OM.Values, Offset, Size, LabelPositions);
                    }
                }
            }
            else
                throw new ScriptException("Invalid vector type.");
        }
 
        public static double[,] Scale(double[,] Matrix, double Min, double Max, double Offset, double Size)
        {
            int c = Matrix.GetLength(0);
            int r = Matrix.GetLength(1);
            int i, j;
            double[,] Result = new double[c, r];
            double Scale = Min == Max ? 1 : Size / (Max - Min);
 
            for (i = 0; i < c; i++)
            {
                for (j = 0; j < r; j++)
                    Result[i, j] = (Matrix[i, j] - Min) * Scale + Offset;
            }
 
            return Result;
        }
 
        public static double[,] Scale(DateTime[,] Matrix, DateTime Min, DateTime Max, double Offset, double Size)
        {
            int c = Matrix.GetLength(0);
            int r = Matrix.GetLength(1);
            int i, j;
            double[,] v = new double[c, r];
 
            for (i = 0; i < c; i++)
            {
                for (j = 0; j < r; j++)
                    v[i, j] = (Matrix[i, j] - referenceTimestamp).TotalDays;
            }
 
            return Scale(v, (Min - referenceTimestamp).TotalDays, (Max - referenceTimestamp).TotalDays, Offset, Size);
        }
 
        public static double[,] Scale(PhysicalQuantity[,] Matrix, double Min, double Max, Unit Unit, double Offset, double Size)
        {
            int c = Matrix.GetLength(0);
            int r = Matrix.GetLength(1);
            int i, j;
            double[,] v = new double[c, r];
            PhysicalQuantity Q;
 
            for (i = 0; i < c; i++)
            {
                for (j = 0; j < r; j++)
                {
                    Q = Matrix[i, j];
                    if (Q.Unit.Equals(Unit) || Q.Unit.IsEmpty)
                        v[i, j] = Q.Magnitude;
                    else if (!Unit.TryConvert(Q.Magnitude, Q.Unit, Unit, out v[i, j]))
                        throw new ScriptException("Incompatible units.");
                }
            }
 
            return Scale(v, Min, Max, Offset, Size);
        }
 
        public static double[,] Scale(object[,] Matrix, double Offset, double Size,
            Dictionary<string, double> LabelPositions)
        {
            Dictionary<object, int> Values = new Dictionary<object, int>();
            int Index = 0;
            int c = Matrix.GetLength(0);
            int r = Matrix.GetLength(1);
            int i, j;
            double[,] v = new double[c, r];
            object Value;
 
            for (i = 0; i < c; i++)
            {
                for (j = 0; j < r; j++)
                {
                    Value = Matrix[i, j];
                    if (!Values.TryGetValue(Value, out int k))
                    {
                        k = Index++;
                        Values[Value] = k;
                    }
 
                    v[i, j] = k + 0.5;
                }
            }
 
            double[,] Result = Scale(v, 0, c, Offset, Size);
 
            if (!(LabelPositions is null))
            {
                for (i = 0; i < c; i++)
                {
                    for (j = 0; j < r; j++)
                    {
                        string s = Matrix[i, j]?.ToString() ?? string.Empty;
 
                        if (LabelPositions.TryGetValue(s, out double d))
                            Result[i, j] = d;
                    }
                }
            }
 
            return Result;
        }
 
        public override string GetBitmapClickScript(double X, double Y, object[] States)
        {
            DrawingArea DrawingArea = (DrawingArea)States[0];
 
            IElement X2 = DrawingArea.DescaleX(X);
            IElement Y2 = DrawingArea.DescaleY(Y);
 
            return "[" + X2.ToString() + "," + Y2.ToString() + "]";
        }
 
        public static I3DShader ToShader(object Argument)
        {
            if (Argument is I3DShader Shader)
                return Shader;
 
            if (!(Argument is SKColor Color))
                Color = Graph.ToColor(Argument);
 
            // TODO: 3D-Graph settings to define default lighting.
 
            return new PhongShader(
                new PhongMaterial(1, 2, 0, 10),
                new PhongIntensity(64, 64, 64, Color.Alpha),
                new PhongLightSource(
                    new PhongIntensity(Color.Red, Color.Green, Color.Blue, Color.Alpha),
                    new PhongIntensity(255, 255, 255, 255),
                    new Vector3(1000, 1000, 0)));
        }
 
        public override void ExportGraph(XmlWriter Output)
        {
            Output.WriteStartElement("Graph3D");
            Output.WriteAttributeString("title", this.title);
            Output.WriteAttributeString("labelX", this.labelX);
            Output.WriteAttributeString("labelY", this.labelY);
            Output.WriteAttributeString("labelZ", this.labelZ);
            Output.WriteAttributeString("axisTypeX", this.axisTypeX.FullName);
            Output.WriteAttributeString("axisTypeY", this.axisTypeY.FullName);
            Output.WriteAttributeString("axisTypeZ", this.axisTypeZ.FullName);
            Output.WriteAttributeString("minX", Graph2D.ReducedXmlString(this.minX));
            Output.WriteAttributeString("maxX", Graph2D.ReducedXmlString(this.maxX));
            Output.WriteAttributeString("minY", Graph2D.ReducedXmlString(this.minY));
            Output.WriteAttributeString("maxY", Graph2D.ReducedXmlString(this.maxY));
            Output.WriteAttributeString("minZ", Graph2D.ReducedXmlString(this.minZ));
            Output.WriteAttributeString("maxZ", Graph2D.ReducedXmlString(this.maxZ));
            Output.WriteAttributeString("showXAxis", this.showXAxis ? "true" : "false");
            Output.WriteAttributeString("showYAxis", this.showYAxis ? "true" : "false");
            Output.WriteAttributeString("showZAxis", this.showZAxis ? "true" : "false");
            Output.WriteAttributeString("showGrid", this.showGrid ? "true" : "false");
            Output.WriteAttributeString("angle", Expression.ToString(this.angle));
            Output.WriteAttributeString("inclination", Expression.ToString(this.inclination));
            Output.WriteAttributeString("overSampling", this.overSampling.ToString());
 
            Dictionary<string, string> Series = new Dictionary<string, string>();
            string Label;
            string s;
            int i = 1;
            
            foreach (IVector v in this.x)
            {
                s = Graph2D.ReducedXmlString(v);
                if (Series.TryGetValue(s, out Label))
                    Output.WriteElementString("X", Label);
                else
                {
                    Label = "X" + (i++).ToString();
                    Series[s] = Label;
                    Output.WriteElementString("X", Label + ":=" + s);
                }
            }
            
            i = 1;
 
            foreach (IVector v in this.y)
            {
                s = Graph2D.ReducedXmlString(v);
                if (Series.TryGetValue(s, out Label))
                    Output.WriteElementString("Y", Label);
                else
                {
                    Label = "Y" + (i++).ToString();
                    Series[s] = Label;
                    Output.WriteElementString("Y", Label + ":=" + s);
                }
            }
 
            i = 1;
 
            foreach (IVector v in this.z)
            {
                s = Graph2D.ReducedXmlString(v);
                if (Series.TryGetValue(s, out Label))
                    Output.WriteElementString("Z", Label);
                else
                {
                    Label = "Z" + (i++).ToString();
                    Series[s] = Label;
                    Output.WriteElementString("Z", Label + ":=" + s);
                }
            }
 
            i = 1;
 
            foreach (Vector4[,] M in this.normals)
            {
                StringBuilder sb = new StringBuilder();
 
                if (M is null)
                    sb.Append("null");
                else
                {
                    int c = M.GetLength(0);
                    int d = M.GetLength(1);
                    int j;
 
                    sb.Append('[');
                    for (i = 0; i < c; i++)
                    {
                        if (i > 0)
                            sb.Append(',');
 
                        sb.Append('[');
 
                        for (j = 0; j < d; j++)
                        {
                            if (j > 0)
                                sb.Append(',');
 
                            sb.Append(Expression.ToString(M[i, j]));
                        }
 
                        sb.Append(']');
                    }
                    sb.Append(']');
                }
 
                s = sb.ToString();
 
                if (Series.TryGetValue(s, out Label))
                    Output.WriteElementString("Normals", Label);
                else
                {
                    Label = "N" + (i++).ToString();
                    Series[s] = Label;
                    Output.WriteElementString("Normals", Label + ":=" + s);
                }
            }
            
            i = 1;
 
            foreach (object[] v in this.parameters)
            {
                s = Expression.ToString(new ObjectVector(v));
                if (Series.TryGetValue(s, out Label))
                    Output.WriteElementString("Parameters", Label);
                else
                {
                    Label = "P" + (i++).ToString();
                    Series[s] = Label;
                    Output.WriteElementString("Parameters", Label + ":=" + s);
                }
            }
 
            foreach (IPainter3D Painter in this.painters)
                Output.WriteElementString("Painter", Painter.GetType().FullName);
 
            Output.WriteEndElement();
        }
 
        public override async Task ImportGraphAsync(XmlElement Xml)
        {
            Variables Variables = new Variables();
 
            foreach (XmlAttribute Attr in Xml.Attributes)
            {
                switch (Attr.Name)
                {
                    case "title":
                        this.title = Attr.Value;
                        break;
 
                    case "labelX":
                        this.labelX = Attr.Value;
                        break;
 
                    case "labelY":
                        this.labelY = Attr.Value;
                        break;
 
                    case "labelZ":
                        this.labelZ = Attr.Value;
                        break;
 
                    case "axisTypeX":
                        this.axisTypeX = Types.GetType(Attr.Value);
                        break;
 
                    case "axisTypeY":
                        this.axisTypeY = Types.GetType(Attr.Value);
                        break;
 
                    case "axisTypeZ":
                        this.axisTypeZ = Types.GetType(Attr.Value);
                        break;
 
                    case "minX":
                        this.minX = await ParseAsync(Attr.Value, Variables);
                        break;
 
                    case "maxX":
                        this.maxX = await ParseAsync(Attr.Value, Variables);
                        break;
 
                    case "minY":
                        this.minY = await ParseAsync(Attr.Value, Variables);
                        break;
 
                    case "maxY":
                        this.maxY = await ParseAsync(Attr.Value, Variables);
                        break;
 
                    case "minZ":
                        this.minZ = await ParseAsync(Attr.Value, Variables);
                        break;
 
                    case "maxZ":
                        this.maxZ = await ParseAsync(Attr.Value, Variables);
                        break;
 
                    case "showXAxis":
                        this.showXAxis = Attr.Value == "true";
                        break;
 
                    case "showYAxis":
                        this.showYAxis = Attr.Value == "true";
                        break;
 
                    case "showZAxis":
                        this.showZAxis = Attr.Value == "true";
                        break;
 
                    case "showGrid":
                        this.showGrid = Attr.Value == "true";
                        break;
 
                    case "angle":
                        if (Expression.TryParse(Attr.Value, out double d))
                            this.angle = d;
                        break;
 
                    case "inclination":
                        if (Expression.TryParse(Attr.Value, out d))
                            this.inclination = d;
                        break;
 
                    case "overSampling":
                        this.overSampling = int.Parse(Attr.Value);
                        break;
                }
            }
 
            foreach (XmlNode N in Xml.ChildNodes)
            {
                if (N is XmlElement E)
                {
                    switch (E.LocalName)
                    {
                        case "X":
                            this.x.AddLast((IMatrix)await ParseAsync(E.InnerText, Variables));
                            break;
 
                        case "Y":
                            this.y.AddLast((IMatrix)await ParseAsync(E.InnerText, Variables));
                            break;
 
                        case "Z":
                            this.z.AddLast((IMatrix)await ParseAsync(E.InnerText, Variables));
                            break;
 
                        case "Normals":
                            IMatrix M = (IMatrix)await ParseAsync(E.InnerText, Variables);
 
                            int i, j, c, d;
 
                            if (M is null)
                                this.normals.AddLast((Vector4[,])null);
                            else
                            {
                                c = M.Rows;
                                d = M.Columns;
                                Vector4[,] M2 = new Vector4[c, d];
 
                                for (i = 0; i < c; i++)
                                {
                                    for (j = 0; i < d; j++)
                                        M2[i, j] = (Vector4)(M.GetElement(i, j).AssociatedObjectValue);
                                }
 
                                this.normals.AddLast(M2);
                            }
                            break;
 
                        case "Parameters":
                            IVector v = (IVector)await ParseAsync(E.InnerText, Variables);
                            this.parameters.AddLast(this.ToObjectArray(v));
                            break;
 
                        case "Painter":
                            this.painters.AddLast((IPainter3D)Activator.CreateInstance(Types.GetType(E.InnerText)));
                            break;
                    }
                }
            }
        }
 
        public override bool UsesDefaultColor
        {
            get
            {
                IEnumerator<object[]> eParameters = this.parameters.GetEnumerator();
                IEnumerator<IPainter3D> ePainter = this.painters.GetEnumerator();
 
                while (eParameters.MoveNext() && ePainter.MoveNext())
                {
                    if (!ePainter.Current.UsesDefaultColor(eParameters.Current))
                        return false;
                }
 
                return true;
            }
        }
 
        public override bool TrySetDefaultColor(SKColor Color)
        {
            if (!this.UsesDefaultColor)
                return false;
 
            IEnumerator<object[]> eParameters = this.parameters.GetEnumerator();
            IEnumerator<IPainter3D> ePainter = this.painters.GetEnumerator();
            bool Result = true;
 
            while (eParameters.MoveNext() && ePainter.MoveNext())
            {
                if (!ePainter.Current.TrySetDefaultColor(Color, eParameters.Current))
                    Result = false;
            }
 
            return Result;
        }
 
    }
}