Added support for n-dimensional rotation angles, implemented demo rendering and simple geometry support.

Demo/AngleBar.Designer.cs

@@ -0,0 +1,95 @@
+
+namespace Demo
+{
+    partial class AngleBar
+    {
+        /// <summary> 
+        /// Required designer variable.
+        /// </summary>
+        private System.ComponentModel.IContainer components = null;
+
+        /// <summary> 
+        /// Clean up any resources being used.
+        /// </summary>
+        /// <param name="disposing">true if managed resources should be disposed; otherwise, false.</param>
+        protected override void Dispose(bool disposing)
+        {
+            if (disposing && (components != null))
+            {
+                components.Dispose();
+            }
+            base.Dispose(disposing);
+        }
+
+        #region Component Designer generated code
+
+        /// <summary> 
+        /// Required method for Designer support - do not modify 
+        /// the contents of this method with the code editor.
+        /// </summary>
+        private void InitializeComponent()
+        {
+            this.trackBar1 = new System.Windows.Forms.TrackBar();
+            this.numericUpDown1 = new System.Windows.Forms.NumericUpDown();
+            this.checkBox1 = new System.Windows.Forms.CheckBox();
+            ((System.ComponentModel.ISupportInitialize)(this.trackBar1)).BeginInit();
+            ((System.ComponentModel.ISupportInitialize)(this.numericUpDown1)).BeginInit();
+            this.SuspendLayout();
+            // 
+            // trackBar1
+            // 
+            this.trackBar1.Dock = System.Windows.Forms.DockStyle.Fill;
+            this.trackBar1.Location = new System.Drawing.Point(0, 0);
+            this.trackBar1.Maximum = 360;
+            this.trackBar1.Minimum = 0;
+            this.trackBar1.Name = "trackBar1";
+            this.trackBar1.Size = new System.Drawing.Size(485, 34);
+            this.trackBar1.TabIndex = 0;
+            this.trackBar1.Scroll += new System.EventHandler(this.trackBar1_Scroll);
+            // 
+            // numericUpDown1
+            // 
+            this.numericUpDown1.AutoSize = true;
+            this.numericUpDown1.Dock = System.Windows.Forms.DockStyle.Right;
+            this.numericUpDown1.Font = new System.Drawing.Font("Segoe UI", 12F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point);
+            this.numericUpDown1.Location = new System.Drawing.Point(485, 0);
+            this.numericUpDown1.Maximum = 360;
+            this.numericUpDown1.Minimum = 0;
+            this.numericUpDown1.Name = "numericUpDown1";
+            this.numericUpDown1.Size = new System.Drawing.Size(53, 29);
+            this.numericUpDown1.TabIndex = 1;
+            this.numericUpDown1.ValueChanged += new System.EventHandler(this.numericUpDown1_ValueChanged);
+            // 
+            // checkBox1
+            // 
+            this.checkBox1.AutoSize = true;
+            this.checkBox1.Dock = System.Windows.Forms.DockStyle.Left;
+            this.checkBox1.Location = new System.Drawing.Point(0, 0);
+            this.checkBox1.Name = "checkBox1";
+            this.checkBox1.Size = new System.Drawing.Size(15, 34);
+            this.checkBox1.TabIndex = 2;
+            this.checkBox1.UseVisualStyleBackColor = true;
+            // 
+            // AngleBar
+            // 
+            this.AutoScaleDimensions = new System.Drawing.SizeF(7F, 15F);
+            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
+            this.Controls.Add(this.trackBar1);
+            this.Controls.Add(this.numericUpDown1);
+            this.Controls.Add(this.checkBox1);
+            this.Name = "AngleBar";
+            this.Size = new System.Drawing.Size(538, 34);
+            ((System.ComponentModel.ISupportInitialize)(this.trackBar1)).EndInit();
+            ((System.ComponentModel.ISupportInitialize)(this.numericUpDown1)).EndInit();
+            this.ResumeLayout(false);
+            this.PerformLayout();
+
+        }
+
+        #endregion
+
+        private System.Windows.Forms.TrackBar trackBar1;
+        private System.Windows.Forms.NumericUpDown numericUpDown1;
+        private System.Windows.Forms.CheckBox checkBox1;
+    }
+}

Demo/AngleBar.cs

@@ -0,0 +1,39 @@
+using System;
+using System.Collections.Generic;
+using System.ComponentModel;
+using System.Data;
+using System.Drawing;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+using System.Windows.Forms;
+
+namespace Demo
+{
+    public partial class AngleBar : UserControl
+    {
+        public AngleBar()
+        {
+            InitializeComponent();
+        }
+
+        public double Angle
+        {
+            get => trackBar1.Value / 180.0 * Math.PI;
+            set => numericUpDown1.Value = (decimal)((value % (Math.PI*2))  / Math.PI * 180);
+        }
+
+        public bool Checked => checkBox1.Checked;
+
+
+        private void trackBar1_Scroll(object sender, EventArgs e)
+        {
+            numericUpDown1.Value = trackBar1.Value;
+        }
+
+        private void numericUpDown1_ValueChanged(object sender, EventArgs e)
+        {
+            trackBar1.Value = (int)numericUpDown1.Value;
+        }
+    }
+}

Demo/AngleBar.resx

@@ -0,0 +1,60 @@
+<root>
+  <xsd:schema id="root" xmlns="" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:msdata="urn:schemas-microsoft-com:xml-msdata">
+    <xsd:import namespace="http://www.w3.org/XML/1998/namespace" />
+    <xsd:element name="root" msdata:IsDataSet="true">
+      <xsd:complexType>
+        <xsd:choice maxOccurs="unbounded">
+          <xsd:element name="metadata">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" />
+              </xsd:sequence>
+              <xsd:attribute name="name" use="required" type="xsd:string" />
+              <xsd:attribute name="type" type="xsd:string" />
+              <xsd:attribute name="mimetype" type="xsd:string" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="assembly">
+            <xsd:complexType>
+              <xsd:attribute name="alias" type="xsd:string" />
+              <xsd:attribute name="name" type="xsd:string" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="data">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+                <xsd:element name="comment" type="xsd:string" minOccurs="0" msdata:Ordinal="2" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" msdata:Ordinal="1" />
+              <xsd:attribute name="type" type="xsd:string" msdata:Ordinal="3" />
+              <xsd:attribute name="mimetype" type="xsd:string" msdata:Ordinal="4" />
+              <xsd:attribute ref="xml:space" />
+            </xsd:complexType>
+          </xsd:element>
+          <xsd:element name="resheader">
+            <xsd:complexType>
+              <xsd:sequence>
+                <xsd:element name="value" type="xsd:string" minOccurs="0" msdata:Ordinal="1" />
+              </xsd:sequence>
+              <xsd:attribute name="name" type="xsd:string" use="required" />
+            </xsd:complexType>
+          </xsd:element>
+        </xsd:choice>
+      </xsd:complexType>
+    </xsd:element>
+  </xsd:schema>
+  <resheader name="resmimetype">
+    <value>text/microsoft-resx</value>
+  </resheader>
+  <resheader name="version">
+    <value>2.0</value>
+  </resheader>
+  <resheader name="reader">
+    <value>System.Resources.ResXResourceReader, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+  <resheader name="writer">
+    <value>System.Resources.ResXResourceWriter, System.Windows.Forms, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089</value>
+  </resheader>
+</root>

Demo/Form1.Designer.cs

@@ -29,7 +29,10 @@ namespace Demo
         /// </summary>
         private void InitializeComponent()
         {
+            this.components = new System.ComponentModel.Container();
             this.pictureBox1 = new System.Windows.Forms.PictureBox();
+            this.timer1 = new System.Windows.Forms.Timer(this.components);
+            this.panel1 = new System.Windows.Forms.Panel();
             ((System.ComponentModel.ISupportInitialize)(this.pictureBox1)).BeginInit();
             this.SuspendLayout();
             // 
@@ -38,27 +41,46 @@ namespace Demo
             this.pictureBox1.Dock = System.Windows.Forms.DockStyle.Fill;
             this.pictureBox1.Location = new System.Drawing.Point(0, 0);
             this.pictureBox1.Name = "pictureBox1";
-            this.pictureBox1.Size = new System.Drawing.Size(800, 450);
+            this.pictureBox1.Size = new System.Drawing.Size(788, 766);
             this.pictureBox1.TabIndex = 0;
             this.pictureBox1.TabStop = false;
-            this.pictureBox1.Click += new System.EventHandler(this.pictureBox1_Click);
+            this.pictureBox1.SizeChanged += new System.EventHandler(this.pictureBox1_SizeChanged);
+            // 
+            // timer1
+            // 
+            this.timer1.Enabled = true;
+            this.timer1.Interval = 50;
+            this.timer1.Tick += new System.EventHandler(this.timer1_Tick);
+            // 
+            // panel1
+            // 
+            this.panel1.AutoSize = true;
+            this.panel1.Dock = System.Windows.Forms.DockStyle.Top;
+            this.panel1.Location = new System.Drawing.Point(0, 0);
+            this.panel1.Name = "panel1";
+            this.panel1.Size = new System.Drawing.Size(788, 0);
+            this.panel1.TabIndex = 1;
             // 
             // Form1
             // 
             this.AutoScaleDimensions = new System.Drawing.SizeF(7F, 15F);
             this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
-            this.ClientSize = new System.Drawing.Size(800, 450);
+            this.ClientSize = new System.Drawing.Size(788, 766);
             this.Controls.Add(this.pictureBox1);
+            this.Controls.Add(this.panel1);
             this.Name = "Form1";
             this.Text = "Form1";
             ((System.ComponentModel.ISupportInitialize)(this.pictureBox1)).EndInit();
             this.ResumeLayout(false);
+            this.PerformLayout();
 
         }
 
         #endregion
 
         private System.Windows.Forms.PictureBox pictureBox1;
+        private System.Windows.Forms.Timer timer1;
+        private System.Windows.Forms.Panel panel1;
     }
 }
 

Demo/Form1.cs

@@ -9,6 +9,8 @@ using System.Linq;
 using System.Text;
 using System.Threading.Tasks;
 using System.Windows.Forms;
+using YMath.Geometry;
+using System.Diagnostics.CodeAnalysis;
 
 namespace Demo
 {
@@ -17,74 +19,156 @@ namespace Demo
         public Form1()
         {
             InitializeComponent();
+            CreateTrackBars();
+            InitializeImage();
         }
         
-        private void pictureBox1_Click(object sender, EventArgs e)
+
+        double angle = 0;
+
+        private void Render(Bitmap bmp)
+        {
+            g.Clear(Color.White); 
+
+            Projector projector3d2d = new Projector(
+                new Camera(1),
+                new CoordSystem(new Vector(0, 0, 2), YMath.Matrix.Ident(3)));
+
+            Projector projector4d3d = new Projector(
+                new Camera(1),
+                new CoordSystem(new Vector(0, 0, 0, 3), YMath.Matrix.Ident(4)));
+
+            Geom geom = Geometries.NewCube(4);
+
+            double[] angles = angleSelectBars.Select(b => b.Angle).ToArray();
+            projector4d3d.CoordSystem.RotationMatrix
+                = YMath.Matrix.Rotation(4, angles);
+            angle += 0.01;
+
+            geom = projector4d3d.Project(geom);
+            geom = projector3d2d.Project(geom);
+
+            foreach (var v in geom.Verticies)
+                DrawPoint(v);
+
+            foreach (var line in geom.Edges)
+                DrawLine(line);
+        }
+
+        private void DrawPoint(Vector v)
+        {
+            var pos = Denormalize(v);
+            var diameter = 2;
+            var rect = new RectangleF(
+                pos.X - diameter, pos.Y - diameter, diameter * 2, diameter * 2);
+            g.FillEllipse(Brushes.Black, rect);
+        }
+
+        private void DrawLine(LineSegment line)
         {
-            /*var g = pictureBox1.CreateGraphics();
-            g.SmoothingMode = SmoothingMode.HighQuality;
             var pen = new Pen(Brushes.Black, 2);
-            var rect = CubePoints(100.0, 2);
+            g.DrawLine(pen, Denormalize(line.Start), Denormalize(line.End));
-            DrawLines(g, pen, rect);*/
-        }/*
-
-        // [-1; 1] -> [0; width]
-        private static Vector[] RelativeToAbsolute(Vector[] points, int width, int height)
-        {
-            return points.Select(p => new Vector(
-                    (p[0] + 1) / 2 * width,
-                    (p[1] + 1) / 2 * height))
-                .ToArray();
         }
 
-        private static void DrawLines(Graphics g, Pen pen, Line[] lines)
+        private PointF Denormalize(Vector p)
         {
-            foreach (var line in lines)
+            p = (p + new Vector(1, 1)) / 2;
-                g.DrawLine(pen,
+            p[0] *= bmp.Width;
-                    new PointF((float)line.Start[0], (float)line.End[1]),
+            p[1] = 1 - p[1];
-                     new PointF((float)line.Start[0], (float)line.End[1]));
+            p[1] *= bmp.Height;
+            return new PointF((float)p[0], (float)p[1]);
         }
 
-        public struct Line
+        private void timer1_Tick(object sender, EventArgs e)
         {
-            public Line(Vector start, Vector end)
+            Render(bmp);
-            {
+            pictureBox1.Refresh();
-                Start = start;
+            foreach (var bar in angleSelectBars)
-                End = end;
+                if (bar.Checked)
+                    bar.Angle += 0.03;
         }
 
-            public Vector Start { get; set; }
+        Bitmap bmp;
-            public Vector End { get; set; }
+        Graphics g;
+
+        private void pictureBox1_SizeChanged(object sender, EventArgs e)
+        {
+            InitializeImage();
         }
 
-        public static Line[] Cube(int nDimensions)
+        [MemberNotNull(nameof(bmp), nameof(g))]
+        private void InitializeImage()
         {
-            if (nDimensions == 0)
+            bmp = new Bitmap(pictureBox1.Width, pictureBox1.Width);
-                return new Vector[] { new Vector(0) };
+            g = Graphics.FromImage(bmp);
-
+            g.SmoothingMode = SmoothingMode.HighQuality;
-            var result = new List<Vector>();
+            pictureBox1.Image = bmp;
-            var offset = new Vector(nDimensions);
-            offset[nDimensions - 1] = 1;
-            var face /*боже*//* = Cube(nDimensions - 1);
-            result.AddRange(face.Select(p => p + offset));
-            result.AddRange(face.Select(p => p - offset));
-
         }
 
-        public static Vector[] CubePoints(double size, int nDimensions)
+
+        AngleBar[] angleSelectBars;
+        private void CreateTrackBars()
         {
-            int n = 1 << nDimensions;
+            angleSelectBars = new AngleBar[6];
-            if (nDimensions >= 32)
+            for (int i = 0; i < angleSelectBars.Length; i++)
+            {
+                var bar = new AngleBar();
+                bar.Dock = DockStyle.Top;
+                panel1.Controls.Add(bar);
+                angleSelectBars[i] = bar;
+                bar.BringToFront();
+            }
+        }
+
+        /*
+
+// [-1; 1] -> [0; width]
+private static Vector[] RelativeToAbsolute(Vector[] points, int width, int height)
+{
+return points.Select(p => new Vector(
+(p[0] + 1) / 2 * width,
+(p[1] + 1) / 2 * height))
+.ToArray();
+}
+
+private static void DrawLines(Graphics g, Pen pen, Line[] lines)
+{
+foreach (var line in lines)
+g.DrawLine(pen,
+new PointF((float)line.Start[0], (float)line.End[1]),
+new PointF((float)line.Start[0], (float)line.End[1]));
+}
+
+
+
+public static Line[] Cube(int nDimensions)
+{
+if (nDimensions == 0)
+return new Vector[] { new Vector(0) };
+
+var result = new List<Vector>();
+var offset = new Vector(nDimensions);
+offset[nDimensions - 1] = 1;
+var face /*боже*//* = Cube(nDimensions - 1);
+result.AddRange(face.Select(p => p + offset));
+result.AddRange(face.Select(p => p - offset));
+
+}
+
+public static Vector[] CubePoints(double size, int nDimensions)
+{
+int n = 1 << nDimensions;
+if (nDimensions >= 32)
     throw new ArgumentException("Fuck yourself");
-            var result = new Vector[n];
+var result = new Vector[n];
-            for (int i = 0; i < n; i++)
+for (int i = 0; i < n; i++)
-            {
+{
     var vec = new Vector(nDimensions);
     for (int j = 0; j < nDimensions; j++)
         vec[j] = ((i >> j) & 1) - 0.5;
     result[i] = vec;
-            }
+}
-            return result;
+return result;
-        }*/
+}*/
     }
 }

Demo/Program.cs

@@ -18,17 +18,6 @@ namespace Demo
             Application.SetHighDpiMode(HighDpiMode.SystemAware);
             Application.EnableVisualStyles();
             Application.SetCompatibleTextRenderingDefault(false);
-            
-
-            Projector p = new Projector(
-                new Camera(1),
-                new CoordSystem(new Vector(), Matrix.Ident(4)));
-            var point = p.Project(new Vector(1, 1, 1, 2));
-
-
-
-
-
             Application.Run(new Form1());
         }
     }

YMath.sln

@@ -3,9 +3,9 @@ Microsoft Visual Studio Solution File, Format Version 12.00
 # Visual Studio Version 16
 VisualStudioVersion = 16.0.30711.63
 MinimumVisualStudioVersion = 10.0.40219.1
-Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "YMath", "YMath\YMath.csproj", "{33638CEC-2BD2-4B91-A1CB-0383F7E429BE}"
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "YMath", "YMath\YMath.csproj", "{33638CEC-2BD2-4B91-A1CB-0383F7E429BE}"
 EndProject
-Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Demo", "Demo\Demo.csproj", "{CE175AF3-5242-4178-BB97-54956FE958D8}"
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "Demo", "Demo\Demo.csproj", "{CE175AF3-5242-4178-BB97-54956FE958D8}"
 EndProject
 Global
 	GlobalSection(SolutionConfigurationPlatforms) = preSolution

YMath/Combinatorics.cs

@@ -0,0 +1,42 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace YMath
+{
+    /// <summary>
+    /// Basic combinatorial functions
+    /// </summary>
+    static class Combinatorics
+    {
+        /// <summary>
+        /// Returns number of k-combinations from set of n elements
+        /// (aka binomial coefficient)
+        /// </summary>
+        public static int C(int n, int k)
+        {
+            // https://stackoverflow.com/questions/9330915/number-of-combinations-n-choose-r-in-c
+            if (k > n) return 0;
+            if (k * 2 > n) k = n - k;
+            if (k == 0) return 1;
+
+            int result = n;
+            for (int i = 2; i <= k; ++i)
+            {
+                result *= (n - i + 1);
+                result /= i;
+            }
+            return result;
+        }
+
+        public static int Factorial(int n)
+        {
+            int res = 1;
+            for (int i = 1; i < n; n++)
+                res *= i;
+            return res;
+        }
+    }
+}

YMath/Geometry/Geom.cs

@@ -0,0 +1,78 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace YMath.Geometry
+{
+    /// <summary>
+    /// Represents geomretry object
+    /// </summary>
+    public class Geom : ICloneable
+    {
+        /// <summary>
+        /// Creates new geometry containing given points and lines
+        /// </summary>
+        public Geom(Vector[] verticies, LineSegment[] edges)
+        {
+            IEnumerable<int> dimensions = verticies
+                .Select(v => v.Dimensions)
+                .Concat(edges.SelectMany(
+                e => new[] { e.Start.Dimensions, e.End.Dimensions }));
+            if (!dimensions.All(d => d == dimensions.First()))
+                throw new ArgumentException("Dimensions inconsistent");
+
+            Verticies = verticies;
+            Edges = edges;
+        }
+
+        /// <summary>
+        /// Creates a new geomretry merging the given set of geometries
+        /// </summary>
+        /// <param name="geometries"></param>
+        public Geom(params Geom[] geometries)
+            : this(geometries.SelectMany( g=> g.Verticies).ToArray(),
+                  geometries.SelectMany(g => g.Edges).ToArray())
+        {
+        }
+
+        /// <summary>
+        /// Verticies of the object
+        /// </summary>
+        public Vector[] Verticies { get; set; }
+
+        /// <summary>
+        /// Edges of the object
+        /// </summary>
+        public LineSegment[] Edges { get; set; }
+
+        public object Clone()
+        {
+            return new Geom(
+                (Vector[])Verticies.Clone(), (LineSegment[])Edges.Clone());
+        }
+
+        /// <summary>
+        /// Shifts the object by a given vector
+        /// </summary>
+        public static Geom operator +(Geom left, Vector shift)
+        {
+            return new Geom(
+                left.Verticies.Select(v => v + shift).ToArray(),
+                left.Edges.Select(l => new LineSegment(l.Start + shift, l.End + shift)).ToArray());
+        }
+
+        public override string ToString()
+        {
+            var b = new StringBuilder();
+            b.AppendLine("Verticies:");
+            foreach (var v in Verticies)
+                b.AppendLine(" " + v.ToString());
+            b.AppendLine("Edges:");
+            foreach (var v in Edges)
+                b.AppendLine(" " + v.ToString());
+            return b.ToString();
+        }
+    }
+}

YMath/Geometry/Geometries.cs

@@ -0,0 +1,41 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace YMath.Geometry
+{
+    /// <summary>
+    /// A helper class to build arbitrary objects
+    /// </summary>
+    public static class Geometries
+    {
+        /// <summary>
+        /// Returns a new n-dimensional cube
+        /// </summary>
+        /// <param name="nDimesions">Number of dimensions</param>
+        /// <returns>A new n-dimensional cubes. All coordinates of all verticies are either +1 or -1.</returns>
+        public static Geom NewCube(uint nDimesions)
+        {
+            if (nDimesions == 0)
+                return new Geom(new Vector[] { new Vector(0) },
+                    new LineSegment[0]);
+
+            // Creating two n-1 dimensional faces
+            var offset = new Vector((int)nDimesions);
+            offset[offset.Dimensions - 1] = 1;
+            var face /*боже*/ = NewCube(nDimesions-1);
+            var face1 = face + offset;
+            var face2 /*боже упаси*/ = face + -offset;
+  
+            // Connecting these faces
+            var lines = face1.Verticies 
+                .Zip(face2.Verticies)
+                .Select(p => new LineSegment(p.First, p.Second))
+                .ToArray();
+            return new Geom(face1, face2, new Geom(new Vector[0], lines));
+
+        }
+    }
+}

YMath/Geometry/LineSegment.cs

@@ -0,0 +1,28 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace YMath.Geometry
+{
+    /// <summary>
+    /// Represents a line segment defined by 2 points
+    /// </summary>
+    public struct LineSegment
+    {
+        public LineSegment(Vector start, Vector end)
+        {
+            Start = start;
+            End = end;
+        }
+
+        public Vector Start { get; set; }
+        public Vector End { get; set; }
+
+        public override string ToString()
+        {
+            return $"{Start} - {End}";
+        }
+    }
+}

YMath/Matrix.cs

@@ -137,5 +137,67 @@ namespace YMath
                 result[i, i] = 1;
             return result;
         }
+
+        /// <summary>
+        /// Returns an n-dimensional rotation matrix.
+        /// Rotates the object by <paramref name="angle"/> (in rad) in the plane formed by <paramref name="axis1"/> and <paramref name="axis2"/>.
+        /// </summary>
+        /// <param name="nDimensions">Order of the output matrix</param>
+        /// <param name="axis1">The first axis index starting from 0</param>
+        /// <param name="axis2">The second axis index starting from 0</param>
+        /// <param name="angle">The angle in radians</param>
+        /// <returns>n-dimensional rotation matrix</returns>
+        public static Matrix Rotation(int nDimensions, int axis1, int axis2, double angle)
+        {
+            if (axis1 == axis2)
+                throw new ArgumentException("axis1 == axis2");
+            if (axis1 >= nDimensions || axis2 >= nDimensions)
+                throw new ArgumentOutOfRangeException("axes");
+            if (axis1 < 0 || axis2 < 0 || nDimensions < 0)
+                throw new ArgumentOutOfRangeException("Dimension number and axis indexes can't be less then 0");
+
+            var res = Matrix.Ident(nDimensions);
+            res[axis1, axis1] = Math.Cos(angle);
+            res[axis2, axis2] = Math.Cos(angle);
+            res[axis1, axis2] = -Math.Sin(angle);
+            res[axis2, axis1] = Math.Sin(angle);
+
+            return res;
+        }
+
+        /// <summary>
+        /// Creates n-dimensional rotation matrixes, which rotates by a given Euiler angles
+        /// </summary>
+        /// <param name="nDimensions">Matrix order</param>
+        /// <param name="angles">Euiler angles in rad</param>
+        /// <returns></returns>
+        public static Matrix Rotation(int nDimensions, double[] angles)
+        {
+            int n = Combinatorics.C(nDimensions, 2);
+            if (angles.Length != n)
+                throw new ArgumentException($"Expected {n} Euiler angles for {nDimensions}-dimensional space, got {angles.Length} angles");
+            var result = Matrix.Ident(nDimensions);
+
+            // Iterate over axis combinations
+            int axis1 = 0;
+            int axis2 = 1;
+            int iAngle = 0;
+            while (axis2 < nDimensions)
+            {
+                double angle = angles[iAngle];
+                result *= Matrix.Rotation(nDimensions, axis1, axis2, angle);
+
+                iAngle++;
+                if (axis1 + 1 == axis2)
+                {
+                    axis2++;
+                    axis1 = 0;
+                }
+                else
+                    axis1++;
+            }
+
+            return result;
+        }
     }
 }

YMath/Projector.cs

@@ -4,6 +4,7 @@ using System.Collections.Generic;
 using System.Linq;
 using System.Text;
 using System.Threading.Tasks;
+using YMath.Geometry;
 
 namespace YMath
 {
@@ -35,5 +36,17 @@ namespace YMath
             point = Camera.WorldToImage(point);
             return point;
         }
+
+        /// <summary>
+        /// Projects the given geometry
+        /// </summary>
+        /// <returns>The N-1 dimensional geometry</returns>
+        public Geom Project(Geom geom)
+        {
+            return new Geom(
+                geom.Verticies.Select(v => Project(v)).ToArray(),
+                geom.Edges.Select(e => new LineSegment(
+                    Project(e.Start), Project(e.End))).ToArray());
+        }
     }
 }