using System using System Collections Generic using System ComponentMo

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;
using System.Diagnostics;

namespace WindowsFormsApplication3
{
  public partial class Form1 : Form
  {
    public Form1()
    {
      InitializeComponent();
    }

    float[,] cube = new float[8, 4] 
      {
        {0,   0,   0,   1},
        {100, 0,   0,   1},
        {100, 100, 0,   1},
        {0,   100, 0,   1},
        {0,   0,   100, 1},
        {100, 0,   100, 1},
        {100, 100, 100, 1},
        {0,   100, 100, 1}
      };

    float angle = 0;

    private void Form1_Load(object sender, EventArgs e)
    {
      cube = rotate(cube, 10, new float[] { 5, 5, 5 });
      draw(cube);
    }

    private float[,] rotate(float[,] original, double angle, float[] vector)
    {
      Debug.Assert(vector.Length >= 3);
      var length = Math.Sqrt(vector[0] * vector[0] + vector[1] * vector[1] + vector[2] * vector[2]);
      var n1 = vector[0] / length;
      var n2 = vector[1] / length;
      var n3 = vector[2] / length;

      var cos = Math.Cos(angle);
      var sin = Math.Sin(angle);

      var trans = new float[4, 4] 
      {
        {(float)(n1 * n1 + (1 - n1 * n1) * cos), (float)(n1 * n2 * (1 - cos) + n2 * sin), (float)(n1 * n3 * (1 - cos) - n2 * sin), 0},
        {(float)(n1 * n2 * (1 - cos) - n3 * sin), (float)(n2 * n2 + (1 - n2 * n2) * cos), (float)(n1 * n2 * (1 - cos) + n2 * sin), 0},
        {(float)(n1 * n3 * (1 - cos) + n2 * sin), (float)(n2 * n3 * (1 - cos) - n1*sin), (float)(n3 * n3 + (1 - n3 * n3) * cos), 0},
        {0, 0, 0, 1}
      };

      return mult(original, trans);
    }

    private void draw(float[,] m)
    {
      var bmp = new Bitmap(400, 400);
      var g = Graphics.FromImage(bmp);
      g.TranslateTransform(200, 200);
      g.Clear(Color.White);
      var p0 = new PointF(m[0, 0], m[0, 1]);
      var p1 = new PointF(m[1, 0], m[1, 1]);
      var p2 = new PointF(m[2, 0], m[2, 1]);
      var p3 = new PointF(m[3, 0], m[3, 1]);
      var p4 = new PointF(m[4, 0], m[4, 1]);
      var p5 = new PointF(m[5, 0], m[5, 1]);
      var p6 = new PointF(m[6, 0], m[6, 1]);
      var p7 = new PointF(m[7, 0], m[7, 1]);

      var pen = new Pen(Brushes.DarkOrange);
      g.DrawPolygon(pen, new PointF[] {p0, p1, p2, p3});
      g.DrawPolygon(pen, new PointF[] { p7, p6, p2, p3 });
      g.DrawPolygon(pen, new PointF[] { p2, p6, p5, p1 });
      g.DrawPolygon(pen, new PointF[] { p1, p0, p4, p5 });
      g.DrawPolygon(pen, new PointF[] { p3, p0, p4, p7 });
      g.DrawPolygon(pen, new PointF[] { p7, p4, p5, p6 });
      pictureBox1.Image = bmp;
    }

    private float[,] mult(float[,] a, float[,] b)
    {
      Debug.Assert(a.GetLength(1) == b.GetLength(0));
      var result = new float[a.GetLength(0), b.GetLength(1)];
      for (int i = 0; i < a.GetLength(0); i++)
      {
        for (int j = 0; j < b.GetLength(1); j++)
        {
          for (int k = 0; k < a.GetLength(1); k++)
          {
            result[i, j] += a[i, k] * b[k, j];
          }
        }
      }

      return result;
    }

    private void timer1_Tick(object sender, EventArgs e)
    {
      angle += 10;
      angle /= 360;

      cube = rotate(cube, angle, new float[] { 5, 5, 5 });
      draw(cube);
    }
  }
}