Metabollar

Jag tänkte visa en komplett implementation av 2-dimensionella metabollar i C#. Denna teknik skulle även kunna användas i 3D. Effekten ser ut så här:

Effekten beskrivs här, och denna implementation prioriterar prestanda för att fungera i realtid. I videon ovan används 20 positiva bollar (alltså bollar som tenderar att smeta ihop) och 10 negativa bollar (alltså bollar som tenderar att sluka andra bollar) och samtliga rör sig i sinusbanor på en yta av 320×200 pixlar. Renderingen bygger på Windows Forms och klassen Bitmap.

För att få rörelserna mjuka har jag satt formulärets egenskap DoubleBuffered till true. Dessutom har jag placerat en Timer på formuläret och satt dess Interval till 1 för att få så bra prestanda som möjligt utan att köra dedikerat, men om man ställer ännu högre krav på användarupplevelsen, skulle man välja ett annat bibliotek än Windows Forms. Dessa inställningar har jag ställt in i Visual Studio, så de syns inte i koden.

Här är formulärets kod:

using System;
using System.Collections.Generic;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Windows.Forms;

namespace Metaballs
{
    public partial class Form1 : Form
    {
        private IRenderer _renderer;
        private Bitmap _bitmap;
        private int[,] _pixels;
        private double _counter = 0.0;
        private readonly List<Ball> _balls = new List<Ball>();
        
        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Shown(object sender, EventArgs e)
        {
            Refresh();
            _renderer = new MetaRenderer();
            _bitmap = new Bitmap(320, 200);
            _pixels = new int[320, 200];
            for (var i = 0; i < 30; i += 3)
            {
                _balls.Add(new Ball(MovementDescription.Randomize(), i, false));
                _balls.Add(new Ball(MovementDescription.Randomize(), i + 1, false));
                _balls.Add(new Ball(MovementDescription.Randomize(), i + 2, true));
            }
            timer1.Enabled = true;
        }

        private void timer1_Tick(object sender, EventArgs e)
        {
            //Clear array.
            for (var y = 0; y < 200; y++)
                for (var x = 0; x < 320; x++)
                    _pixels[x, y] = 0;

            foreach (var ball in _balls)
                _renderer.Apply(ball, _pixels);
            
            //Draw.
            _renderer.Draw(_pixels, _bitmap);
            foreach (var ball in _balls)
                ball.Tick(_counter);

            _counter += 1.0;
            Refresh();
        }

        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            if (_bitmap == null)
                return;
            e.Graphics.InterpolationMode = InterpolationMode.NearestNeighbor;
            e.Graphics.DrawImage(_bitmap, 0, 0, 640, 400);
        }
    }
}

De resurser som används är _renderer som ansvarar för att bestämma hur bollarna påverkar varandra och hur det ska se ut, _bitmap som är ytan jag renderar till, _pixels som är min matris för beräkningar, _counter som används för sinusbanorna och _balls som är mina metabollar. Notera att jag, likt inställningarna jag nämnde tidigare, låtit Visual Studio mappa upp mina events, så dessa syns inte i koden. Men de kan läsas av från namngivningen av procedurerna.

Som synes av den sista kodraden zoomar jag resultatet med 50%. Om man vill se resultatet i naturlig storlek behöver man inte ange InterpolationMode (efter som ingen pixelinterpolering då sker) eller någon ny storlek (640, 400).

Jag har valt att peka ut renderingen med ett interface (IRenderer) eftersom det är mycket troligt att man vill ha olika renderingskod under tiden man designar sitt alster och när man är nöjd. T.ex. är det rimligt att man tydligt vill se sina bollar flytta sig över skärmen när man kalibrerar deras banor, men när det är färdigt vill man självklart se hur de påverkar varandra, eftersom det är det som är syftet (och det som visas i videon ovan). Här är IRenderer:

using System.Drawing;

namespace Metaballs
{
    public interface IRenderer
    {
        void Apply(Ball source, int[,] target);
        void Draw(int[,] source, Bitmap target);
    }
}

En debug-implementation kanske skulle låta Apply färgsätta de individuella bollarna olika och låta Draw visa det. Däremot är en produktionsimplementation av IRenderer hjärtat i programmet. Där skulle Apply addera eller subtrahera en boll på spelplanen, och Draw skulle visa en kontur baserat på det. En boll (Ball) representerar en position och en rörelse för en boll, och för att kunna hitta tröskelvärden när två bollar är nära varandra, består dessa av en cirkel med låga värden nära konturen och höga värden nära centrum. På så vis kan en godtycklig kontur skapas från summan som skapas när bollarna adderats till ytan (eller subtraherats, för de negativa bollarna). I min implementation är varje boll 98×98 pixlar stor, varför deras centrum ligger 49 pixlar i varje riktning från sin position, vilket framgår av Apply:

using System.Drawing;

namespace Metaballs
{
    public class MetaRenderer : IRenderer
    {
        private Color[] _colors;

        public MetaRenderer()
        {
            _colors = new Color[100];
            for (var i = 0; i < _colors.Length; i++)
                _colors[i] = Color.Black;
            var j = 60;
            for (var c = 0; c < 255; c += 30)
            {
                _colors[j] = Color.FromArgb(c, c, c);
                j++;
            }
            for (var c = 255; c >= 0; c -= 30)
            {
                _colors[j] = Color.FromArgb(c, c, c);
                j++;
            }
        }

        public void Apply(Ball source, int[,] target)
        {
            var ballX = (int)source.X - 49;
            var ballY = (int)source.Y - 49;
            for (var y = 0; y < 98; y++)
            {
                for (var x = 0; x < 98; x++)
                {
                    var xp = ballX + x;
                    if (xp < 0 || xp >= 320)
                        continue;
                    var yp = ballY + y;
                    if (yp < 0 || yp >= 200)
                        continue;
                    if (source.Negative)
                        target[xp, yp] -= DataDefinitions.Ball98[x, y];
                    else
                        target[xp, yp] += DataDefinitions.Ball98[x, y];
                }
            }
        }
        
        public void Draw(int[,] source, Bitmap target)
        {
            for (var y = 0; y < 200; y++)
            {
                for (var x = 0; x < 320; x++)
                {
                    target.SetPixel(x, y,
                        source[x, y] < _colors.Length
                        && source[x, y] >= 0
                            ? _colors[source[x, y]]
                            : Color.Black);
                }
            }
        }
    }
}

(Anti-aliasing-effekten uppnås av den toning som konfigureras i konstruktorn ovan.) Så här ser en boll ut:

using System;
   
   namespace Metaballs
   {
       public class Ball
       {
           private const double CenterX = 159.0;
           private const double CenterY = 99.0;
           private readonly MovementDescription _d;
           
           public double X { get; private set; }
           public double Y { get; private set; }
           public int Index { get; }
           public bool Negative { get; }
           
           public Ball(MovementDescription movementDescription, int index, bool negative)
           {
               _d = movementDescription;
               Index = index;
               Negative = negative;
               X = 159;
               Y = 99;
           }
   
           public void Tick(double counter)
           {
               X = CenterX + Math.Sin(counter / _d.SinFactor1) * _d.SinRadius1
                           + Math.Sin(counter / _d.SinFactor2) * _d.SinRadius2;
               Y = CenterY + Math.Cos(counter / _d.CosFactor1) * _d.CosRadius1
                           + Math.Cos(counter / _d.CosFactor2) * _d.CosRadius2;
           }
       }
   }

MovementDescription är en struktur som samlar data om hur sinusbanan ska se ut. Som man kunde ana från huvudprogrammet erbjuder strukturen en möjlighet att låta slumpen avgöra hastighet och radie.

using System;

namespace Metaballs
{
    public struct MovementDescription
    {
        private static Random Rnd;
        public double SinFactor1 { get; }
        public double SinFactor2 { get; }
        public double CosFactor1 { get; }
        public double CosFactor2 { get; }
        public double SinRadius1 { get; }
        public double SinRadius2 { get; }
        public double CosRadius1 { get; }
        public double CosRadius2 { get; }

        
        static MovementDescription()
        {
            Rnd = new Random();
        }
        
        public MovementDescription(
            double sinFactor1,
            double sinFactor2,
            double cosFactor1,
            double cosFactor2,
            double sinRadius1,
            double sinRadius2,
            double cosRadius1,
            double cosRadius2)
        {
            SinFactor1 = sinFactor1;
            SinFactor2 = sinFactor2;
            CosFactor1 = cosFactor1;
            CosFactor2 = cosFactor2;
            SinRadius1 = sinRadius1;
            SinRadius2 = sinRadius2;
            CosRadius1 = cosRadius1;
            CosRadius2 = cosRadius2;
        }

        public static MovementDescription Randomize() =>
            new MovementDescription(
                Rnd.Next(10, 100),
                Rnd.Next(10, 100),
                Rnd.Next(10, 100),
                Rnd.Next(10, 100),
                Rnd.Next(10, 100),
                Rnd.Next(10, 100),
                Rnd.Next(10, 100),
                Rnd.Next(10, 100)
            );
    }
}

Därmed är det enda som återstår själva bollen som ovan refereras till som Ball98, uppkallad efter sina sidors storlek. För att göra det enkelt, ritade jag boll genom att välja penselverktyget i Photoshop och skrev ett enkelt program som konverterade det hela till en int array i C#, enligt följande:

namespace Metaballs
{
    public class DataDefinitions
    {
        public static int[,] Ball98 = new int[98, 98]
{
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 5, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 3, 4, 3, 4, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 5, 5, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 3, 2, 2, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 6, 7, 8, 9, 9, 9, 9, 9, 10, 10, 9, 9, 10, 10, 10, 9, 9, 10, 9, 9, 8, 9, 8, 8, 8, 7, 7, 6, 6, 5, 4, 5, 4, 4, 3, 2, 3, 3, 3, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 12, 12, 12, 11, 11, 11, 10, 10, 10, 9, 9, 8, 7, 7, 6, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 14, 14, 15, 15, 14, 14, 13, 13, 13, 12, 11, 12, 11, 10, 9, 8, 8, 7, 6, 6, 5, 5, 4, 5, 3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8, 8, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 16, 16, 16, 15, 15, 14, 14, 14, 13, 11, 11, 10, 10, 9, 8, 8, 7, 7, 6, 5, 5, 4, 4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 9, 11, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 19, 20, 20, 20, 20, 21, 20, 20, 20, 20, 19, 19, 18, 18, 17, 16, 16, 15, 14, 13, 12, 12, 11, 9, 9, 8, 7, 6, 6, 5, 4, 4, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 11, 13, 13, 14, 15, 16, 16, 17, 19, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 23, 23, 22, 21, 21, 21, 19, 19, 19, 18, 17, 14, 15, 14, 12, 11, 10, 9, 8, 7, 7, 5, 5, 5, 4, 4, 3, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 7, 7, 7, 9, 11, 11, 12, 13, 15, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26, 26, 27, 27, 28, 27, 27, 27, 27, 26, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 14, 13, 12, 11, 11, 9, 7, 8, 6, 6, 6, 5, 4, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 7, 7, 9, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 23, 23, 25, 25, 26, 28, 28, 29, 31, 31, 31, 32, 32, 31, 31, 31, 31, 31, 30, 29, 28, 26, 25, 25, 23, 22, 21, 19, 18, 17, 15, 14, 13, 11, 11, 10, 8, 8, 7, 6, 6, 5, 4, 3, 3, 3, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 18, 20, 20, 21, 23, 26, 26, 28, 29, 30, 32, 33, 33, 35, 35, 36, 36, 36, 36, 36, 36, 35, 35, 34, 33, 32, 30, 29, 28, 27, 25, 23, 21, 21, 20, 18, 16, 15, 13, 12, 11, 9, 8, 8, 6, 6, 5, 4, 4, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 20, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 37, 39, 40, 41, 42, 42, 42, 42, 42, 42, 41, 40, 38, 37, 36, 35, 33, 32, 30, 29, 27, 25, 23, 22, 20, 18, 17, 15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 4, 4, 3, 3, 2, 1, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}, 
{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 5, 5, 7, 8, 10, 10, 11, 12, 14, 16, 17, 19, 22, 24, 26, 27, 29, 31, 33, 35, 37, 39, 40, 42, 43, 44, 45, 46, 47, 48, 48, 48, 48, 47, 46, 46, 44, 44, 42, 40, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 20, 18, 16, 15, 13, 11, 10, 9, 8, 7, 5, 5, 5, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}, 
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};
    }
}

Mycket nöje!

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