gistfile1.cs

using System;
using System.Diagnostics;
using System.Drawing;

namespace ProcessingTest {
	class Program {
		// N.B. KnownGood[-y,+x]
		static int[,] KnownGoodData = new int[,]
			{ { 36, 35, 34, 33, 32, 31, 30, 55 }
			, { 37, 16, 15, 14, 13, 12, 29, 54 }
			, { 38, 17,  4,  3,  2, 11, 28, 53 }
			, { 39, 18,  5,  0,  1, 10, 27, 52 }
			, { 40, 19,  6,  7,  8,  9, 26, 51 }
			, { 41, 20, 21, 22, 23, 24, 25, 50 }
			, { 42, 43, 44, 45, 46, 47, 48, 49 }
			};

		static int CenterX;
		static int CenterY;

		static Program() {
			var w = KnownGoodData.GetLength(1);
			var h = KnownGoodData.GetLength(0);

			for ( int x=0 ; x<w ; ++x )
			for ( int y=0 ; y<h ; ++y )
			{
				if ( KnownGoodData[y,x]==0 )
				{
					CenterX = x;
					CenterY = y;
					return;
				}
			}

			Debug.Fail("Failed to find center");
		}

		static void AssertValueAt( int x, int y, int value )
		{
			Debug.Assert( KnownGoodData[ CenterY-y, CenterX+x ] == value );
		}

		static Point CalculatePositionOf( int n )
		{
			var ring = (int)Math.Ceiling( 0.5 * ( 1 + Math.Sqrt( n + 1 ) ) ) - 1;
			var corner_value = ring * (ring+1) * 4;

			var missing = corner_value-n;
			var left  = Math.Max(0,Math.Min(2*ring,missing-0*ring));
			var up    = Math.Max(0,Math.Min(2*ring,missing-2*ring));
			var right = Math.Max(0,Math.Min(2*ring,missing-4*ring));
			var down  = Math.Max(0,Math.Min(2*ring,missing-6*ring));

			Debug.Assert( missing <= 8*ring );

			var x = +ring - left + right;
			var y = -ring - down + up;
			return new Point(x,y);
		}

		static void Main() {
			for ( int i=0 ; i<=55 ; ++i )
			{
				var xy = CalculatePositionOf(i);
				AssertValueAt(xy.X,xy.Y,i);
			}
		}
	}
}