public SpiralSegment Next()
{
var nextSegment = new SpiralSegment();
// Update X and Y direction according to the cycle:
// ... Right -> Down -> Left -> Up -> Right ...
//
// dX dY Direction
//-------------------
// 1 0 Right
// 0 1 Down
// -1 0 Left
// 0 -1 Up
nextSegment.Direction = new Vector2D(
x: -1 * this.Direction.Y,
y: this.Direction.X);
// If changing from vertical to horizontal movement, increase the length of the segment by 1
nextSegment.Length = nextSegment.Direction.X == 0 ? this.Length : this.Length + 1;
return nextSegment;
}
/// <summary>
/// Calculates the dimensions required for the spiral data matrix
/// by simulating a run through the spiral.
/// </summary>
/// <param name="width">Output: width of matrix</param>
/// <param name="height">Output: height of matrix</param>
private void CalculateGridDimensions(out int width, out int height)
{
int minX = 0;
int minY = 0;
int maxX = 0;
int maxY = 0;
var location = new Vector2D(0, 0);
var segment = new SpiralSegment(1, UnitVectors.Right);
int index = 0;
do
{
int remainingCells = _maxValue - index;
Vector2D distanceToTravel;
if (remainingCells >= segment.Length)
{
// travel the full segment and then get the next segment
index += segment.Length;
distanceToTravel = segment.Direction.Multiply(segment.Length);
segment = segment.Next();
}
else
{
// travel the remaining cells
index += remainingCells;
distanceToTravel = segment.Direction.Multiply(remainingCells);
}
location = location.Add(distanceToTravel);
// Update the observed bounds
minX = (int)Math.Min(minX, location.X);
minY = (int)Math.Min(minY, location.Y);
maxX = (int)Math.Max(maxX, location.X);
maxY = (int)Math.Max(maxY, location.Y);
} while (index < _maxValue);
width = maxX - minX + 1;
height = maxY - minY + 1;
}
/// <summary>
/// Generates a matrix representing a clockwise spiral of numbers
/// with zero at the center
/// </summary>
/// <returns>Returns a matrix representing a spiral of numbers</returns>
private int[,] GenerateSpiral()
{
// initialize the grid
var output = InitializeGrid();
int width = output.GetLength(0);
int height = output.GetLength(1);
// Start at the center of the grid
var location = new Vector2D(
x: (int)((width - 1) / 2),
y: (int)((height - 1) / 2));
// Set the initial segment (move 1 cell to the right)
var segment = new SpiralSegment(1, UnitVectors.Right);
int segmentIndex = 0;
for (var i = 0; i <= _maxValue; i++)
{
output[location.X, location.Y] = i;
// Move to the next cell
segmentIndex++;
location = location.Add(segment.Direction);
// If this is the end of a segment, then change directions
// and start a new segment
if (segmentIndex >= segment.Length)
{
segmentIndex = 0;
segment = segment.Next();
}
}
return output;
}