TilingUtil.cs

using System;
using System.Collections.Generic;

namespace g3
{
	public static class TilingUtil
	{


		/// <summary>
		/// Regular-grid tiling of element inside bounds, with spacing between elements
		/// Returns list of translations to element.
		/// Always allows at least one row and column, even if element overflows bounds in that dimension.
		/// </summary>
		public static List<Vector2d> BoundedRegularTiling2(AxisAlignedBox2d element, AxisAlignedBox2d bounds,
														   double spacing)
		{
			Vector2d oshift = -element.Min;
			double w = element.Width; double h = element.Height;

			int nx = Math.Max(1, (int)(bounds.Width / w));
			double spacew = (nx - 1) * spacing;
			while (nx > 1 && bounds.Width - (w * nx + spacew) < 0)
			{
				nx--;
			}

			int ny = Math.Max(1, (int)(bounds.Height / h));
			double spaceh = (ny - 1) * spacing;
			while (ny > 1 && bounds.Height - (h * ny + spaceh) < 0)
			{
				ny--;
			}

			var translations = new List<Vector2d>();
			for (int yi = 0; yi < ny; ++yi)
			{
				double dy = yi * h + yi * spacing;
				for (int xi = 0; xi < nx; ++xi)
				{
					double dx = xi * w + xi * spacing;
					translations.Add(new Vector2d(dx, dy) + oshift + bounds.Min);
				}
			}

			return translations;
		}





		/// <summary>
		/// hex-grid tiling of circles inside bounds, with spacing between elements
		/// Returns list of translations to element.
		/// Always allows at least one row and column, even if element overflows bounds in that dimension.
		/// </summary>
		public static List<Vector2d> BoundedCircleTiling2(AxisAlignedBox2d element, AxisAlignedBox2d bounds,
															 double spacing)
		{
			Vector2d oshift = -element.Min;
			double w = element.Width; double h = element.Height;
			if (MathUtil.EpsilonEqual(w, h, MathUtil.Epsilonf) == false)
			{
				throw new Exception("BoundedHexTiling2: input box is not square");
			}

			// note: this is a circle tiling, not a hex tiling, so even though we are
			// starting in top-left with a "tip" hex, we don't have to offset down so that tip is inside
			// the box (circle cuts off)

			double r = w / 2;
			var hex = new Hexagon2d(element.Center, r, Hexagon2d.TopModes.Tip);
			hex.InnerRadius = r;

			double stepx = hex.HorzSpacing;
			double stepy = hex.VertSpacing;

			double spacingy = spacing;
			double spacingx = spacing;

			// half-rows on top and bottom add up to full row-height
			int ny = Math.Max(1, (int)(bounds.Height / stepy));
			// reduce count so that we fit w/ spacing
			double spaceh = (ny - 1) * spacingy;
			while (ny > 1 && bounds.Height - (stepy * ny + spaceh) < 0)
			{
				ny--;
			}

			// even rows start at x=0
			int nx_even = Math.Max(1, (int)(bounds.Width / stepx));
			// reduce count if we spill over w/ spacing
			double spacew = (nx_even - 1) * spacingx;
			while (nx_even > 1 && bounds.Width - (stepx * nx_even + spacew) < 0)
			{
				nx_even--;
			}

			// odd rows have an extra half-step added to left side,
			// so we may need to reduce count
			int nx_odd = nx_even;
			spacew = (nx_odd - 1) * spacingx;
			if (ny > 0 && (stepx * nx_odd + spacew + stepx * 0.5) > bounds.Width)
			{
				nx_odd--;
				spacew = (nx_odd - 1) * spacingx;
			}


			var translations = new List<Vector2d>();
			for (int yi = 0; yi < ny; ++yi)
			{
				double dy = yi * stepy + yi * spacingy;

				// x shift and count are different on odd rows
				double shiftx = stepx * 0.5;
				int nx = nx_odd;
				if (yi % 2 == 0)
				{
					shiftx = 0;
					nx = nx_even;
				}

				for (int xi = 0; xi < nx; ++xi)
				{
					double dx = shiftx + xi * stepx + xi * spacingx;
					translations.Add(new Vector2d(dx, dy) + oshift + bounds.Min);
				}
			}

			return translations;
		}

	}
}