Line -> Grid intersection code (all plotted cells directly connected)

Shared Code
#1

Usage:


int[] xy = new int[...];
int len = LineGridIntersection.plot(xSrc, ySrc, xDest, yDest, TILE_SIZE, TILE_SIZE, xy];
for(int i=0; i<len; i++) {
   int x = xy[i*2+0];
   int y = xy[i*2+1];
   // ...
}

Implementation:


	public static int plot(int x1, int y1, int x2, int y2, int wCell, int hCell, int[] xy) {
		// support negative input values
		int xOffset = (-Math.min(0, Math.min(x1, x2)) + wCell - 1) / -wCell;
		int yOffset = (-Math.min(0, Math.min(y1, y2)) + hCell - 1) / -hCell;
		x1 -= xOffset * wCell;
		y1 -= yOffset * hCell;
		x2 -= xOffset * wCell;
		y2 -= yOffset * hCell;
		assert (x1 | y1 | x2 | y2) >= 0;

		// ensure x1 <= x2
		if (x1 > x2) {
			int t;

			t = x1;
			x1 = x2;
			x2 = t;

			t = y1;
			y1 = y2;
			y2 = t;
		}

		int p = 0;

		int xCell1 = (int) ((x1 + 0.5f) / wCell);
		int yCell1 = (int) ((y1 + 0.5f) / hCell);
		int xCell2 = (int) ((x2 + 0.5f) / wCell);
		int yCell2 = (int) ((y2 + 0.5f) / hCell);

		int yMin = Math.min(y1, y2);
		int yMax = Math.max(y1, y2);
		int yCellMin = Math.min(yCell1, yCell2);
		int yCellMax = Math.max(yCell1, yCell2);

		if (xCell1 == xCell2) {
			// handle vertical line
			for (int yCell = yCellMin; yCell <= yCellMax; yCell++) {
				xy[p++] = xOffset + xCell1;
				xy[p++] = yOffset + yCell;
			}
		} else if (yCell1 == yCell2) {
			// handle horizontal line
			for (int xCell = xCell1; xCell <= xCell2; xCell++) {
				xy[p++] = xOffset + xCell;
				xy[p++] = yOffset + yCell1;
			}
		} else {
			// handle diagonal line
			int xCell = xCell1;
			int yCell = yCell1;

			// calculate normal of path
			double nx, ny;
			{
				double dx = x2 - x1;
				double dy = y2 - y1;
				double dist = Math.sqrt(dx * dx + dy * dy);
				nx = dx / dist;
				ny = dy / dist;
			}

			final double advancePerCell = wCell / nx;

			double firstStepRatio = (((xCell + 1) * wCell) - (double) x1) / wCell;
			double x = x1 + nx * advancePerCell * firstStepRatio;
			double y = y1 + ny * advancePerCell * firstStepRatio;

			while (true) {
				// handle cases where adjecent cells are also touched
				//  - this happens when we advanced a cell and the Y-cell doesn't have the expected value 
				if (ny > 0.0f) {
					for (int yEnd = Math.min((int) y / hCell - 1, yCell2); yCell <= yEnd; yCell++) {
						xy[p++] = xOffset + xCell;
						xy[p++] = yOffset + yCell;
					}
				} else {
					for (int yOff = Math.max((int) y / hCell - 0, yCell2); yCell > yOff; yCell--) {
						xy[p++] = xOffset + xCell;
						xy[p++] = yOffset + yCell;
					}
				}

				if (x >= x2 || y <= yMin || y >= yMax) {
					break;
				}

				// advance with 1 cell
				x += nx * advancePerCell;
				y += ny * advancePerCell;

				xy[p++] = xOffset + xCell++;
				xy[p++] = yOffset + yCell;
			}

			// handle last cell
			if (p == 0 || xy[p - 2] != xOffset + xCell2 || xy[p - 1] != yOffset + yCell2) {
				xy[p++] = xOffset + xCell2;
				xy[p++] = yOffset + yCell2;
			}
		}

		return p >> 1;
	}

	public static final int plotReferenceImpl(int x1, int y1, int x2, int y2, int wCell, int hCell, int[] xy) {
		// support negative input values
		int xOffset = (-Math.min(0, Math.min(x1, x2)) + wCell - 1) / -wCell;
		int yOffset = (-Math.min(0, Math.min(y1, y2)) + hCell - 1) / -hCell;
		x1 -= xOffset * wCell;
		y1 -= yOffset * hCell;
		x2 -= xOffset * wCell;
		y2 -= yOffset * hCell;
		assert (x1 | y1 | x2 | y2) >= 0;

		int p = 0;

		int dist = Math.max(Math.abs(x2 - x1), Math.abs(y2 - y1));
		if (dist == 0) {
			xy[p++] = xOffset + x1;
			xy[p++] = yOffset + x2;
		} else {
			float dx = (float) (x2 - x1) / dist;
			float dy = (float) (y2 - y1) / dist;
			int lastRegX = (int) (x1 + dx + 0.5f) / wCell;
			int lastRegY = (int) (y1 + dy + 0.5f) / hCell;

			xy[p++] = xOffset + lastRegX;
			xy[p++] = yOffset + lastRegY;

			for (int d = 2; d <= dist; d++) {
				int x = (int) (x1 + 0.5f + dx * d);
				int y = (int) (y1 + 0.5f + dy * d);
				int regX = x / wCell;
				int regY = y / hCell;
				if (regX != lastRegX || regY != lastRegY) {
					xy[p++] = xOffset + regX;
					xy[p++] = yOffset + regY;
				}
				lastRegX = regX;
				lastRegY = regY;
			}
		}

		return p >> 1;
	}



plotting 1048576 lines in 256x256 grid (array) took:      485ms
plotting 1048576 lines in 256x256 grid (ref.impl) took: 10348ms
#2

I have some code to do this, except the start and end points don’t need to be on the grid… and I don’t pass a start and end point, I have a start point, direction vector, and maximum number of cells to traverse.

http://pastebin.com/35ZiZQnx

#3

Could you tell me how this yields useful results?

If you travel in a straight line on one axis, your algorithm would travel three times as far than when traveling diagonally in 3D space. Even very slight changes in your direction vector will strongly influence its reach.

#4

You can set the limit to some large number, then easily keep track of distance squared yourself to ensure you don’t go outside some sphere. Like you mentioned, the limit doesn’t mean length at all… it’s not supposed to be used in that sense. You should decide when to stop it based on distance or some other factor (hitting a certain type of cell).

#5

Then why is that limit configurable at all…?

#6

Maybe the person who uses it cares about how many blocks are iterated over, and want to stop at a specific number vs. distance.

It’s also faster to just check number of blocks iterated versus calculate distance squared for each block.

In my engine I don’t really care about distance, I just want the code to be quick since I could be doing tonnnnns of these every frame… not that that would affect performance =P