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2D Thick Lines

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I'm trying to develop a sand game, like PyroSand or Burning Sand, in C++, and I'm running into problems when it comes to drawing. I've tried drawing a box at the mouse's position, but that doesn't look right because it leaves gaps, so I need a thick line function, which should be as optimised as possible. What I've tried: This uses Bresenham's algorithm, and places a box at each point - this works, but is quite slow, since it draws a whole box at each point.
void Particle::drawThickLine(ParticleType *ept, int width, int x1, int y1, int x2, int y2)
{
	bool steep = abs(y2 - y1) > abs(x2 - x1);
	int hw = width/2;

	if (steep)
	{
		swap(x1, y1);
		swap(x2, y2);
	}
	if (x1 > x2)
	{
		swap(x1, x2);
		swap(y1, y2);
	}

	int dx	= x2 - x1;
	int dy	= abs(y2 - y1);
	int e	= dx/2;
	int ys	= y1 < y2 ? 1 : -1;
	int y	= y1;

	for(int x = x1; x < x2; x ++)
	{
		if (steep) new Particle(ept, y-hw, x-hw, y+hw, x+hw); else drawBox(ept, x-hw, y-hw, x+hw, y+hw);
		e -= dy;
		if (e < 0)
		{
			y += ys;
			e += dx;
		}
	}
}
I tried to make a "parallel line" algorithm, but it screwed up on perfectly diagonal lines, so I scrapped it. A more efficient version of the above would be great, if anyone knows how to do this stuff.

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