function distance_to_line(px, py, x0, y0, x1, y1) {
	  var l2 = sqr(x0 - x1) + sqr(y0 - y1);
	  if (l2 == 0) return point_distance(px, py, x0, y0);
	  
	  var t = ((px - x0) * (x1 - x0) + (py - y0) * (y1 - y0)) / l2;
	  t = clamp(t, 0, 1);
	  
	  return point_distance(px, py, x0 + t * (x1 - x0), y0 + t * (y1 - y0));
}

function distance_to_line_infinite(px, py, x0, y0, x1, y1) {
	return abs((x1 - x0) * (y0 - py) - (x0 - px) * (y1 - y0)) / sqrt(sqr(x1 - x0) + sqr(y1 - y0));	
}

function point_project_line(px, py, l0x, l0y, l1x, l1y) {
	var mag = point_distance(l0x, l0y, l1x, l1y);
	var dir = point_direction(l0x, l0y, l1x, l1y);
	var dt  = dot_product(px - l0x, py - l0y, l1x - l0x, l1y - l0y) / mag;
	
	return [l0x + lengthdir_x(dt, dir), l0y + lengthdir_y(dt, dir)];
}

function point_project_curve(mx, my, x0, y0, x1, y1) {
	var xc = (x0 + x1) / 2;
	var sample = ceil((abs(x0 - x1) + abs(y0 - y1)) / 16 * PREF_MAP[? "connection_line_sample"]);
	sample = clamp(sample, 8, 128);
	
	var dist = 999999;
	var ox, oy, nx, ny, t, it;
	var pp = [mx, my];
	
	for( var i = 0; i <= sample; i++ )  {
		t = i / sample;
		it = 1 - t;
		
		nx = x0 * t * t * t + 3 * xc * it * t * t + 3 * xc * it * it * t + x1 * it * it * it;
		ny = y0 * t * t * t + 3 * y0 * it * t * t + 3 * y1 * it * it * t + y1 * it * it * it;
		
		if(i && dist < distance_to_line(mx, my, ox, oy, nx, ny)) {
			dist = distance_to_line(mx, my, ox, oy, nx, ny);
			pp = point_project_line(mx, my, ox, oy, nx, ny);
		}
		
		ox = nx;
		oy = ny;
	}
	
	return pp;
}

function point_project_elbow(px, py, x0, y0, x1, y1) {
	var cx = (x0 + x1) / 2;
	var maxy = max(y0, y1);
	var miny = min(y0, y1);
	
	if(py < miny) return [ px, miny ];
	if(py > maxy) return [ px, maxy ];
	return [ cx, py ];
}