You are given the center $$$(C_x, C_y)$$$ and the radii $$$(R_x, R_y)$$$ of an ellipse. You are also given a list $$$L$$$ of points, $$$(x_i, y_i)$$$ where $$$1\leq i\leq |L|$$$. You need to output the score of the list $$$L$$$ as described above.

I determine the error instead of the score since it's easier, and do:

$$$score = 1 - error$$$

The error of a point is scored as a combination of two different errors.

1. The distance error: How far a point is from the circumference.

2. The space error: How far a point is from its neighbor from the expected distance.

The space error is calculated between the projections of the point on the circumference to remove any distance bias it might have, since the distance error is handled differently.

The root-mean square values of these errors are calculated and passed into a function, which returns a value $$$E$$$. There is a maximum tolerance value for the error $$$M$$$.

The score is $$$1 - clamp(E/M, 0, 1)$$$.

function get_projection_on_circumference(point) {
	var angle = point_direction(center_x, center_y, point.x, point.y);
	return new Point(
		center_x + radius * cos(angle),
		center_y + radius * sin(angle),
	);
}

function get_score(points) {
	static max_error = 100;
	var n_points = array_length(points);
	
	// error: distance from circumference
	var dis_error = 0;
	for (var i = 0; i < n_points; ++i) {
		var point = points[i];
		var dis = distance(center_x, center_y, point.x, point.y);
		dis_error += sqr(radius - dis);
	}
	dis_error /= n_points;
	dis_error = sqrt(dis_error);
	
	// project points on the circumference
	for (var i = 0; i < n_points; ++i) {
		points[i] = get_projection_on_circumference(points[i]);
	}
	
	// sort "points" in anti-clockwise order
	array_sort(points, function(p1, p2) {
		var dir1 = point_direction(center_x, center_y, p1.x, p1.y);
		var dir2 = point_direction(center_x, center_y, p2.x, p2.y);
		return ((dir1 < dir2) ? -1 : 1);
	});
	
	// error: evenly spaced
	var space_error = 0;
	var expected_angle = 360 / n_points;
	var j = n_points-1;
	for (var i = 0; i < n_points; ++i) {
		var p1 = points[j];
		var p2 = points[i];
		var dis = distance(p1.x, p1.y, p2.x, p2.y);
		var _val = clamp(1 - sqr(dis)/(2 * sqr(radius)), -1, 1);
		var _angle = darccos(_val);
		space_error += sqr(_angle - expected_angle);
		j = i;
	}
	space_error /= n_points;
	space_error = sqrt(space_error);
	
	// normalize error
	var error = F(dis_error, space_error);
	var error_normalized = clamp(error/max_error, 0, 1);
	
	// get score
	return (1 - error_normalized);
}