function p=minDist2points02(points, x0, showPlot)
% minDist2points: Compute the point that has the min total distance to a set of points
if nargin<2||isempty(x0), x0=mean(points, 2); end	% Initial guess
p=fminsearch(@(x)dist2pointsInner(x, points), x0);

if showPlot && length(x0)==2
	% ====== Create the objective function surface
	minValue=min(points, [], 2);
	maxValue=max(points, [], 2);
	x=linspace(minValue(1), maxValue(1), 51);
	y=linspace(minValue(2), maxValue(2), 51);
	zz=zeros(length(y), length(x));
	for i=1:length(x)
		for j=1:length(y);
			zz(j,i)=dist2points([x(i), y(j)]', points);
		end
	end
	% ====== Mesh & contour plot
	subplot(121); h=meshc(x, y, zz); axis image; box on
	xlabel('X'); ylabel('Y'); zlabel('Z');
	set(h(1), 'faceAlpha', 0.1);	% Make the mesh transparent
	axisLimit=axis;
	line(p(1), p(2), axisLimit(5), 'marker', '.', 'color', 'r');
	for i=1:size(points,2)
		line(points(1,i), points(2,i), axisLimit(5)*[1 1 1 1], 'marker', '.', 'color', 'k', 'markerSize', 20);
	end
	% ====== Detailed contour plot
	subplot(122); contour(x, y, zz, 100); axis image
	xlabel('X'); ylabel('Y'); zlabel('Z');
	line(p(1), p(2), 'marker', '.', 'color', 'r', 'markerSize', 20);
	for i=1:size(points,2)
		line(points(1,i), points(2,i), 'marker', '.', 'color', 'k', 'markerSize', 20);
	end
end

function sumDistance=dist2pointsInner(x, points)
% dist2points: The sum of distance sum to points
sumDistance=0;
for i=1:size(points,2)
	sumDistance=sumDistance+norm(x-points(:,i));
end