schemaball.m

function schemaball(strNames, corrMatrix, fontsize, positive_color_hs, negative_color_hs, theta)
%% SCHEMABALL(strNames, corrMatrix, fontsize, positive_color_hs, negative_color_hs, theta)
%	inspired by http://mkweb.bcgsc.ca/schemaball
%	discussion at http://stackoverflow.com/questions/17038377
%
%	Draws a circular represenation of a correlation matrix.
%	Use no input arguments for a demo.
%
%INPUT ARGUMENTS
%	strNames	The names of variables of the correlation matrix
%				Format: Mx1 cell array of strings
%	corrMatrix	Correlation matrix (MxM)
%OPTIONAL:
%	fontsize	Font size of the labels along the edge
%				Default: 30/exp(M/30)
%	positive_color_hs:
%				The hue and saturation of the connection lines for
%				variables with a positive correlation.
%	negative_color_hs:
%				The hue and saturation of the connection lines for
%				variables with a negative correlation.
%	theta		Mx1 vector of angles at which the labels and connector
%				lines must be placed. If not supplied, they are evenly
%				distributed along the whole edge of the circle.
%

	if nargin==0 % DEMO
		strNames = {'Lorem','ipsum','dolor','sit','amet','consectetur', ...
			'adipisicing','elit','sed','do','eiusmod','tempor','incididunt',...
			'ut','labore','et','dolore','magna','aliqua'};
		
		% generate random symmetric matrix:
		a=rand(numel(strNames));
		corrMatrix=triu(a) + triu(a,1)';
		corrMatrix = 2*corrMatrix-max(corrMatrix(:));
		corrMatrix = corrMatrix.^5;
	else
		narginchk(2,6);
	end
	%% Check input arguments
	M = numel(strNames);
	if ndims(corrMatrix)~=2 || size(corrMatrix,1)~=size(corrMatrix,2) || length(corrMatrix)~=M
		error('SchemaBall:InvalidInputArguments','Invalid size of ''corrMatrix''');
	end
	if nargin<3
		fontsize = 30/exp(M/30);
	end
	if nargin<4
		theta = linspace(0,2*pi,M+1);
		theta(end)=[];
	elseif ~all(size(theta)==size(strNames))
		error('SchemaBall:InvalidInputArguments','Invalid size of ''theta''');
	end
	if nargin<5
		positive_color_hs = [0.1587 0.8750]; % yellow
		negative_color_hs = [0.8333 1]; % magenta
	end
	
	%% Configuration
	R = 1;
	Nbezier = 100;
	bezierR = 0.1;
	markerR = 0.025;
	labelR = 1.1;
	
	%% Create figure with invisible axes, just black background
	figure;%('Renderer','zbuffer');
	hold on
	set(gca,'color','black','XTick',[],'YTick',[]);
	set(gca,'position',[0 0 1 1],'xlim',2*[-1 1]*R,'ylim',2*[-1 1]*R);
	axis equal
	
	%% draw diagonals
	% if you draw the brightest lines first and then the darker lines, the
	% latter will cut through the former and make it look like they have
	% holes. Therefore, sort and draw them in order (darkest first).
	idx = nonzeros(triu(reshape(1:M^2,M,M),1));
	[~,sort_idx]=sort(abs(corrMatrix(idx)));
	idx = idx(sort_idx);
	
	[Px,Py] = pol2cart(theta,R);
	P = [Px ;Py];
	
	for ii=idx'
		[jj,kk]=ind2sub([M M],ii);
		[P1x,P1y] = pol2cart((theta(jj)+theta(kk))/2,bezierR);
		Bt = getQuadBezier(P(:,jj),[P1x;P1y],P(:,kk), Nbezier);
		if corrMatrix(jj,kk)>=0
			clr = hsv2rgb([positive_color_hs abs(corrMatrix(jj,kk))]);
		else
			clr = hsv2rgb([negative_color_hs abs(corrMatrix(jj,kk))]);
		end
		plot(Bt(:,1),Bt(:,2),'color',clr);%,'LineSmoothing','on');
	end
	
	%% draw edge markers
	[Px,Py] = pol2cart(theta,R+markerR);
	% base the color of the node on the 'degree of correlation' with other
	% variables:
	corrMatrix(logical(eye(M)))=0;
	V = mean(abs(corrMatrix),2);
	V=V./max(V);
	clr = hsv2rgb([ones(M,1)*[0.585 0.5765] V(:)]);
	
	%scatter(Px,Py,20,clr);%,'filled'); % non-filled looks better imho
	for ii=1:M
		rectangle('Curvature',[1 1],'edgeColor',clr(ii,:),...
			'Position',[Px(ii)-markerR Py(ii)-markerR 2*markerR*[1 1]]);
	end
	
	%% draw labels
	[Px,Py] = pol2cart(theta,labelR);
	for ii=1:M
		text(Px(ii),Py(ii),strNames{ii},'Rotation',theta(ii)*180/pi,'color',0.8*[1 1 1], ...
			'FontName','FixedWidth','FontSize',fontsize, 'VerticalAlignment','baseline');
	end
end
function Bt = getQuadBezier(p0,p1,p2,N)
	% defining Bezier Geometric Matrix B
	B = [p0(:) p1(:) p2(:)]';
	
	% Bezier Basis transformation Matrix M
	M =[1	0	0;
		-2	2	0;
		1	-2	1];
	% Calculation of Algebraic Coefficient Matrix A
	A = M*B;
	% defining t axis
	t = linspace(0,1,N)';
	T = [ones(size(t)) t t.^2];
	% calculation of value of function Bt for each value of t
	Bt = T*A;
end