function J = l2cmap(m,hue)
% function J = l2cmap(m,hue)
% 
% Two-Sided Linear Color Map
%   L2CMAP(M) is an M-by-3 matrix
%   Hue, Saturation and Intensity linearly ramped from an achromatic center.
%   Saturation from 0.5 to 1, Intensity from 0.5 to 1 (half-scales chosen
%   to avoid white,black...perhaps on better screens)
%   Hue linearly ramped 0 to 1/3 (color components are cyclic with period
%   1/3).  Center hue forced to secondary color.
%   L2CMAP, by itself, is the same length as the current figure's
%   colormap.
%
% optional second input "hue" is the center color. For very interesting
% reasons it must be on a secondary color; 'c',{'m'},'y'
%
% Following IBM research on human color perception:
% Why Should Engineers and Scientists Be Worried About Color?
% http://www.research.ibm.com/people/l/lloydt/color/color.HTM
%
% T.Hilmer UH
% 2010.03.14  version 1

if nargin < 1 || isempty(m)
   m = size(get(gcf,'colormap'),1);
   hue = 'c'; % MUST be on primary color for linear saturation
end
if nargin < 2
    if ischar(m)
        hue = m;
        m = size(get(gcf,'colormap'),1);
    else
        hue = 'c'; % MUST be on primary color for linear saturation
    end
end

if strcmp(hue,'c')
    hue = 2/3;
elseif strcmp(hue,'m')
    hue = 1/3;
elseif strcmp(hue,'y')
    hue = 0;
else
    error('"hue" must be ''c'',''m'',or ''y''')
end

J = zeros(m,3);

n = floor(m/2);

if rem(m,2) % odd
    z = 0; % zero resolved
else  % even
    z = [];
end

% Hue has period 1, but the primary colors R,G,B have period 1/3.  I don't
% know how to describe it better, but these components are "orthogonal",
% and thus Hue is best separated into thirds. Transitions across hue don't
% seem visually linear to me.  Simply do a colormap(hsv),colorbar.  The
% primary colors are flat, and the strongest gradients are across c,m,y.
% Almost sinusoidal...
jh = linspace(0,1/3,m);
jh = jh - hue; % apply hue shift
j = jh < 0;
jh(j) = jh(j) + 1;
j = jh >= 1;
jh(j) = jh(j) - 1;

% The effect of a 2-sided linear saturation is very interesting.  It maps
% sinusoidally to rgb, depending on /where/ the center Hue is,
% soecifically, whether it maps to a primary color  

% It's fascinating that the visual resolution of the colormap seems "tuned"
% to work if the center is on a secondary color (c,m,y), and completely out
% of tune on a primary color.

js = 0.5;% half or whole scale, (0 or 0.5)
js = js : (1-js)/(n-1) : 1; % nice and symmetric
js = [ fliplr(js) z js ];
% js = [ js z fliplr(js) ];

% js = 1;

jv = 0.5;% half or whole scale
jv = jv : (1-jv)/(n-1) : 1; % nice and symmetric
% jv = [ fliplr(jv) z jv ];
jv = [ jv z fliplr(jv) ];

% jv = 1;


% HSV ramps:
J(:,1) = jh; % HUE
J(:,2) = js; % SATURATION
J(:,3) = jv; % INTENSITY

J = hsv2rgb(J);