Bivariate colorscale for color plot

Is there a way to have a bivariate colorscale for a 2D colorplot? Meaning, lets say I have two sets of data that both depend on the same 2 variables, e.g. f(x,y) and g(x,y). Is there a way to make a 2D color map where the color at point (x,y) depends on both the values of f(x, y) and g(x, y), where I have constructed a 2D colormap in the f,g space?

[DGM]

Perhaps related:

2D colormap question (links to user's solution on github)

https://www.mathworks.com/matlabcentral/answers/1592664-use-of-2d-colormaps-possible-in-matlab

2D colormapping example (also links to (1592664))

https://www.mathworks.com/matlabcentral/answers/1957629-can-this-plot-be-recreated-in-matlab#answer_1228794

2D colormapping using HSx models (with/without quantization) (links to 1592664,1957629)

https://www.mathworks.com/matlabcentral/answers/2034689-applying-a-color-for-each-pair-of-spherical-angles-through-the-hue-and-lightness-parameters

Answer 1

[Mathieu NOE]

hello

maybe this ?

I simply assumed for the demo that f and g would be describing a circle in a 2D space

the second plot is just a check of my code , but I guess the final goal is not to use f,g but x,y instead (simple change, see commented lines)

%% create f,g functions 
dx = 1/8;
N = 100;
x = linspace(-pi/2,pi/2,N);
y = linspace(-pi/2,pi/2,N);
zf =  sin(x+y);% function f
zg =  cos(x+y);% function g

%% create 2D colormap 
% https://fr.mathworks.com/matlabcentral/answers/588934-how-can-i-make-a-2d-color-map
R=[1 0;
   1 0];
G=[1 1
   0 0];
B=[0 0
   0 1];
R = interp2(R,8);
G = interp2(G,8);
B = interp2(B,8);
I = uint8(255*cat(3,R,G,B));
[m,n,p] = size(I);

%% find row, col  indexes of I mapping f and g 
% f : x axis
% g : y axis
xx = linspace(min(zf),max(zf),m);
yy = linspace(min(zg),max(zg),n);

for k = 1:numel(zf)
[val,xxi(k)] = min(abs(zf(k)-xx));
end

for k = 1:numel(zg)
[val,yyi(k)] = min(abs(zg(k)-yy));
end

figure
axis square
image(I)
set(gca,'YDir','normal');
hold on
plot(xxi,yyi);
ind = 1:3:N-3;
for cc = 1:numel(ind)
text(xxi(ind(cc)),yyi(ind(cc)),num2str(ind(cc)));
end
hold off

figure
grid on
hold on

for k = 1:N
    c(k,:) = squeeze(I(yyi(k),xxi(k),:));
%     h = plot(x(k),y(k),'o'); 
    h = plot(zf(k),zg(k),'o'); 
    h.Color = c(k,:);
end

for cc = 1:numel(ind)
% text(x(ind(cc)),y(ind(cc)),num2str(ind(cc)));
text(zf(ind(cc)),zg(ind(cc)),num2str(ind(cc)));

end

[William Rose]

Nice answer from @Mathieu NOE.

Answer 2

[William Rose]

Another approach is to map f in one color and map g in another color, then combine them.

x=-10:0.5:10; y=-10:0.5:10;
[X,Y]=meshgrid(x,y);
f=10*exp(-(X.^2+Y.^2)/32);
g=(X+Y)/10;
% Color values for f (range from 0 to 1)
cf=(f-min(f,[],"all"))/(max(f,[],"all")-min(f,[],"all"));
% Color values for g (range from 0 to 1)
cg=(g-min(g,[],"all"))/(max(g,[],"all")-min(g,[],"all"));
Cf=cat(3,cf,zeros(size(X)),zeros(size(X)));  % red colors for f
Cg=cat(3,zeros(size(X)),cg,zeros(size(X)));  % green colors for g
% Plot f in red and g in green
subplot(2,2,1); surf(X,Y,f,Cf,'EdgeColor','none'); 
xlabel('X'); ylabel('Y'); title('f(x,y)'); grid on
subplot(2,2,2); surf(X,Y,g,Cg,'EdgeColor','none'); 
xlabel('X'); ylabel('Y'); title('g(x,y)'); grid on
% PLot a flat surface with colors based on f an g
Cfg=cat(3,cf,cg,zeros(size(X)));
subplot(2,3,5); surf(X,Y,ones(size(X)),Cfg,'EdgeColor','none'); 
xlabel('X'); ylabel('Y'); title('f(x,y) and g(x,y)'); grid on