Wsrtjtyk

I'm trying to create a gradient fill inside a circular area according to a given function. I hope the plot below explains it at best

I'm not sure how to approach this, as in the simulation I'm working on the direction of the gradient changes (not always in the x direction as below, but free to be along all the defined angles), so I'm looking for a solution that will be flexible in that manner as well.

The code I have is below

    clear t

N=10;

for i=0:N 

    t(i+1) = 0+(2*i*pi) / N;

end

F = exp(-cos(t))./(2.*pi*besseli(1,1));

figure(1)

subplot(1,3,1)

plot(t*180/pi,F,'-ob')

xlim([0 360])

xlabel('angle')

subplot(1,3,2)

hold on

plot(cos([t 2*pi]), sin([t 2*pi]),'-k','linewidth',2);

plot(cos([t 2*pi]), sin([t 2*pi]),'ob');

plot(cos(t).*F,sin(t).*F,'b','linewidth',2);

subplot(1,3,3)    

hold on

plot(cos([t 2*pi]), sin([t 2*pi]),'-k','linewidth',2);

plot(cos([t 2*pi]), sin([t 2*pi]),'ob');

To fill surface, you need to use the patch command.

t = linspace(0, 2*pi, 100);

x = cos(t);

y = sin(t);

c = x; % colored following x value and current colormap



figure

patch(x,y,c)

hold on

scatter(x,y)

hold off

colorbar

Resulting graph:

Colors are defined in c per point, and are interpolated inside the shape, so I'm sure that you should have all freedom to color as you want!

For example, the rotated version:

t = linspace(0, 2*pi, 100);

x = cos(t);

y = sin(t);

c = cos(t+pi/4) 



figure

patch(x,y,c)

colorbar

To understand how it is going on, just think that every point has a color, and matlab interpolate inside. So here I just rotated the intensity per point by pi /4.

For this to work you need to have a filled shape, and you may need to customize the color (c) parameter so that it matches your need. For example, if your gradient direction is encoded in a vector, you want to project all your point onto that vector to get the value along the gradient for all points.

For example:

% v controls the direction of the gradient

v = [0.1, 1];



t = linspace(0, 2*pi, 100);

F = exp(-cos(t))./(2.*pi*besseli(1,1));



% reconstructing point coordinate all around the surface

% this closes the path so with enough points so that interpolation works correctly

pts = [[t', F']; [t(end:-1:1)', ones(size(t'))*min(F)]];



% projecting all points on the vector to get the color

c = pts * (v');

clf

patch(pts(:,1),pts(:,2),c)

hold on

scatter(t, F)

hold off