Making an image follow the path of a spiral / an equation in matlab / octave

Question

I know I can make spirals with the example code below but how do I get an image to follow the spiral path of an equation like the one below.

t = linspace(0,4*pi,400);
x = t.*cos(t);
y = t.*sin(t);
plot(x,y)

Example: I have an image (RGB) see below and I convert it to a 1 x N matrix. My thoughts were to make a 1 XN matrix and have that matrix follow the path of the spiral. How can I get the image to follow the path of a spiral equation?

f=imread('/tmp/rgb_line.png');
[Frows Fcols Fdims]=size(f)

f=double(f); %need to convert to double to do math functions on it

for ii=1:Fdims
  img(:,:,ii)=reshape(f(:,:,ii)',1,numel(f(:,:,ii))); %reshape array as one row and 3 dimensions 
end

Rainbow line (input/reshaped matrix):

So the rainbow spiral output would look something like this. Please note that the order of the colours are not correct due to the fact that this was the closest image I could find that showed what I'm trying to do.

PS: I'm using Octave 4.0 which is similar to Matlab

Answer 1

you can try something like this:

rgb1 = jet(256);
len1 = size(rgb1,1);
RGB1 = permute(rgb1,[3 1 2]);
figure; imshow(RGB1);
len2 = 400;
t = linspace(0,4*pi,len2);
x = t.*cos(t);
y = t.*sin(t);
rgb2 = interp1(1:len1,rgb1,linspace(1,len1,len2));
[xg,yg] = meshgrid([-t(end:-1:2) t],[-t(end:-1:2) t]);
RGB2 = zeros([size(xg) 3]);
% interpolate for the desired coordinates
for c = 1:3
    RGB2(:,:,c) = griddata(x,y,rgb2(:,c),xg,yg);
end
figure; imshow(RGB2)

then you need to eliminate unwanted pixels using some sort of mask.