MATLAB: How to plot a variable density spiral(or any other mathematical 2D- graphs ) on to a image( 512* 512, zero matrix)

k_spacesampling

N_k = 64^2;                         % number of k-samples
t   = linspace(0,sqrt(0.5),N_k)';   % dummy variable to parameterise spiral
k_x = (1 + randn(N_k,1)/20).*t.^2.*cos(2*pi*32*t);  % spiral kx-coords
k_y = (1 + randn(N_k,1)/20).*t.^2.*sin(2*pi*32*t);  % spiral ky-coords
% show scatterplot of trajectory
figure();
z = scatter(k_x,k_y,5, 'filled'); grid off;
OUTPUT:
% now i want to plot this onto a image space for example, zeros(512×512)
EXPECTED OUTPUT:
% basically i wanted to apply mathematical plots such as ( variable density spiral , radial spiral ) on to a kspace image matrix to sample it on those plot points.

Best Answer

Here is an way by translating and scaling the random numbers.
N_k = 64^2;                         % number of k-samples
t   = linspace(0,sqrt(0.5),N_k)';   % dummy variable to parameterise spiral
k_x = (1 + randn(N_k,1)/20).*t.^2.*cos(2*pi*32*t);  % spiral kx-coords
k_y = (1 + randn(N_k,1)/20).*t.^2.*sin(2*pi*32*t);  % spiral ky-coords
% translate and scale the numbers to make them in range [0 512] 
k_x = 256 + 300*k_x;
k_y = 256 + 300*k_y;
% show scatterplot of trajectory
img = zeros(512, 512);
fig = figure();
ax = axes();
ax.Visible = 'off';
hold(ax);
imshow(img)
scatter(ax, k_x, k_y, 3, 'w', 'filled')
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