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Is it possible to convert Polar to Cartesian coordinates and map result to an image?

I want to get the output same as the distort depolar 0 from image magick.

https://legacy.imagemagick.org/Usage/distorts/#depolar

Is it possible to get the same output using opengl?

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1 Answer 1

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You'd be doing a change of coordinates from polar to Cartesian; at output point $(x,y)$ draw polar coordinate $(\theta = 2 \pi x, r = y)$. The coordinates in a unit circle drawn in the input image are $(r \cos \theta, r \sin \theta)$. In OpenGL this'd be drawn from a sampler, so the input image $u$ and $v$ coordinates would be in $[0,1]$ and you'd have to sample instead from a circle of radius 0.5 centered at $(0.5,0.5)$, resulting in $\mathrm{out}(x,y) = \mathrm{in}(0.5 + 0.5 * r * \cos \theta, 0.5 + 0.5 * r * \sin \theta)$.

Here's a fragment shader function I tested at Shadertoy that performs this transformation:

void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    // Normalized pixel coordinates (from 0 to 1)
    vec2 xy = fragCoord/iResolution.xy;

    // map x to theta and y to r on unit circle
    float theta = 2.0 * 3.14159265368979 * xy.x;
    float r = xy.y;
    
    // map unit circle to circle of radius 0.5 centered at (0.5,0.5)
    vec2 uv = vec2(0.5 + 0.5*r*cos(theta), 0.5 + 0.5*r*sin(theta));

    // texture lookup
    float v = texture(iChannel0,uv).x;

    // Output to screen
    fragColor = vec4(v,v,v,1.0);
}
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