LYGIA Shader Library

Use:

<vec2|vec3> cart2polar(<vec2|vec3> st)

Check it on Github

#ifndef FNC_CART2POLAR
#define FNC_CART2POLAR

vec2 cart2polar(in vec2 st) {
    return vec2(atan(st.y, st.x), length(st));
}

vec3 cart2polar( in vec3 st ) {
    float r = length(st);
    float theta = acos(st.z/r);
    float phi = atan(st.y, st.x);
    return vec3(r, theta, phi);
}

#endif

Use:

<float2|float3> cart2polar(<float2|float3> st)

Check it on Github

#ifndef FNC_CART2POLAR
#define FNC_CART2POLAR

float2 cart2polar(in float2 st) {
    return float2(atan2(st.y, st.x), length(st));
}

float3 cart2polar( in float3 st) {
   float r = length(st);
   float theta = atan2( length(st.xy), st.z);
   float phi = atan2(st.y, st.x);
   return float3(r, theta, phi);
}
#endif