void PolygonEdgeDistance_float(float2 P, float n, out float distance) {
    float R = 0.5;
    float TAU = 2.0 * 3.14159265359;
    n = round(n);

    float rP = length(P);
    float thetaP = atan2(P.y, P.x);
    thetaP = fmod(thetaP + TAU, TAU);
    
    float angleStep = TAU / n;

    int k = int(floor(thetaP / angleStep)) % int(n);
    float theta_k = k * angleStep;

    float2 p1 = R * float2(cos(theta_k), sin(theta_k));
    float2 p2 = R * float2(cos(theta_k + angleStep), sin(theta_k + angleStep));

    float2 edgeDir = p2 - p1;
    float2 toP = P - p1;
    float edgeLength = length(edgeDir);

    float t = dot(toP, edgeDir) / (edgeLength * edgeLength);
    t = saturate(t);

    float2 closestPoint = p1 + t * edgeDir;
    distance = length(P - closestPoint);
}