float singular_weight(Vec3 a, Vec3 b, float radius, int w)
{
    float r = (a-b).length();
    if (r < radius)
        return pow(r / radius, -w);
    else
        return 0.f;
}

float gaussian_weight(Vec3 a, Vec3 b, float radius)
{
    float r = (a-b).length();
    if (r < radius)
        return exp(- r * r / (radius * radius));
    else
        return 0.f;
}

float wendland_weight(Vec3 a, Vec3 b, float radius)
{
    float r = (a-b).length();
    if (r < radius)
        return pow(1 - r / radius, 4) * (1 + 4 * r / radius);
    else
        return 0.f;
}