Face-Centered Cubic Lattice

Designed with sdf2stl.saej.in

Untested. Print at your own risk.

Rendered with the following signed-distance function

// exponential smooth minumum of a and b, with smoothing factor k.
float smoothMin( float a, float b, float k)
{
    float r = 1. + exp2(-abs(a-b)/k);
    return min(a,b) - k * log2(r);
}
// A smooth face-centered-cubic lattice.
float sdSmoothLattice(vec3 position, float radius, float smoothness)
{
    position -= round(position);
    position = abs(position);
    if(position.x + position.y > .5){
        position.yx = vec2(.5) - position.xy;
    }
    if(position.x + position.z > .5){
        position.zx = vec2(.5) - position.xz;
    }
    if(position.y + position.z > .5){
        position.zy = vec2(.5) - position.yz;
    }
    vec3 v = vec3(1., -1.,0.)/sqrt(2.);
    return smoothMin(smoothMin(smoothMin(smoothMin(smoothMin(
        length(position - dot(position, v.xxz) * v.xxz) - radius,
        length(position - dot(position, v.xyz) * v.xyz) - radius, smoothness),
        length(position - dot(position, v.xzx) * v.xzx) - radius, smoothness),
        length(position - dot(position, v.xzy) * v.xzy) - radius, smoothness),
        length(position - dot(position, v.zxx) * v.zxx) - radius, smoothness),
        length(position - dot(position, v.zxy) * v.zxy) - radius, smoothness
    );
}
float map(in vec3 position)
{
    vec3 q = abs(position);
    float n = 8.;
    float k = 100./n;
    return max(
        sdSmoothLattice(position / k + .5, .6/k, .15/k) * k,
        max(max(q.x,q.y),q.z)-50. - .6
    );
}