// TAKES: a polygon 'in', a clipped polygon 'out'
// RETURNS: number of vertices in polygon 'out'; clipped polygon 'out'
// MEMBERS: point on plane 'pos', normal of plane 'nor'
void plane3::clip(const array<vec3> &in, array<vec3> &out) const
{
    out.alloc(in.size() + 1); // make room for max number of out verts
    array<float> dist;
    dist.alloc(in.size());
    int numOut = 0;
    for (int i = 0; i < dist.size(); ++i) {
        dist[i] = dot(in[i] - pos, nor);
        if (dist[i] <= 0.0f) { ++numOut; }
    }
    if (numOut == dist.size()) { // all verts are either behind, or on, plane
        out.dealloc();
        return;
    }
    int numIn = 0;
    for (int i = 0, j = in.size() - 1; i < in.size(); j=i, ++i) {
        if ((dist[i] < 0.0f) == (dist[j] >= 0.0f)) {
            out[numIn++] = in[i] + (in[j] - in[i]) * (dist[i] / (dist[i] - dist[j]));
        }
        if (dist[i] >= 0.0f) {
            out[numIn++] = in[i];
        }
    }
    out.resize(numIn); // resize to actual size of output poly (numIn <= out.size())
}