#
# Create a square cross-section piecewise linear tube for protein backbone
# sculptures of the type made by Daniel Gurnon.
#
def box_path(points, width, twist = 0):

    from Matrix import normalize_vector as nv
    import Matrix as M
    from numpy import dot, concatenate, array

    # Find normal to bisecting plane through each point.
    n = len(points)
    p = array(points)
    tangents = array([nv(array(nv(p[min(i+1,n-1)]-p[i]))
                         + array(nv(p[i]-p[max(i-1,0)]))) for i in range(n)])

    # Trace edge of square cross-section from start to finish.
    edges = []
    y, z = p[2]-p[0], tangents[0]
    if twist != 0:
        y = M.apply_matrix(M.rotation_transform(z, twist), y)
    f = M.orthonormal_frame(z, y)
    xa, ya = array(f[0]), array(f[1])
    corners = ((1,1), (-1,1), (-1,-1), (1,-1))
    for x, y in corners:
        ep = [points[0] + (x*0.5*width)*xa + (y*0.5*width)*ya]
        for i in range(n-1):
            e0, p0, p1, t = ep[i], p[i], p[i+1], tangents[i+1]
            ep.append(e0 + (dot(p1-e0, t)/dot(p1-p0, t))*(p1-p0))
        edges.append(ep)

    # Calculate triangles for each face of a surface model.
    # Make sharp edges.
    va = concatenate(edges + edges + edges + edges)
    ta = []
    nc = len(corners)
    for s in range(n-1):
        for c in range(nc):
            c1 = (c+1)%nc + nc
            t = s + (s % 2)*2*nc*n
            ta.append((c*n+t,c1*n+1+t,c*n+1+t))
            ta.append((c*n+t,c1*n+t,c1*n+1+t))

    # Add end caps.
    ta.extend([(nc*n+0,nc*n+(2+c)*n,nc*n+(1+c)*n) for c in range(nc-2)])
    ta.extend([(n-1,(1+c)*n+n-1,(2+c)*n+n-1) for c in range(nc-2)])
    ta = array(ta)

    return va, ta

#
# Cut distances along box edges.
#
def cut_distances(va, nc = 4):

    from Matrix import norm
    cuts = []
    cut = [0]*nc
    n = len(va)/(4*nc)
    for s in range(n-1):
        for c in range(nc):
            e = va[c*n:] if s%2 == 0 else va[((c + nc/2) % nc)*n:]
            cut[c] += norm(e[s+1] - e[s])
        cuts.append(tuple(cut))
    return cuts