"""Drawing partition basis diagrams [pi] of S_t.

Boundary points: bottom b1..bm at x = 0..m-1 (y = 0), top t1..tn at
x = j + (m-n)/2 (y = H).  Blocks of size 2 are strands, blocks of size 3 are
the trivalent vertex (black dot), blocks of size >= 4 are hollow nodes.
Strands of different blocks may cross; such a crossing is the crossing c.
"""
from diag import fmt


def pt(lbl, m, n, H):
    if lbl[0] == "b":
        return (int(lbl[1:]) - 1, 0.0)
    j = int(lbl[1:]) - 1
    return (j + (m - n) / 2.0, H)


def part_tikz(m, n, blocks, H=1.9, scale=0.5, vpos=None, yscale=None):
    vpos = vpos or {}
    cmds = []
    ys = yscale or scale

    def P(x, y):
        return "(%s,%s)" % (fmt(x), fmt(y))
    for bi, blk in enumerate(blocks):
        pts = [pt(l, m, n, H) for l in blk]
        if len(blk) == 2:
            (x1, y1), (x2, y2) = pts
            if y1 == y2:
                d = abs(x2 - x1)
                h = min(0.32 + 0.22 * (d - 1), 0.75) * H
                yy = h if y1 == 0 else H - h
                cmds.append("\\draw %s .. controls %s and %s .. %s;" % (P(x1, y1), P(x1, yy), P(x2, yy), P(x2, y2)))
            else:
                if y1 > y2:
                    (x1, y1), (x2, y2) = (x2, y2), (x1, y1)
                cmds.append("\\draw %s .. controls %s and %s .. %s;" % (P(x1, 0), P(x1, H / 2), P(x2, H / 2), P(x2, H)))
        else:
            if bi in vpos:
                vx, vy = vpos[bi]
                vy = vy * H
            else:
                vx = sum(p[0] for p in pts) / len(pts)
                nb = sum(1 for p in pts if p[1] == 0)
                vy = H * (0.5 + 0.12 * (len(pts) - 2 * nb) / max(1, len(pts) - 2))
            for (x, y) in pts:
                cy = y + (0.3 * H if y == 0 else -0.3 * H)
                cmds.append("\\draw %s .. controls %s .. %s;" % (P(x, y), P(x, cy), P(vx, vy)))
            if len(blk) == 3:
                cmds.append("\\fill %s circle (1.5pt);" % P(vx, vy))
            else:
                cmds.append("\\draw[fill=white] %s circle (2.2pt);" % P(vx, vy))
    body = "\n".join(cmds)
    return ("\\begin{tikzpicture}[x=%scm,y=%scm,baseline={([yshift=-0.55ex]current bounding box.center)},line width=0.6pt]\n"
            % (fmt(scale), fmt(ys)) + body + "\n\\end{tikzpicture}")


def to_cyclic_blocks(m, n, blocks):
    """labels -> cyclic positions (b1..bm, tn..t1)"""
    def pos(l):
        if l[0] == "b":
            return int(l[1:]) - 1
        j = int(l[1:])
        return m + (n - j)
    from deligne import canon
    return canon([[pos(l) for l in b] for b in blocks])