Tikz

tikz_lattice_path.sage

N = (0,1)
E = (1,0)

def normalize(path):
    """ convert path to a list of (0,1) and (1,0) """

    l = len(path)
    if l % 2 != 0:
        raise ValueError("Not a lattice path: len(path)=%d is not even." % l)
    
    if type(path) == type("NE"):
        p = map( lambda step: {"N": N, "E": E}[step], path)
    elif type(path) == type([N,E]):
        p = path
    else:
        raise ValueError("Unknown type")
    
    return (p, int(l/2))

def lattice_path(path, label=[]):
    p,n = normalize(path)
    labelled_path = []
    label = label + ['' for i in range(n-len(label))]
    
    i = 0
    for step in p:
        if step == N:
            labelled_path.append((step,label[i]))
            i = i + 1
        else:
            labelled_path.append((step, ''))
    return labelled_path


def tikz_to_step( (dx,dy), node=''):
    """ '-- ++(dx,dy)' with an optional node. """
    return "-- ++(%d,%d)%s" % (dx,dy,node)

def tikz_to_point( (x,y), node=''):
    """ '-- (x,y)' with an optional node. """
    return "-- (%d,%d)%s" % (x,y,node)

def tikz_grid((x0,y0),(x1,y1)):
    return "(%d,%d) grid (%d,%d)" % (x0,y0,x1,y1)

def tikz_draw(path, options):
    return "\\draw[%s] %s;" % (options, path)

def tikz_draw_grid(start, end, options=''):
    return tikz_draw(tikz_grid(start,end), options)

def tikz_draw_lattice_path(path, grid=True, diagonal=True, scale=1):
    """ draw a lattice path with specified steps given by (direction, label) """
    n = int(len(path)/2)
    format_step = lambda (s,label): tikz_to_step(s, "node[below left] {%s}" % str(label))
    
    lines = [
        "\\begin{tikzpicture}[every node/.style={transform shape}, scale=%.1f]" % scale,
        (not grid and ' ') or tikz_draw_grid((0,0), (n,n), 'dotted, very thin'),
        (not diagonal and ' ') or tikz_draw('(0,0) -- (%d,%d)' % (n,n), 'thin'),
        tikz_draw(' '.join(['(0,0)'] + map(format_step, path)), 'very thick'),
        "\\end{tikzpicture}"
    ]
    
    return "\n".join([ line for line in lines if line != ' '])  # leave out blank lines

p = lattice_path("NNEENNEE", [1,2,3])
print tikz_draw_lattice_path(p)