diff --git a/lattices2d.py b/lattices2d.py
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+++ b/lattices2d.py
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+import numpy as np
+from enum import Enum
+
+nx = None
+
+class LatticeType(Enum):
+    """
+    All the five Bravais lattices in 2D
+    """
+    OBLIQUE=1
+    RECTANGULAR=2
+    SQUARE=4
+    RHOMBIC=5
+    EQUILATERAL_TRIANGULAR=3
+    RIGHT_ISOSCELES=SQUARE
+    PARALLELOGRAMMIC=OBLIQUE
+    CENTERED_RHOMBIC=RECTANGULAR
+    RIGHT_TRIANGULAR=RECTANGULAR
+    CENTERED_RECTANGULAR=RHOMBIC
+    ISOSCELE_TRIANGULAR=RHOMBIC
+    RIGHT_ISOSCELE_TRIANGULAR=SQUARE
+    HEXAGONAL=EQUILATERAL_TRIANGULAR
+
+def reduceBasisSingle(b1, b2):
+    """
+    Lagrange-Gauss reduction of a 2D basis.
+    cf. https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch17.pdf
+    inputs and outputs are (2,)-shaped numpy arrays
+    The output shall satisfy |b1| <= |b2| <= |b2 - b1| 
+    TODO doc
+    
+    TODO perhaps have the (on-demand?) guarantee of obtuse angle between b1, b2?
+    TODO possibility of returning the (in-order, no-obtuse angles) b as well?
+    """
+    b1 = np.array(b1)
+    b2 = np.array(b2)
+    if b1.shape != (2,) or b2.shape != (2,):
+        raise ValueError('Shape of b1 and b2 must be (2,)')
+    B1 = np.sum(b1 * b1, axis=-1, keepdims=True)
+    mu = np.sum(b1 * b2, axis=-1, keepdims=True) / B1
+    b2 = b2 - np.rint(mu) * b1
+    B2 = np.sum(b2 * b2, axis=-1, keepdims=True)
+    while(np.any(B2 < B1)):
+        b2t = b1
+        b1 = b2
+        b2 = b2t
+        B1 = B2
+        mu = np.sum(b1 * b2, axis=-1, keepdims=True) / B1
+        b2 = b2 - np.rint(mu) * b1
+        B2 = np.sum(b2*b2, axis=-1, keepdims=True)
+    return(b1,b2)
+
+def shortestBase3(b1, b2):
+    ''' 
+    returns the "ordered shortest triple" of base vectors (each pair from 
+    the triple is a base) and there may not be obtuse angle between b1, b2
+    and between b2, b3
+    '''
+    b1, b2 = reduceBasisSingle(b1,b2)
+    if is_obtuse(b1, b2, tolerance=0):
+        b3 = b2
+        b2 = b2 + b1
+    else:
+        b3 = b2 - b1
+    return (b1, b2, b3)
+
+def shortestBase46(b1, b2, tolerance=1e-13):
+    b1, b2 = reduceBasisSingle(b1,b2)
+    b1s = np.sum(b1 ** 2)
+    b2s = np.sum(b2 ** 2)
+    b3 = b2 - b1
+    b3s = np.sum(b3 ** 2)
+    eps = tolerance * (b2s + b1s)
+    if abs(b3s - b2s - b1s) < eps:
+        return(b1, b2, -b1, -b2)
+    else:
+        if b3s - b2s - b1s > eps: #obtuse
+            b3 = b2
+            b2 = b2 + b1
+        return (b1, b2, b3, -b1, -b2, -b3)
+    
+
+def is_obtuse(b1, b2, tolerance=1e-13):
+    b1s = np.sum(b1 ** 2)
+    b2s = np.sum(b2 ** 2)
+    b3 = b2 - b1
+    b3s = np.sum(b3 ** 2)
+    eps = tolerance * (b2s + b1s)
+    return (b3s - b2s - b1s > eps)
+
+def classifyLatticeSingle(b1, b2, tolerance=1e-13):
+    """
+    Given two basis vectors, returns 2D Bravais lattice type.
+    Tolerance is relative.
+    TODO doc
+    """
+    b1, b2 = reduceBasisSingle(b1, b2)
+    b1s = np.sum(b1 ** 2)
+    b2s = np.sum(b2 ** 2)
+    b3 = b2 - b1
+    b3s = np.sum(b3 ** 2)
+    eps = tolerance * (b2s + b1s)
+    # Avoid obtuse angle between b1 and b2. TODO This should be yet thoroughly tested.
+    # TODO use is_obtuse here?
+    if b3s - b2s - b1s > eps:
+        b3 = b2
+        b2 = b2 + b1
+        # N. B. now the assumption |b3| >= |b2| is no longer valid
+        #b3 = b2 - b1
+        b2s = np.sum(b2 ** 2)
+        b3s = np.sum(b3 ** 2)
+    if abs(b2s - b1s) < eps or abs(b2s - b3s) < eps: # isoscele
+        if abs(b3s - b1s) < eps:
+            return LatticeType.EQUILATERAL_TRIANGULAR
+        elif abs(b3s - 2 * b1s) < eps:
+            return LatticeType.SQUARE
+        else:
+            return LatticeType.RHOMBIC
+    elif abs(b3s - b2s - b1s) < eps:
+        return LatticeType.RECTANGULAR
+    else:
+        return LatticeType.OBLIQUE
+
+def range2D(maxN, mini=1, minj=0, minN = 0):
+    """
+    "Triangle indices"
+    Generates pairs of non-negative integer indices (i, j) such that
+    minN ≤ i + j ≤ maxN, i ≥ mini, j ≥ minj.
+    TODO doc and possibly different orderings
+    """
+    for maxn in range(min(mini, minj, minN), floor(maxN+1)): # i + j == maxn
+        for i in range(mini, maxn + 1):
+            yield (i, maxn - i)
+
+            
+def generateLattice(b1, b2, maxlayer=5, include_origin=False, order='leaves'):
+    bvs = shortestBase46(b1, b2)
+    cc = len(bvs) # "corner count"
+    
+    if order == 'leaves':
+        indices = np.array(list(range2D(maxlayer)))
+        ia = indices[:,0]
+        ib = indices[:,1]
+        cc = len(bvs) # 4 for square/rec,
+        leaves = list()
+        if include_origin: leaves.append(np.array([[0,0]]))
+        for c in range(cc):
+            ba = bvs[c]
+            bb = bvs[(c+1)%cc]
+            leaves.append(ia[:,nx]*ba + ib[:,nx]*bb)
+        return np.concatenate(leaves)
+    else: 
+        raise ValueError('Lattice point order not implemented: ', order)
+        
+def generateLatticeDisk(b1, b2, r, include_origin=False, order='leaves'):
+    b1, b2 = reduceBasisSingle(b1,b2)
+    blen = np.linalg.norm(b1, ord=2)
+    maxlayer = 2*r/blen # FIXME kanon na vrabce? Nestačí odmocnina ze 2?
+    points = generateLattice(b1,b2, maxlayer=maxlayer, include_origin=include_origin, order=order)
+    mask = (np.linalg.norm(points, axis=-1, ord=2) <= r)
+    return points[mask]
+
+def cellCornersWS(b1, b2,):
+    """
+    Given basis vectors, returns the corners of the Wigner-Seitz unit cell
+    (w1, w2, -w1, w2) for rectangular and square lattice or
+    (w1, w2, w3, -w1, -w2, -w3) otherwise
+    """
+    def solveWS(v1, v2):
+        v1x = v1[0]
+        v1y = v1[1]
+        v2x = v2[0]
+        v2y = v2[1]
+        lsm = ((-v1y, v2y), (v1x, -v2x))
+        rs = ((v1x-v2x)/2, (v1y - v2y)/2)
+        t = np.linalg.solve(lsm, rs)
+        return np.array(v1)/2 + t[0]*np.array((v1y, -v1x))
+    b1, b2 = reduceBasisSingle(b1, b2)
+    latticeType = classifyLatticeSingle(b1, b2)
+    if latticeType is LatticeType.RECTANGULAR or latticeType is LatticeType.SQUARE:
+        return np.array( (
+            (+b1+b2),
+            (+b2-b1),
+            (-b1-b2),
+            (-b2+b1),
+        )) / 2
+    else:
+        bvs = shortestBase46(b1,b2,tolerance=0)
+        return np.array([solveWS(bvs[i], bvs[(i+1)%6]) for i in range(6)])
+
+def cutWS(points, b1, b2, scale=1., tolerance=1e-13):
+    """ 
+    From given points, return only those that are inside (or on the edge of)
+    the Wigner-Seitz cell of a (scale*b1, scale*b2)-based lattice.
+    """
+    # TODO check input dimensions?
+    bvs = shortestBase46(b1, b2)
+    points = np.array(points)
+    for b in bvs: 
+        mask = (np.tensordot(points, b, axes=(-1, 0)) <=  (scale * (1+tolerance) / 2) *np.linalg.norm(b, ord=2)**2 )
+        points = points[mask]
+    return points
+
+def filledWS(b1, b2, density=10, scale=1.):
+    """
+    TODO doc
+    TODO more intelligent generation, anisotropy balancing etc.
+    """
+    points = generateLattice(b1,b2,maxlayer=density*scale, include_origin=True)
+    points = cutWS(points/density, np.array(b1)*scale, np.array(b2)*scale)
+    return points
+    
+    
+rot90_ = np.array([[0,1],[-1,0]])
+def reciprocalBasis(a1, a2):
+    a1, a2 = reduceBasisSingle(a1,a2) # this can be replaced with the vector version of reduceBasis when it is made
+    prefac = 2*np.pi/np.sum(np.tensordot(a1, rot90_, axes=[-1,0]) * a2, axis=-1)
+    b1 = np.tensordot(rot90_, a2, axes=[-1,-1]) * prefac
+    b2 = np.tensordot(rot90_, a1, axes=[-1,-1]) * prefac
+    return (b1, b2)
+
+
+# TODO fill it with "points from reciprocal space" instead
+def filledWS2(b1,b2, density=10, scale=1.):
+    b1, b2 = reduceBasisSingle(b1,b2)
+    b1r, b2r = reciprocalBasis(b1,b2)
+    b1l = np.linalg.norm(b1, ord=2)
+    b2l = np.linalg.norm(b2, ord=2)
+    b1rl = np.linalg.norm(b1r, ord=2)
+    b2rl = np.linalg.norm(b2r, ord=2)
+    # Black magick. Think later.™ Really. FIXME
+    sicher_ratio = np.maximum(b1rl/b2rl, b2rl/b1rl) * np.maximum(b1l/b2l, b2l/b1l) # This really has to be adjusted
+    points = generateLattice(b1r,b2r,maxlayer=density*scale*sicher_ratio, include_origin=True)
+    points = cutWS(points*b1l/b1rl/density, b1*scale, b2*scale)
+    return points
+
+
+
+"""
+TODO
+====
+
+- DOC!!!!!
+- (nehoří) výhledově pořešit problém „hodně anisotropních“ mřížek (tj. kompensovat
+rozdílné délky základních vektorů).
+
+"""