Commit 920fd933 authored by Luke Campagnola's avatar Luke Campagnola
Browse files

OpenGL scenegraph updates

 - volumetric rendering
 - isosurfaces, mesh rendering
 - basic transformation and parent/child functionality
parent 269374ef
# -*- coding: utf-8 -*-
## This example uses the isosurface function to convert a scalar field
## (a hydrogen orbital) into a mesh for 3D display.
## Add path to library (just for examples; you do not need this)
import sys, os
sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..'))
from pyqtgraph.Qt import QtCore, QtGui
import pyqtgraph as pg
import pyqtgraph.opengl as gl
app = QtGui.QApplication([])
w = gl.GLViewWidget()
w.show()
g = gl.GLGridItem()
g.scale(2,2,1)
w.addItem(g)
import numpy as np
def psi(i, j, k, offset=(25, 25, 50)):
x = i-offset[0]
y = j-offset[1]
z = k-offset[2]
th = np.arctan2(z, (x**2+y**2)**0.5)
phi = np.arctan2(y, x)
r = (x**2 + y**2 + z **2)**0.5
a0 = 1
#ps = (1./81.) * (2./np.pi)**0.5 * (1./a0)**(3/2) * (6 - r/a0) * (r/a0) * np.exp(-r/(3*a0)) * np.cos(th)
ps = (1./81.) * 1./(6.*np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * np.exp(-r/(3*a0)) * (3 * np.cos(th)**2 - 1)
return ps
#return ((1./81.) * (1./np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * (r/a0) * np.exp(-r/(3*a0)) * np.sin(th) * np.cos(th) * np.exp(2 * 1j * phi))**2
print "Generating scalar field.."
data = np.abs(np.fromfunction(psi, (50,50,100)))
#data = np.fromfunction(lambda i,j,k: np.sin(0.2*((i-25)**2+(j-15)**2+k**2)**0.5), (50,50,50));
print "Generating isosurface.."
faces = pg.isosurface(data, data.max()/4.)
m = gl.GLMeshItem(faces)
w.addItem(m)
m.translate(-25, -25, -50)
#data = np.zeros((5,5,5))
#data[2,2,1:4] = 1
#data[2,1:4,2] = 1
#data[1:4,2,2] = 1
#tr.translate(-2.5, -2.5, 0)
#data = np.ones((2,2,2))
#data[0, 1, 0] = 0
#faces = pg.isosurface(data, 0.5)
#m = gl.GLMeshItem(faces)
#w.addItem(m)
#m.setTransform(tr)
## Start Qt event loop unless running in interactive mode.
if sys.flags.interactive != 1:
app.exec_()
...@@ -8,12 +8,21 @@ import pyqtgraph.opengl as gl ...@@ -8,12 +8,21 @@ import pyqtgraph.opengl as gl
app = QtGui.QApplication([]) app = QtGui.QApplication([])
w = gl.GLViewWidget() w = gl.GLViewWidget()
w.opts['distance'] = 20
w.show() w.show()
ax = gl.GLAxisItem()
ax.setSize(5,5,5)
w.addItem(ax)
b = gl.GLBoxItem() b = gl.GLBoxItem()
w.addItem(b) w.addItem(b)
v = gl.GLVolumeItem() ax2 = gl.GLAxisItem()
w.addItem(v) ax2.setParentItem(b)
b.translate(1,1,1)
## Start Qt event loop unless running in interactive mode.
if sys.flags.interactive != 1:
app.exec_()
# -*- coding: utf-8 -*-
## Add path to library (just for examples; you do not need this)
import sys, os
sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..'))
from pyqtgraph.Qt import QtCore, QtGui
import pyqtgraph.opengl as gl
app = QtGui.QApplication([])
w = gl.GLViewWidget()
w.opts['distance'] = 200
w.show()
#b = gl.GLBoxItem()
#w.addItem(b)
g = gl.GLGridItem()
g.scale(10, 10, 1)
w.addItem(g)
import numpy as np
## Hydrogen electron probability density
def psi(i, j, k, offset=(50,50,100)):
x = i-offset[0]
y = j-offset[1]
z = k-offset[2]
th = np.arctan2(z, (x**2+y**2)**0.5)
phi = np.arctan2(y, x)
r = (x**2 + y**2 + z **2)**0.5
a0 = 2
#ps = (1./81.) * (2./np.pi)**0.5 * (1./a0)**(3/2) * (6 - r/a0) * (r/a0) * np.exp(-r/(3*a0)) * np.cos(th)
ps = (1./81.) * 1./(6.*np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * np.exp(-r/(3*a0)) * (3 * np.cos(th)**2 - 1)
return ps
#return ((1./81.) * (1./np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * (r/a0) * np.exp(-r/(3*a0)) * np.sin(th) * np.cos(th) * np.exp(2 * 1j * phi))**2
data = np.fromfunction(psi, (100,100,200))
positive = np.log(np.clip(data, 0, data.max())**2)
negative = np.log(np.clip(-data, 0, -data.min())**2)
d2 = np.empty(data.shape + (4,), dtype=np.ubyte)
d2[..., 0] = positive * (255./positive.max())
d2[..., 1] = negative * (255./negative.max())
d2[..., 2] = d2[...,1]
d2[..., 3] = d2[..., 0]*0.3 + d2[..., 1]*0.3
d2[..., 3] = (d2[..., 3].astype(float) / 255.) **2 * 255
v = gl.GLVolumeItem(d2)
v.translate(-50,-50,-100)
w.addItem(v)
## Start Qt event loop unless running in interactive mode.
if sys.flags.interactive != 1:
app.exec_()
...@@ -67,6 +67,21 @@ y = np.sin(np.linspace(0, 10, 1000)) + np.random.normal(size=1000, scale=0.1) ...@@ -67,6 +67,21 @@ y = np.sin(np.linspace(0, 10, 1000)) + np.random.normal(size=1000, scale=0.1)
p7.plot(y, fillLevel=-0.3, brush=(50,50,200,100)) p7.plot(y, fillLevel=-0.3, brush=(50,50,200,100))
x2 = np.linspace(-100, 100, 1000)
data2 = np.sin(x2) / x2
p8 = win.addPlot(title="Region Selection")
p8.plot(data2, pen=(255,255,255,200))
lr = pg.LinearRegionItem([400,700])
lr.setZValue(-10)
p8.addItem(lr)
p9 = win.addPlot(title="Zoom on selected region")
p9.plot(data2)
def update():
p9.setXRange(*lr.getRegion())
lr.sigRegionChanged.connect(update)
update()
## Start Qt event loop unless running in interactive mode. ## Start Qt event loop unless running in interactive mode.
if sys.flags.interactive != 1: if sys.flags.interactive != 1:
app.exec_() app.exec_()
...@@ -120,6 +120,18 @@ def siEval(s): ...@@ -120,6 +120,18 @@ def siEval(s):
return v * 1000**n return v * 1000**n
class Color(QtGui.QColor):
def __init__(self, *args):
QtGui.QColor.__init__(self, mkColor(*args))
def glColor(self):
"""Return (r,g,b,a) normalized for use in opengl"""
return (self.red()/255., self.green()/255., self.blue()/255., self.alpha()/255.)
def __getitem__(self, ind):
return (self.red, self.green, self.blue, self.alpha)[ind]()
def mkColor(*args): def mkColor(*args):
""" """
Convenience function for constructing QColor from a variety of argument types. Accepted arguments are: Convenience function for constructing QColor from a variety of argument types. Accepted arguments are:
...@@ -632,4 +644,526 @@ def rescaleData(data, scale, offset): ...@@ -632,4 +644,526 @@ def rescaleData(data, scale, offset):
data = newData.reshape(data.shape) data = newData.reshape(data.shape)
return data return data
#def isosurface(data, level):
#"""
#Generate isosurface from volumetric data using marching tetrahedra algorithm.
#See Paul Bourke, "Polygonising a Scalar Field Using Tetrahedrons" (http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/)
#*data* 3D numpy array of scalar values
#*level* The level at which to generate an isosurface
#"""
#facets = []
### mark everything below the isosurface level
#mask = data < level
#### make eight sub-fields
#fields = np.empty((2,2,2), dtype=object)
#slices = [slice(0,-1), slice(1,None)]
#for i in [0,1]:
#for j in [0,1]:
#for k in [0,1]:
#fields[i,j,k] = mask[slices[i], slices[j], slices[k]]
### split each cell into 6 tetrahedra
### these all have the same 'orienation'; points 1,2,3 circle
### clockwise around point 0
#tetrahedra = [
#[(0,1,0), (1,1,1), (0,1,1), (1,0,1)],
#[(0,1,0), (0,1,1), (0,0,1), (1,0,1)],
#[(0,1,0), (0,0,1), (0,0,0), (1,0,1)],
#[(0,1,0), (0,0,0), (1,0,0), (1,0,1)],
#[(0,1,0), (1,0,0), (1,1,0), (1,0,1)],
#[(0,1,0), (1,1,0), (1,1,1), (1,0,1)]
#]
### each tetrahedron will be assigned an index
### which determines how to generate its facets.
### this structure is:
### facets[index][facet1, facet2, ...]
### where each facet is triangular and its points are each
### interpolated between two points on the tetrahedron
### facet = [(p1a, p1b), (p2a, p2b), (p3a, p3b)]
### facet points always circle clockwise if you are looking
### at them from below the isosurface.
#indexFacets = [
#[], ## all above
#[[(0,1), (0,2), (0,3)]], # 0 below
#[[(1,0), (1,3), (1,2)]], # 1 below
#[[(0,2), (1,3), (1,2)], [(0,2), (0,3), (1,3)]], # 0,1 below
#[[(2,0), (2,1), (2,3)]], # 2 below
#[[(0,3), (1,2), (2,3)], [(0,3), (0,1), (1,2)]], # 0,2 below
#[[(1,0), (2,3), (2,0)], [(1,0), (1,3), (2,3)]], # 1,2 below
#[[(3,0), (3,1), (3,2)]], # 3 above
#[[(3,0), (3,2), (3,1)]], # 3 below
#[[(1,0), (2,0), (2,3)], [(1,0), (2,3), (1,3)]], # 0,3 below
#[[(0,3), (2,3), (1,2)], [(0,3), (1,2), (0,1)]], # 1,3 below
#[[(2,0), (2,3), (2,1)]], # 0,1,3 below
#[[(0,2), (1,2), (1,3)], [(0,2), (1,3), (0,3)]], # 2,3 below
#[[(1,0), (1,2), (1,3)]], # 0,2,3 below
#[[(0,1), (0,3), (0,2)]], # 1,2,3 below
#[] ## all below
#]
#for tet in tetrahedra:
### get the 4 fields for this tetrahedron
#tetFields = [fields[c] for c in tet]
### generate an index for each grid cell
#index = tetFields[0] + tetFields[1]*2 + tetFields[2]*4 + tetFields[3]*8
### add facets
#for i in xrange(index.shape[0]): # data x-axis
#for j in xrange(index.shape[1]): # data y-axis
#for k in xrange(index.shape[2]): # data z-axis
#for f in indexFacets[index[i,j,k]]: # faces to generate for this tet
#pts = []
#for l in [0,1,2]: # points in this face
#p1 = tet[f[l][0]] # tet corner 1
#p2 = tet[f[l][1]] # tet corner 2
#pts.append([(p1[x]+p2[x])*0.5+[i,j,k][x]+0.5 for x in [0,1,2]]) ## interpolate between tet corners
#facets.append(pts)
#return facets
def isosurface(data, level):
"""
Generate isosurface from volumetric data using marching tetrahedra algorithm.
See Paul Bourke, "Polygonising a Scalar Field"
(http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/)
*data* 3D numpy array of scalar values
*level* The level at which to generate an isosurface
This function is SLOW; plenty of room for optimization here.
"""
## map from grid cell index to edge index.
## grid cell index tells us which corners are below the isosurface,
## edge index tells us which edges are cut by the isosurface.
## (Data stolen from Bourk; see above.)
edgeTable = [
0x0 , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0 ]
## Table of triangles to use for filling each grid cell.
## Each set of three integers tells us which three edges to
## draw a triangle between.
## (Data stolen from Bourk; see above.)
triTable = [
[],
[0, 8, 3],
[0, 1, 9],
[1, 8, 3, 9, 8, 1],
[1, 2, 10],
[0, 8, 3, 1, 2, 10],
[9, 2, 10, 0, 2, 9],
[2, 8, 3, 2, 10, 8, 10, 9, 8],
[3, 11, 2],
[0, 11, 2, 8, 11, 0],
[1, 9, 0, 2, 3, 11],
[1, 11, 2, 1, 9, 11, 9, 8, 11],
[3, 10, 1, 11, 10, 3],
[0, 10, 1, 0, 8, 10, 8, 11, 10],
[3, 9, 0, 3, 11, 9, 11, 10, 9],
[9, 8, 10, 10, 8, 11],
[4, 7, 8],
[4, 3, 0, 7, 3, 4],
[0, 1, 9, 8, 4, 7],
[4, 1, 9, 4, 7, 1, 7, 3, 1],
[1, 2, 10, 8, 4, 7],
[3, 4, 7, 3, 0, 4, 1, 2, 10],
[9, 2, 10, 9, 0, 2, 8, 4, 7],
[2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4],
[8, 4, 7, 3, 11, 2],
[11, 4, 7, 11, 2, 4, 2, 0, 4],
[9, 0, 1, 8, 4, 7, 2, 3, 11],
[4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1],
[3, 10, 1, 3, 11, 10, 7, 8, 4],
[1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4],
[4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3],
[4, 7, 11, 4, 11, 9, 9, 11, 10],
[9, 5, 4],
[9, 5, 4, 0, 8, 3],
[0, 5, 4, 1, 5, 0],
[8, 5, 4, 8, 3, 5, 3, 1, 5],
[1, 2, 10, 9, 5, 4],
[3, 0, 8, 1, 2, 10, 4, 9, 5],
[5, 2, 10, 5, 4, 2, 4, 0, 2],
[2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8],
[9, 5, 4, 2, 3, 11],
[0, 11, 2, 0, 8, 11, 4, 9, 5],
[0, 5, 4, 0, 1, 5, 2, 3, 11],
[2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5],
[10, 3, 11, 10, 1, 3, 9, 5, 4],
[4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10],
[5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3],
[5, 4, 8, 5, 8, 10, 10, 8, 11],
[9, 7, 8, 5, 7, 9],
[9, 3, 0, 9, 5, 3, 5, 7, 3],
[0, 7, 8, 0, 1, 7, 1, 5, 7],
[1, 5, 3, 3, 5, 7],
[9, 7, 8, 9, 5, 7, 10, 1, 2],
[10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3],
[8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2],
[2, 10, 5, 2, 5, 3, 3, 5, 7],
[7, 9, 5, 7, 8, 9, 3, 11, 2],
[9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11],
[2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7],
[11, 2, 1, 11, 1, 7, 7, 1, 5],
[9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11],
[5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0],
[11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0],
[11, 10, 5, 7, 11, 5],
[10, 6, 5],
[0, 8, 3, 5, 10, 6],
[9, 0, 1, 5, 10, 6],
[1, 8, 3, 1, 9, 8, 5, 10, 6],
[1, 6, 5, 2, 6, 1],
[1, 6, 5, 1, 2, 6, 3, 0, 8],
[9, 6, 5, 9, 0, 6, 0, 2, 6],
[5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8],
[2, 3, 11, 10, 6, 5],
[11, 0, 8, 11, 2, 0, 10, 6, 5],
[0, 1, 9, 2, 3, 11, 5, 10, 6],
[5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11],
[6, 3, 11, 6, 5, 3, 5, 1, 3],
[0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6],
[3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9],
[6, 5, 9, 6, 9, 11, 11, 9, 8],
[5, 10, 6, 4, 7, 8],
[4, 3, 0, 4, 7, 3, 6, 5, 10],
[1, 9, 0, 5, 10, 6, 8, 4, 7],
[10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4],
[6, 1, 2, 6, 5, 1, 4, 7, 8],
[1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7],
[8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6],
[7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9],
[3, 11, 2, 7, 8, 4, 10, 6, 5],
[5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11],
[0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6],
[9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6],
[8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6],
[5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11],
[0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7],
[6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9],
[10, 4, 9, 6, 4, 10],
[4, 10, 6, 4, 9, 10, 0, 8, 3],
[10, 0, 1, 10, 6, 0, 6, 4, 0],
[8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10],
[1, 4, 9, 1, 2, 4, 2, 6, 4],
[3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4],
[0, 2, 4, 4, 2, 6],
[8, 3, 2, 8, 2, 4, 4, 2, 6],
[10, 4, 9, 10, 6, 4, 11, 2, 3],
[0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6],
[3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10],
[6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1],
[9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3],
[8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1],
[3, 11, 6, 3, 6, 0, 0, 6, 4],
[6, 4, 8, 11, 6, 8],
[7, 10, 6, 7, 8, 10, 8, 9, 10],
[0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10],
[10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0],
[10, 6, 7, 10, 7, 1, 1, 7, 3],
[1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7],
[2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9],
[7, 8, 0, 7, 0, 6, 6, 0, 2],
[7, 3, 2, 6, 7, 2],
[2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7],
[2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7],
[1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11],
[11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1],
[8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6],
[0, 9, 1, 11, 6, 7],
[7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0],
[7, 11, 6],
[7, 6, 11],
[3, 0, 8, 11, 7, 6],
[0, 1, 9, 11, 7, 6],
[8, 1, 9, 8, 3, 1, 11, 7, 6],
[10, 1, 2, 6, 11, 7],
[1, 2, 10, 3, 0, 8, 6, 11, 7],
[2, 9, 0, 2, 10, 9, 6, 11, 7],
[6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8],
[7, 2, 3, 6, 2, 7],
[7, 0, 8, 7, 6, 0, 6, 2, 0],
[2, 7, 6, 2, 3, 7, 0, 1, 9],
[1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6],
[10, 7, 6, 10, 1, 7, 1, 3, 7],
[10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8],
[0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7],
[7, 6, 10, 7, 10, 8, 8, 10, 9],
[6, 8, 4, 11, 8, 6],
[3, 6, 11, 3, 0, 6, 0, 4, 6],
[8, 6, 11, 8, 4, 6, 9, 0, 1],
[9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6],
[6, 8, 4, 6, 11, 8, 2, 10, 1],
[1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6],
[4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9],
[10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3],
[8, 2, 3, 8, 4, 2, 4, 6, 2],
[0, 4, 2, 4, 6, 2],
[1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8],
[1, 9, 4, 1, 4, 2, 2, 4, 6],
[8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1],
[10, 1, 0, 10, 0, 6, 6, 0, 4],
[4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3],
[10, 9, 4, 6, 10, 4],
[4, 9, 5, 7, 6, 11],
[0, 8, 3, 4, 9, 5, 11, 7, 6],
[5, 0, 1, 5, 4, 0, 7, 6, 11],
[11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5],
[9, 5, 4, 10, 1, 2, 7, 6, 11],
[6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5],
[7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2],
[3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6],
[7, 2, 3, 7, 6, 2, 5, 4, 9],
[9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7],
[3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0],
[6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8],
[9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7],
[1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4],
[4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10],
[7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10],
[6, 9, 5, 6, 11, 9, 11, 8, 9],
[3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5],
[0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11],
[6, 11, 3, 6, 3, 5, 5, 3, 1],
[1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6],
[0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10],
[11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5],
[6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3],
[5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2],
[9, 5, 6, 9, 6, 0, 0, 6, 2],
[1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8],
[1, 5, 6, 2, 1, 6],
[1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6],
[10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0],
[0, 3, 8, 5, 6, 10],
[10, 5, 6],
[11, 5, 10, 7, 5, 11],
[11, 5, 10, 11, 7, 5, 8, 3, 0],
[5, 11, 7, 5, 10, 11, 1, 9, 0],
[10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1],
[11, 1, 2, 11, 7, 1, 7, 5, 1],
[0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11],
[9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7],
[7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2],
[2, 5, 10, 2, 3, 5, 3, 7, 5],
[8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5],
[9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2],
[9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2],
[1, 3, 5, 3, 7, 5],
[0, 8, 7, 0, 7, 1, 1, 7, 5],
[9, 0, 3, 9, 3, 5, 5, 3, 7],
[9, 8, 7, 5, 9, 7],
[5, 8, 4, 5, 10, 8, 10, 11, 8],