Expand source code
#!/usr/bin/env python
# -*- coding: utf-8 -*-
__author__ = ['Benjamin Dillenburger','Demetris Shammas','Mathias Bernhard']
__copyright__ = 'Copyright 2019 / Digital Building Technologies DBT / ETH Zurich'
__license__ = 'MIT License'
__email__ = ['<dbt@arch.ethz.ch>']
import math
from mola.core_vertex import Vertex
from mola.core_face import Face
from mola.core_mesh import Mesh
def _v( v1, v2, iso):
if (abs(v2 - v1) < 0.0000001):
return 0
return (iso - v1) / (v2 - v1)
def marching_cubes_from_grid(grid,iso):
return marching_cubes(grid.nx,grid.ny,grid.nz,grid.values,iso,grid.scale_to_canvas)
def marching_cubes(nX,nY,nZ,values,iso, scale_to_canvas=False):
mesh = Mesh()
nYZ = nY * nZ
index = 0
n =[0]*8
switcher = {
0:lambda: Vertex(x + _v(n[0], n[1], iso), y + 1, z),
1:lambda: Vertex(x + 1, y + _v(n[2], n[1], iso), z),
2:lambda: Vertex(x + _v(n[3], n[2], iso), y, z),
3:lambda: Vertex(x, y + _v(n[3], n[0], iso), z),
4:lambda: Vertex(x + _v(n[4], n[5], iso), y + 1, z + 1),
5:lambda: Vertex(x + 1, y + _v(n[6], n[5], iso), z + 1),
6:lambda: Vertex(x + _v(n[7], n[6], iso), y, z + 1),
7:lambda: Vertex(x, y + _v(n[7], n[4], iso), z + 1),
8:lambda: Vertex(x, y + 1, z + _v(n[0], n[4], iso)),
9:lambda: Vertex(x + 1, y + 1, z + _v(n[1], n[5], iso)),
10:lambda: Vertex(x, y, z + _v(n[3], n[7], iso)),
11:lambda: Vertex(x + 1, y, z + _v(n[2], n[6], iso))
}
for x in range(nX - 1):
for y in range(nY - 1):
for z in range(nZ - 1):
caseNumber = 0
index = z + y * nZ + x * nYZ
# collecting the values
n[0] = values[index + nZ]# 0,1,0
n[1] = values[index + nYZ + nZ]#1,1,0
n[2] = values[index + nYZ]# 1,0,0
n[3] = values[index]# 0,0,0
n[4] = values[index + nZ + 1]# 0,1,1
n[5] = values[index + nYZ + nZ + 1]# 1,1,1
n[6] = values[index + nYZ + 1]# 1,0,1
n[7] = values[index + 1]# 0,0,1
for i in range(7,-1,-1):
if n[i] > iso:
caseNumber+=1
if i > 0:
caseNumber = caseNumber << 1
# collecting the faces
offset = caseNumber * 15
for i in range(offset,offset + 15,3):
if _faces[i] > -1:
vs=[]
for j in range(i,i+3):
v = switcher[_faces[j]]()
mesh.vertices.append(v)
vs.append(v)
if len(vs) == 3:
mesh.faces.append(Face(vs))
mesh.update_topology()
if(scale_to_canvas):
mesh.translate(-nX/2.0,-nY/2.0,-nZ/2.0)
sc = 20.0/max(nX,nY)
mesh.scale(sc,sc,sc)
return mesh
_faces = ( -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 3, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 8, 3, 9, 8, 1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 3, 1, 2,
11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 2, 11, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 8, 3, 2,
11, 8, 11, 9, 8, -1, -1, -1, -1, -1, -1, 3, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 10, 2,
8, 10, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 9, 0, 2, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 10,
2, 1, 9, 10, 9, 8, 10, -1, -1, -1, -1, -1, -1, 3, 11, 1, 10, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0,
11, 1, 0, 8, 11, 8, 10, 11, -1, -1, -1, -1, -1, -1, 3, 9, 0, 3, 10, 9, 10, 11, 9, -1, -1, -1, -1, -1, -1, 9,
8, 11, 11, 8, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, 4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1,
-1, 4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, 1, 2, 11, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1,
-1, 3, 4, 7, 3, 0, 4, 1, 2, 11, -1, -1, -1, -1, -1, -1, 9, 2, 11, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1,
2, 11, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, 8, 4, 7, 3, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10,
4, 7, 10, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, 9, 0, 1, 8, 4, 7, 2, 3, 10, -1, -1, -1, -1, -1, -1, 4, 7,
10, 9, 4, 10, 9, 10, 2, 9, 2, 1, -1, -1, -1, 3, 11, 1, 3, 10, 11, 7, 8, 4, -1, -1, -1, -1, -1, -1, 1, 10,
11, 1, 4, 10, 1, 0, 4, 7, 10, 4, -1, -1, -1, 4, 7, 8, 9, 0, 10, 9, 10, 11, 10, 0, 3, -1, -1, -1, 4, 7, 10,
4, 10, 9, 9, 10, 11, -1, -1, -1, -1, -1, -1, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 5,
4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 5,
4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, 1, 2, 11, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 0, 8,
1, 2, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, 5, 2, 11, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, 2, 11, 5, 3,
2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, 9, 5, 4, 2, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 10, 2, 0, 8,
10, 4, 9, 5, -1, -1, -1, -1, -1, -1, 0, 5, 4, 0, 1, 5, 2, 3, 10, -1, -1, -1, -1, -1, -1, 2, 1, 5, 2, 5, 8,
2, 8, 10, 4, 8, 5, -1, -1, -1, 11, 3, 10, 11, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, 4, 9, 5, 0, 8, 1, 8,
11, 1, 8, 10, 11, -1, -1, -1, 5, 4, 0, 5, 0, 10, 5, 10, 11, 10, 0, 3, -1, -1, -1, 5, 4, 8, 5, 8, 11, 11, 8,
10, -1, -1, -1, -1, -1, -1, 9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 3, 0, 9, 5, 3, 5, 7, 3,
-1, -1, -1, -1, -1, -1, 0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, 1, 5, 3, 3, 5, 7, -1, -1, -1, -1,
-1, -1, -1, -1, -1, 9, 7, 8, 9, 5, 7, 11, 1, 2, -1, -1, -1, -1, -1, -1, 11, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3,
-1, -1, -1, 8, 0, 2, 8, 2, 5, 8, 5, 7, 11, 5, 2, -1, -1, -1, 2, 11, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1,
-1, 7, 9, 5, 7, 8, 9, 3, 10, 2, -1, -1, -1, -1, -1, -1, 9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 10, -1, -1, -1, 2,
3, 10, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, 10, 2, 1, 10, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, 9, 5, 8,
8, 5, 7, 11, 1, 3, 11, 3, 10, -1, -1, -1, 5, 7, 0, 5, 0, 9, 7, 10, 0, 1, 0, 11, 10, 11, 0, 10, 11, 0, 10, 0,
3, 11, 5, 0, 8, 0, 7, 5, 7, 0, 10, 11, 5, 7, 10, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 11, 6, 5, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 3, 5, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 0, 1, 5,
11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 8, 3, 1, 9, 8, 5, 11, 6, -1, -1, -1, -1, -1, -1, 1, 6, 5, 2,
6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, 9, 6, 5, 9, 0,
6, 0, 2, 6, -1, -1, -1, -1, -1, -1, 5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, 2, 3, 10, 11, 6, 5, -1,
-1, -1, -1, -1, -1, -1, -1, -1, 10, 0, 8, 10, 2, 0, 11, 6, 5, -1, -1, -1, -1, -1, -1, 0, 1, 9, 2, 3, 10, 5,
11, 6, -1, -1, -1, -1, -1, -1, 5, 11, 6, 1, 9, 2, 9, 10, 2, 9, 8, 10, -1, -1, -1, 6, 3, 10, 6, 5, 3, 5, 1,
3, -1, -1, -1, -1, -1, -1, 0, 8, 10, 0, 10, 5, 0, 5, 1, 5, 10, 6, -1, -1, -1, 3, 10, 6, 0, 3, 6, 0, 6, 5, 0,
5, 9, -1, -1, -1, 6, 5, 9, 6, 9, 10, 10, 9, 8, -1, -1, -1, -1, -1, -1, 5, 11, 6, 4, 7, 8, -1, -1, -1, -1,
-1, -1, -1, -1, -1, 4, 3, 0, 4, 7, 3, 6, 5, 11, -1, -1, -1, -1, -1, -1, 1, 9, 0, 5, 11, 6, 8, 4, 7, -1, -1,
-1, -1, -1, -1, 11, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, 6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1,
-1, -1, 1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, 8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, 7,
3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, 3, 10, 2, 7, 8, 4, 11, 6, 5, -1, -1, -1, -1, -1, -1, 5, 11, 6, 4,
7, 2, 4, 2, 0, 2, 7, 10, -1, -1, -1, 0, 1, 9, 4, 7, 8, 2, 3, 10, 5, 11, 6, -1, -1, -1, 9, 2, 1, 9, 10, 2, 9,
4, 10, 7, 10, 4, 5, 11, 6, 8, 4, 7, 3, 10, 5, 3, 5, 1, 5, 10, 6, -1, -1, -1, 5, 1, 10, 5, 10, 6, 1, 0, 10,
7, 10, 4, 0, 4, 10, 0, 5, 9, 0, 6, 5, 0, 3, 6, 10, 6, 3, 8, 4, 7, 6, 5, 9, 6, 9, 10, 4, 7, 9, 7, 10, 9, -1,
-1, -1, 11, 4, 9, 6, 4, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 11, 6, 4, 9, 11, 0, 8, 3, -1, -1, -1, -1,
-1, -1, 11, 0, 1, 11, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, 8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 11, -1, -1,
-1, 1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, 3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, 0, 2,
4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, 11, 4, 9,
11, 6, 4, 10, 2, 3, -1, -1, -1, -1, -1, -1, 0, 8, 2, 2, 8, 10, 4, 9, 11, 4, 11, 6, -1, -1, -1, 3, 10, 2, 0,
1, 6, 0, 6, 4, 6, 1, 11, -1, -1, -1, 6, 4, 1, 6, 1, 11, 4, 8, 1, 2, 1, 10, 8, 10, 1, 9, 6, 4, 9, 3, 6, 9, 1,
3, 10, 6, 3, -1, -1, -1, 8, 10, 1, 8, 1, 0, 10, 6, 1, 9, 1, 4, 6, 4, 1, 3, 10, 6, 3, 6, 0, 0, 6, 4, -1, -1,
-1, -1, -1, -1, 6, 4, 8, 10, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 11, 6, 7, 8, 11, 8, 9, 11, -1, -1,
-1, -1, -1, -1, 0, 7, 3, 0, 11, 7, 0, 9, 11, 6, 7, 11, -1, -1, -1, 11, 6, 7, 1, 11, 7, 1, 7, 8, 1, 8, 0, -1,
-1, -1, 11, 6, 7, 11, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, 1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1,
2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, 7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, 7, 3, 2, 6,
7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 10, 11, 6, 8, 11, 8, 9, 8, 6, 7, -1, -1, -1, 2, 0, 7, 2, 7,
10, 0, 9, 7, 6, 7, 11, 9, 11, 7, 1, 8, 0, 1, 7, 8, 1, 11, 7, 6, 7, 11, 2, 3, 10, 10, 2, 1, 10, 1, 7, 11, 6,
1, 6, 7, 1, -1, -1, -1, 8, 9, 6, 8, 6, 7, 9, 1, 6, 10, 6, 3, 1, 3, 6, 0, 9, 1, 10, 6, 7, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 7, 8, 0, 7, 0, 6, 3, 10, 0, 10, 6, 0, -1, -1, -1, 7, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 7, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 0, 8, 10, 7, 6, -1, -1, -1, -1,
-1, -1, -1, -1, -1, 0, 1, 9, 10, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 1, 9, 8, 3, 1, 10, 7, 6, -1,
-1, -1, -1, -1, -1, 11, 1, 2, 6, 10, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 11, 3, 0, 8, 6, 10, 7, -1,
-1, -1, -1, -1, -1, 2, 9, 0, 2, 11, 9, 6, 10, 7, -1, -1, -1, -1, -1, -1, 6, 10, 7, 2, 11, 3, 11, 8, 3, 11,
9, 8, -1, -1, -1, 7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1,
-1, -1, -1, -1, 2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, 1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1,
-1, -1, 11, 7, 6, 11, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, 11, 7, 6, 1, 7, 11, 1, 8, 7, 1, 0, 8, -1, -1,
-1, 0, 3, 7, 0, 7, 11, 0, 11, 9, 6, 11, 7, -1, -1, -1, 7, 6, 11, 7, 11, 8, 8, 11, 9, -1, -1, -1, -1, -1, -1,
6, 8, 4, 10, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 6, 10, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1,
8, 6, 10, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, 9, 4, 6, 9, 6, 3, 9, 3, 1, 10, 3, 6, -1, -1, -1, 6, 8,
4, 6, 10, 8, 2, 11, 1, -1, -1, -1, -1, -1, -1, 1, 2, 11, 3, 0, 10, 0, 6, 10, 0, 4, 6, -1, -1, -1, 4, 10, 8,
4, 6, 10, 0, 2, 9, 2, 11, 9, -1, -1, -1, 11, 9, 3, 11, 3, 2, 9, 4, 3, 10, 3, 6, 4, 6, 3, 8, 2, 3, 8, 4, 2,
4, 6, 2, -1, -1, -1, -1, -1, -1, 0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 9, 0, 2, 3, 4, 2,
4, 6, 4, 3, 8, -1, -1, -1, 1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, 8, 1, 3, 8, 6, 1, 8, 4, 6, 6,
11, 1, -1, -1, -1, 11, 1, 0, 11, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, 4, 6, 3, 4, 3, 8, 6, 11, 3, 0, 3, 9,
11, 9, 3, 11, 9, 4, 6, 11, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 9, 5, 7, 6, 10, -1, -1, -1, -1, -1, -1,
-1, -1, -1, 0, 8, 3, 4, 9, 5, 10, 7, 6, -1, -1, -1, -1, -1, -1, 5, 0, 1, 5, 4, 0, 7, 6, 10, -1, -1, -1, -1,
-1, -1, 10, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, 9, 5, 4, 11, 1, 2, 7, 6, 10, -1, -1, -1, -1, -1,
-1, 6, 10, 7, 1, 2, 11, 0, 8, 3, 4, 9, 5, -1, -1, -1, 7, 6, 10, 5, 4, 11, 4, 2, 11, 4, 0, 2, -1, -1, -1, 3,
4, 8, 3, 5, 4, 3, 2, 5, 11, 5, 2, 10, 7, 6, 7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, 9, 5, 4, 0,
8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, 3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, 6, 2, 8, 6, 8, 7, 2, 1,
8, 4, 8, 5, 1, 5, 8, 9, 5, 4, 11, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, 1, 6, 11, 1, 7, 6, 1, 0, 7, 8, 7, 0,
9, 5, 4, 4, 0, 11, 4, 11, 5, 0, 3, 11, 6, 11, 7, 3, 7, 11, 7, 6, 11, 7, 11, 8, 5, 4, 11, 4, 8, 11, -1, -1,
-1, 6, 9, 5, 6, 10, 9, 10, 8, 9, -1, -1, -1, -1, -1, -1, 3, 6, 10, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, 0,
10, 8, 0, 5, 10, 0, 1, 5, 5, 6, 10, -1, -1, -1, 6, 10, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, 1, 2,
11, 9, 5, 10, 9, 10, 8, 10, 5, 6, -1, -1, -1, 0, 10, 3, 0, 6, 10, 0, 9, 6, 5, 6, 9, 1, 2, 11, 10, 8, 5, 10,
5, 6, 8, 0, 5, 11, 5, 2, 0, 2, 5, 6, 10, 3, 6, 3, 5, 2, 11, 3, 11, 5, 3, -1, -1, -1, 5, 8, 9, 5, 2, 8, 5, 6,
2, 3, 8, 2, -1, -1, -1, 9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, 1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8,
2, 6, 2, 8, 1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 3, 6, 1, 6, 11, 3, 8, 6, 5, 6, 9, 8, 9,
6, 11, 1, 0, 11, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, 0, 3, 8, 5, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1,
11, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 5, 11, 7, 5, 10, -1, -1, -1, -1, -1, -1, -1,
-1, -1, 10, 5, 11, 10, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, 5, 10, 7, 5, 11, 10, 1, 9, 0, -1, -1, -1, -1,
-1, -1, 11, 7, 5, 11, 10, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, 10, 1, 2, 10, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1,
-1, 0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 10, -1, -1, -1, 9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 10, 7, -1, -1, -1, 7, 5,
2, 7, 2, 10, 5, 9, 2, 3, 2, 8, 9, 8, 2, 2, 5, 11, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, 8, 2, 0, 8, 5,
2, 8, 7, 5, 11, 2, 5, -1, -1, -1, 9, 0, 1, 5, 11, 3, 5, 3, 7, 3, 11, 2, -1, -1, -1, 9, 8, 2, 9, 2, 1, 8, 7,
2, 11, 2, 5, 7, 5, 2, 1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 7, 0, 7, 1, 1, 7, 5, -1,
-1, -1, -1, -1, -1, 9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, 9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 5, 8, 4, 5, 11, 8, 11, 10, 8, -1, -1, -1, -1, -1, -1, 5, 0, 4, 5, 10, 0, 5, 11, 10, 10, 3,
0, -1, -1, -1, 0, 1, 9, 8, 4, 11, 8, 11, 10, 11, 4, 5, -1, -1, -1, 11, 10, 4, 11, 4, 5, 10, 3, 4, 9, 4, 1,
3, 1, 4, 2, 5, 1, 2, 8, 5, 2, 10, 8, 4, 5, 8, -1, -1, -1, 0, 4, 10, 0, 10, 3, 4, 5, 10, 2, 10, 1, 5, 1, 10,
0, 2, 5, 0, 5, 9, 2, 10, 5, 4, 5, 8, 10, 8, 5, 9, 4, 5, 2, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 5,
11, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, 5, 11, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, 3, 11, 2, 3,
5, 11, 3, 8, 5, 4, 5, 8, 0, 1, 9, 5, 11, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, 8, 4, 5, 8, 5, 3, 3, 5,
1, -1, -1, -1, -1, -1, -1, 0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 4, 5, 8, 5, 3, 9, 0, 5,
0, 3, 5, -1, -1, -1, 9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 10, 7, 4, 9, 10, 9, 11, 10,
-1, -1, -1, -1, -1, -1, 0, 8, 3, 4, 9, 7, 9, 10, 7, 9, 11, 10, -1, -1, -1, 1, 11, 10, 1, 10, 4, 1, 4, 0, 7,
4, 10, -1, -1, -1, 3, 1, 4, 3, 4, 8, 1, 11, 4, 7, 4, 10, 11, 10, 4, 4, 10, 7, 9, 10, 4, 9, 2, 10, 9, 1, 2,
-1, -1, -1, 9, 7, 4, 9, 10, 7, 9, 1, 10, 2, 10, 1, 0, 8, 3, 10, 7, 4, 10, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1,
-1, 10, 7, 4, 10, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, 2, 9, 11, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, 9,
11, 7, 9, 7, 4, 11, 2, 7, 8, 7, 0, 2, 0, 7, 3, 7, 11, 3, 11, 2, 7, 4, 11, 1, 11, 0, 4, 0, 11, 1, 11, 2, 8,
7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, 4, 9, 1, 4, 1,
7, 0, 8, 1, 8, 7, 1, -1, -1, -1, 4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 8, 7, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 11, 8, 11, 10, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 0, 9, 3, 9,
10, 10, 9, 11, -1, -1, -1, -1, -1, -1, 0, 1, 11, 0, 11, 8, 8, 11, 10, -1, -1, -1, -1, -1, -1, 3, 1, 11, 10,
3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 10, 1, 10, 9, 9, 10, 8, -1, -1, -1, -1, -1, -1, 3, 0, 9, 3,
9, 10, 1, 2, 9, 2, 10, 9, -1, -1, -1, 0, 2, 10, 8, 0, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 2, 10, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 8, 2, 8, 11, 11, 8, 9, -1, -1, -1, -1, -1, -1, 9, 11, 2,
0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 8, 2, 8, 11, 0, 1, 8, 1, 11, 8, -1, -1, -1, 1, 11, 2, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 9, 1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 )