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MarchingCubes.js
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/**
* @author alteredq / http://alteredqualia.com/
*
* Port of greggman's ThreeD version of marching cubes to Three.js
* http://webglsamples.googlecode.com/hg/blob/blob.html
*/
THREE.MarchingCubes = function ( resolution, material, enableUvs, enableColors ) {
THREE.ImmediateRenderObject.call( this );
this.material = material;
this.enableUvs = enableUvs !== undefined ? enableUvs : false;
this.enableColors = enableColors !== undefined ? enableColors : false;
// functions have to be object properties
// prototype functions kill performance
// (tested and it was 4x slower !!!)
this.init = function( resolution ) {
this.resolution = resolution;
// parameters
this.isolation = 80.0;
// size of field, 32 is pushing it in Javascript :)
this.size = resolution;
this.size2 = this.size * this.size;
this.size3 = this.size2 * this.size;
this.halfsize = this.size / 2.0;
// deltas
this.delta = 2.0 / this.size;
this.yd = this.size;
this.zd = this.size2;
this.field = new Float32Array( this.size3 );
this.normal_cache = new Float32Array( this.size3 * 3 );
// temp buffers used in polygonize
this.vlist = new Float32Array( 12 * 3 );
this.nlist = new Float32Array( 12 * 3 );
this.firstDraw = true;
// immediate render mode simulator
this.maxCount = 4096; // TODO: find the fastest size for this buffer
this.count = 0;
this.hasPositions = false;
this.hasNormals = false;
this.hasColors = false;
this.hasUvs = false;
this.positionArray = new Float32Array( this.maxCount * 3 );
this.normalArray = new Float32Array( this.maxCount * 3 );
if ( this.enableUvs ) {
this.uvArray = new Float32Array( this.maxCount * 2 );
}
if ( this.enableColors ) {
this.colorArray = new Float32Array( this.maxCount * 3 );
}
};
///////////////////////
// Polygonization
///////////////////////
this.lerp = function( a, b, t ) { return a + ( b - a ) * t; };
this.VIntX = function( q, pout, nout, offset, isol, x, y, z, valp1, valp2 ) {
var mu = ( isol - valp1 ) / ( valp2 - valp1 ),
nc = this.normal_cache;
pout[ offset ] = x + mu * this.delta;
pout[ offset + 1 ] = y;
pout[ offset + 2 ] = z;
nout[ offset ] = this.lerp( nc[ q ], nc[ q + 3 ], mu );
nout[ offset + 1 ] = this.lerp( nc[ q + 1 ], nc[ q + 4 ], mu );
nout[ offset + 2 ] = this.lerp( nc[ q + 2 ], nc[ q + 5 ], mu );
};
this.VIntY = function( q, pout, nout, offset, isol, x, y, z, valp1, valp2 ) {
var mu = ( isol - valp1 ) / ( valp2 - valp1 ),
nc = this.normal_cache;
pout[ offset ] = x;
pout[ offset + 1 ] = y + mu * this.delta;
pout[ offset + 2 ] = z;
var q2 = q + this.yd * 3;
nout[ offset ] = this.lerp( nc[ q ], nc[ q2 ], mu );
nout[ offset + 1 ] = this.lerp( nc[ q + 1 ], nc[ q2 + 1 ], mu );
nout[ offset + 2 ] = this.lerp( nc[ q + 2 ], nc[ q2 + 2 ], mu );
};
this.VIntZ = function( q, pout, nout, offset, isol, x, y, z, valp1, valp2 ) {
var mu = ( isol - valp1 ) / ( valp2 - valp1 ),
nc = this.normal_cache;
pout[ offset ] = x;
pout[ offset + 1 ] = y;
pout[ offset + 2 ] = z + mu * this.delta;
var q2 = q + this.zd * 3;
nout[ offset ] = this.lerp( nc[ q ], nc[ q2 ], mu );
nout[ offset + 1 ] = this.lerp( nc[ q + 1 ], nc[ q2 + 1 ], mu );
nout[ offset + 2 ] = this.lerp( nc[ q + 2 ], nc[ q2 + 2 ], mu );
};
this.compNorm = function( q ) {
var q3 = q * 3;
if ( this.normal_cache[ q3 ] === 0.0 ) {
this.normal_cache[ q3 ] = this.field[ q - 1 ] - this.field[ q + 1 ];
this.normal_cache[ q3 + 1 ] = this.field[ q - this.yd ] - this.field[ q + this.yd ];
this.normal_cache[ q3 + 2 ] = this.field[ q - this.zd ] - this.field[ q + this.zd ];
}
};
// Returns total number of triangles. Fills triangles.
// (this is where most of time is spent - it's inner work of O(n3) loop )
this.polygonize = function( fx, fy, fz, q, isol, renderCallback ) {
// cache indices
var q1 = q + 1,
qy = q + this.yd,
qz = q + this.zd,
q1y = q1 + this.yd,
q1z = q1 + this.zd,
qyz = q + this.yd + this.zd,
q1yz = q1 + this.yd + this.zd;
var cubeindex = 0,
field0 = this.field[ q ],
field1 = this.field[ q1 ],
field2 = this.field[ qy ],
field3 = this.field[ q1y ],
field4 = this.field[ qz ],
field5 = this.field[ q1z ],
field6 = this.field[ qyz ],
field7 = this.field[ q1yz ];
if ( field0 < isol ) cubeindex |= 1;
if ( field1 < isol ) cubeindex |= 2;
if ( field2 < isol ) cubeindex |= 8;
if ( field3 < isol ) cubeindex |= 4;
if ( field4 < isol ) cubeindex |= 16;
if ( field5 < isol ) cubeindex |= 32;
if ( field6 < isol ) cubeindex |= 128;
if ( field7 < isol ) cubeindex |= 64;
// if cube is entirely in/out of the surface - bail, nothing to draw
var bits = THREE.edgeTable[ cubeindex ];
if ( bits === 0 ) return 0;
var d = this.delta,
fx2 = fx + d,
fy2 = fy + d,
fz2 = fz + d;
// top of the cube
if ( bits & 1 ) {
this.compNorm( q );
this.compNorm( q1 );
this.VIntX( q * 3, this.vlist, this.nlist, 0, isol, fx, fy, fz, field0, field1 );
};
if ( bits & 2 ) {
this.compNorm( q1 );
this.compNorm( q1y );
this.VIntY( q1 * 3, this.vlist, this.nlist, 3, isol, fx2, fy, fz, field1, field3 );
};
if ( bits & 4 ) {
this.compNorm( qy );
this.compNorm( q1y );
this.VIntX( qy * 3, this.vlist, this.nlist, 6, isol, fx, fy2, fz, field2, field3 );
};
if ( bits & 8 ) {
this.compNorm( q );
this.compNorm( qy );
this.VIntY( q * 3, this.vlist, this.nlist, 9, isol, fx, fy, fz, field0, field2 );
};
// bottom of the cube
if ( bits & 16 ) {
this.compNorm( qz );
this.compNorm( q1z );
this.VIntX( qz * 3, this.vlist, this.nlist, 12, isol, fx, fy, fz2, field4, field5 );
};
if ( bits & 32 ) {
this.compNorm( q1z );
this.compNorm( q1yz );
this.VIntY( q1z * 3, this.vlist, this.nlist, 15, isol, fx2, fy, fz2, field5, field7 );
};
if ( bits & 64 ) {
this.compNorm( qyz );
this.compNorm( q1yz );
this.VIntX( qyz * 3, this.vlist, this.nlist, 18, isol, fx, fy2, fz2, field6, field7 );
};
if ( bits & 128 ) {
this.compNorm( qz );
this.compNorm( qyz );
this.VIntY( qz * 3, this.vlist, this.nlist, 21, isol, fx, fy, fz2, field4, field6 );
};
// vertical lines of the cube
if ( bits & 256 ) {
this.compNorm( q );
this.compNorm( qz );
this.VIntZ( q * 3, this.vlist, this.nlist, 24, isol, fx, fy, fz, field0, field4 );
};
if ( bits & 512 ) {
this.compNorm( q1 );
this.compNorm( q1z );
this.VIntZ( q1 * 3, this.vlist, this.nlist, 27, isol, fx2, fy, fz, field1, field5 );
};
if ( bits & 1024 ) {
this.compNorm( q1y );
this.compNorm( q1yz );
this.VIntZ( q1y * 3, this.vlist, this.nlist, 30, isol, fx2, fy2, fz, field3, field7 );
};
if ( bits & 2048 ) {
this.compNorm( qy );
this.compNorm( qyz );
this.VIntZ( qy * 3, this.vlist, this.nlist, 33, isol, fx, fy2, fz, field2, field6 );
};
cubeindex <<= 4; // re-purpose cubeindex into an offset into triTable
var o1, o2, o3, numtris = 0, i = 0;
// here is where triangles are created
while ( THREE.triTable[ cubeindex + i ] != -1 ) {
o1 = cubeindex + i;
o2 = o1 + 1;
o3 = o1 + 2;
this.posnormtriv( this.vlist, this.nlist,
3 * THREE.triTable[ o1 ],
3 * THREE.triTable[ o2 ],
3 * THREE.triTable[ o3 ],
renderCallback );
i += 3;
numtris ++;
}
return numtris;
};
/////////////////////////////////////
// Immediate render mode simulator
/////////////////////////////////////
this.posnormtriv = function( pos, norm, o1, o2, o3, renderCallback ) {
var c = this.count * 3;
// positions
this.positionArray[ c ] = pos[ o1 ];
this.positionArray[ c + 1 ] = pos[ o1 + 1 ];
this.positionArray[ c + 2 ] = pos[ o1 + 2 ];
this.positionArray[ c + 3 ] = pos[ o2 ];
this.positionArray[ c + 4 ] = pos[ o2 + 1 ];
this.positionArray[ c + 5 ] = pos[ o2 + 2 ];
this.positionArray[ c + 6 ] = pos[ o3 ];
this.positionArray[ c + 7 ] = pos[ o3 + 1 ];
this.positionArray[ c + 8 ] = pos[ o3 + 2 ];
// normals
this.normalArray[ c ] = norm[ o1 ];
this.normalArray[ c + 1 ] = norm[ o1 + 1 ];
this.normalArray[ c + 2 ] = norm[ o1 + 2 ];
this.normalArray[ c + 3 ] = norm[ o2 ];
this.normalArray[ c + 4 ] = norm[ o2 + 1 ];
this.normalArray[ c + 5 ] = norm[ o2 + 2 ];
this.normalArray[ c + 6 ] = norm[ o3 ];
this.normalArray[ c + 7 ] = norm[ o3 + 1 ];
this.normalArray[ c + 8 ] = norm[ o3 + 2 ];
// uvs
if ( this.enableUvs ) {
var d = this.count * 2;
this.uvArray[ d ] = pos[ o1 ];
this.uvArray[ d + 1 ] = pos[ o1 + 2 ];
this.uvArray[ d + 2 ] = pos[ o2 ];
this.uvArray[ d + 3 ] = pos[ o2 + 2 ];
this.uvArray[ d + 4 ] = pos[ o3 ];
this.uvArray[ d + 5 ] = pos[ o3 + 2 ];
}
// colors
if ( this.enableColors ) {
this.colorArray[ c ] = pos[ o1 ];
this.colorArray[ c + 1 ] = pos[ o1 + 1 ];
this.colorArray[ c + 2 ] = pos[ o1 + 2 ];
this.colorArray[ c + 3 ] = pos[ o2 ];
this.colorArray[ c + 4 ] = pos[ o2 + 1 ];
this.colorArray[ c + 5 ] = pos[ o2 + 2 ];
this.colorArray[ c + 6 ] = pos[ o3 ];
this.colorArray[ c + 7 ] = pos[ o3 + 1 ];
this.colorArray[ c + 8 ] = pos[ o3 + 2 ];
}
this.count += 3;
if ( this.count >= this.maxCount - 3 ) {
this.hasPositions = true;
this.hasNormals = true;
if ( this.enableUvs ) {
this.hasUvs = true;
}
if ( this.enableColors ) {
this.hasColors = true;
}
renderCallback( this );
}
};
this.begin = function( ) {
this.count = 0;
this.hasPositions = false;
this.hasNormals = false;
this.hasUvs = false;
this.hasColors = false;
};
this.end = function( renderCallback ) {
if ( this.count === 0 )
return;
for ( var i = this.count * 3; i < this.positionArray.length; i ++ )
this.positionArray[ i ] = 0.0;
this.hasPositions = true;
this.hasNormals = true;
if ( this.enableUvs ) {
this.hasUvs = true;
}
if ( this.enableColors ) {
this.hasColors = true;
}
renderCallback( this );
};
/////////////////////////////////////
// Metaballs
/////////////////////////////////////
// Adds a reciprocal ball (nice and blobby) that, to be fast, fades to zero after
// a fixed distance, determined by strength and subtract.
this.addBall = function( ballx, bally, ballz, strength, subtract ) {
// Let's solve the equation to find the radius:
// 1.0 / (0.000001 + radius^2) * strength - subtract = 0
// strength / (radius^2) = subtract
// strength = subtract * radius^2
// radius^2 = strength / subtract
// radius = sqrt(strength / subtract)
var radius = this.size * Math.sqrt( strength / subtract ),
zs = ballz * this.size,
ys = bally * this.size,
xs = ballx * this.size;
var min_z = Math.floor( zs - radius ); if ( min_z < 1 ) min_z = 1;
var max_z = Math.floor( zs + radius ); if ( max_z > this.size - 1 ) max_z = this.size - 1;
var min_y = Math.floor( ys - radius ); if ( min_y < 1 ) min_y = 1;
var max_y = Math.floor( ys + radius ); if ( max_y > this.size - 1 ) max_y = this.size - 1;
var min_x = Math.floor( xs - radius ); if ( min_x < 1 ) min_x = 1;
var max_x = Math.floor( xs + radius ); if ( max_x > this.size - 1 ) max_x = this.size - 1;
// Don't polygonize in the outer layer because normals aren't
// well-defined there.
var x, y, z, y_offset, z_offset, fx, fy, fz, fz2, fy2, val;
for ( z = min_z; z < max_z; z++ ) {
z_offset = this.size2 * z,
fz = z / this.size - ballz,
fz2 = fz * fz;
for ( y = min_y; y < max_y; y++ ) {
y_offset = z_offset + this.size * y;
fy = y / this.size - bally;
fy2 = fy * fy;
for ( x = min_x; x < max_x; x++ ) {
fx = x / this.size - ballx;
val = strength / ( 0.000001 + fx*fx + fy2 + fz2 ) - subtract;
if ( val > 0.0 ) this.field[ y_offset + x ] += val;
}
}
}
};
this.addPlaneX = function( strength, subtract ) {
var x, y, z, xx, val, xdiv, cxy,
// cache attribute lookups
size = this.size,
yd = this.yd,
zd = this.zd,
field = this.field,
dist = size * Math.sqrt( strength / subtract );
if ( dist > size ) dist = size;
for ( x = 0; x < dist; x ++ ) {
xdiv = x / size;
xx = xdiv * xdiv;
val = strength / ( 0.0001 + xx ) - subtract;
if ( val > 0.0 ) {
for ( y = 0; y < size; y ++ ) {
cxy = x + y * yd;
for ( z = 0; z < size; z ++ ) {
field[ zd * z + cxy ] += val;
}
}
}
}
};
this.addPlaneY = function( strength, subtract ) {
var x, y, z, yy, val, ydiv, cy, cxy,
// cache attribute lookups
size = this.size,
yd = this.yd,
zd = this.zd,
field = this.field,
dist = size * Math.sqrt( strength / subtract );
if ( dist > size ) dist = size;
for ( y = 0; y < dist; y ++ ) {
ydiv = y / size;
yy = ydiv * ydiv;
val = strength / ( 0.0001 + yy ) - subtract;
if ( val > 0.0 ) {
cy = y * yd;
for ( x = 0; x < size; x ++ ) {
cxy = cy + x;
for ( z = 0; z < size; z ++ )
field[ zd * z + cxy ] += val;
}
}
}
};
this.addPlaneZ = function( strength, subtract ) {
var x, y, z, zz, val, zdiv, cz, cyz,
// cache attribute lookups
size = this.size,
yd = this.yd,
zd = this.zd,
field = this.field,
dist = size * Math.sqrt( strength / subtract );
if ( dist > size ) dist = size;
for ( z = 0; z < dist; z ++ ) {
zdiv = z / size;
zz = zdiv * zdiv;
val = strength / ( 0.0001 + zz ) - subtract;
if ( val > 0.0 ) {
cz = zd * z;
for ( y = 0; y < size; y ++ ) {
cyz = cz + y * yd;
for ( x = 0; x < size; x ++ )
field[ cyz + x ] += val;
}
}
}
};
/////////////////////////////////////
// Updates
/////////////////////////////////////
this.reset = function() {
var i;
// wipe the normal cache
for ( i = 0; i < this.size3; i ++ ) {
this.normal_cache[ i * 3 ] = 0.0;
this.field[ i ] = 0.0;
}
};
this.render = function( renderCallback ) {
this.begin();
// Triangulate. Yeah, this is slow.
var q, x, y, z, fx, fy, fz, y_offset, z_offset, smin2 = this.size - 2;
for ( z = 1; z < smin2; z ++ ) {
z_offset = this.size2 * z;
fz = ( z - this.halfsize ) / this.halfsize; //+ 1
for ( y = 1; y < smin2; y ++ ) {
y_offset = z_offset + this.size * y;
fy = ( y - this.halfsize ) / this.halfsize; //+ 1
for ( x = 1; x < smin2; x ++ ) {
fx = ( x - this.halfsize ) / this.halfsize; //+ 1
q = y_offset + x;
this.polygonize( fx, fy, fz, q, this.isolation, renderCallback );
}
}
}
this.end( renderCallback );
};
this.generateGeometry = function() {
var start = 0, geo = new THREE.Geometry();
var normals = [];
var geo_callback = function( object ) {
var i, x, y, z, vertex, normal,
face, a, b, c, na, nb, nc, nfaces;
for ( i = 0; i < object.count; i ++ ) {
a = i * 3;
b = a + 1;
c = a + 2;
x = object.positionArray[ a ];
y = object.positionArray[ b ];
z = object.positionArray[ c ];
vertex = new THREE.Vector3( x, y, z );
x = object.normalArray[ a ];
y = object.normalArray[ b ];
z = object.normalArray[ c ];
normal = new THREE.Vector3( x, y, z );
normal.normalize();
geo.vertices.push( vertex );
normals.push( normal );
}
nfaces = object.count / 3;
for ( i = 0; i < nfaces; i ++ ) {
a = ( start + i ) * 3;
b = a + 1;
c = a + 2;
na = normals[ a ];
nb = normals[ b ];
nc = normals[ c ];
face = new THREE.Face3( a, b, c, [ na, nb, nc ] );
geo.faces.push( face );
}
start += nfaces;
object.count = 0;
};
this.render( geo_callback );
// console.log( "generated " + geo.faces.length + " triangles" );
return geo;
};
this.init( resolution );
};
THREE.MarchingCubes.prototype = Object.create( THREE.ImmediateRenderObject.prototype );
/////////////////////////////////////
// Marching cubes lookup tables
/////////////////////////////////////
// These tables are straight from Paul Bourke's page:
// http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/
// who in turn got them from Cory Gene Bloyd.
THREE.edgeTable = new Int32Array([
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])
THREE.triTable = new Int32Array([
-1, -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, -1,
0, 1, 9, -1, -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,
1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1,
3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1,
3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1,
3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1,
9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
4, 7, 8, -1, -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, -1,
0, 1, 9, 8, 4, 7, -1, -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,
1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1,
9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1,
2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1,
8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1,
9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1,
4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1,
3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1,
1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1,
4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1,
4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1,
9, 5, 4, -1, -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, -1,
0, 5, 4, 1, 5, 0, -1, -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,
1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1,
5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1,
2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1,
9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1,
0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1,
2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1,
10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1,
4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1,
5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1,
5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1,
9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1,
0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1,
1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1,
10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1,
8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1,
2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1,
7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1,
9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1,
2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1,
11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1,
9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1,
5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1,
11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1,
11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1,
1, 6, 5, 2, 6, 1, -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, -1,
9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1,
5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1,
2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1,
0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1,
5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1,
6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1,
0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1,
3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1,
6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1,
5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1,
1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1,
10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1,
6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1,
1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1,
8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1,
7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1,
3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1,
5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1,
0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1,
9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1,
8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1,
5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1,
0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1,
6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1,
10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1,
10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1,
8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1,
1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1,
3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1,
0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1,
10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1,
0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1,
3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1,
6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1,
9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1,
8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1,
3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1,
6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1,
0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1,
10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1,
10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1,
1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1,
2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1,
7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1,
7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1,
2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1,
1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1,
11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1,
8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1,
0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1,
7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1,
10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1,
2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1,
6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1,
7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1,
2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1,
1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1,
10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1,
10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1,
0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1,
7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1,
6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1,
8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1,
9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1,
6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1,
1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1,
4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1,
10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1,
8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1,
0, 4, 2, 4, 6, 2, -1, -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,
1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1,
8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1,
10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1,
4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1,
10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1,
5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1,
11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1,
9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1,
6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1,
7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1,
3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1,
7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1,
9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1,
3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1,
6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1,
9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1,
1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1,
4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1,
7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1,
6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1,
3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1,
0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1,
6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1,
1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1,
0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1,
11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1,
6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1,
5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1,
9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1,
1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1,
1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1,
10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1,
0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1,
5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1,
10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1,
11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1,
0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1,
9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1,
7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1,
2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1,
8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1,