import { BufferAttribute, BufferGeometry, Color, DynamicDrawUsage, Mesh, Sphere, Vector3 } from 'three'; /** * Port of http://webglsamples.org/blob/blob.html */ class MarchingCubes extends Mesh { constructor( resolution, material, enableUvs = false, enableColors = false, maxPolyCount = 10000 ) { const geometry = new BufferGeometry(); super( geometry, material ); this.isMarchingCubes = true; const scope = this; // temp buffers used in polygonize const vlist = new Float32Array( 12 * 3 ); const nlist = new Float32Array( 12 * 3 ); const clist = new Float32Array( 12 * 3 ); this.enableUvs = enableUvs; this.enableColors = enableColors; // 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 ); this.palette = new Float32Array( this.size3 * 3 ); // this.count = 0; const maxVertexCount = maxPolyCount * 3; this.positionArray = new Float32Array( maxVertexCount * 3 ); const positionAttribute = new BufferAttribute( this.positionArray, 3 ); positionAttribute.setUsage( DynamicDrawUsage ); geometry.setAttribute( 'position', positionAttribute ); this.normalArray = new Float32Array( maxVertexCount * 3 ); const normalAttribute = new BufferAttribute( this.normalArray, 3 ); normalAttribute.setUsage( DynamicDrawUsage ); geometry.setAttribute( 'normal', normalAttribute ); if ( this.enableUvs ) { this.uvArray = new Float32Array( maxVertexCount * 2 ); const uvAttribute = new BufferAttribute( this.uvArray, 2 ); uvAttribute.setUsage( DynamicDrawUsage ); geometry.setAttribute( 'uv', uvAttribute ); } if ( this.enableColors ) { this.colorArray = new Float32Array( maxVertexCount * 3 ); const colorAttribute = new BufferAttribute( this.colorArray, 3 ); colorAttribute.setUsage( DynamicDrawUsage ); geometry.setAttribute( 'color', colorAttribute ); } geometry.boundingSphere = new Sphere( new Vector3(), 1 ); }; /////////////////////// // Polygonization /////////////////////// function lerp( a, b, t ) { return a + ( b - a ) * t; } function VIntX( q, offset, isol, x, y, z, valp1, valp2, c_offset1, c_offset2 ) { const mu = ( isol - valp1 ) / ( valp2 - valp1 ), nc = scope.normal_cache; vlist[ offset + 0 ] = x + mu * scope.delta; vlist[ offset + 1 ] = y; vlist[ offset + 2 ] = z; nlist[ offset + 0 ] = lerp( nc[ q + 0 ], nc[ q + 3 ], mu ); nlist[ offset + 1 ] = lerp( nc[ q + 1 ], nc[ q + 4 ], mu ); nlist[ offset + 2 ] = lerp( nc[ q + 2 ], nc[ q + 5 ], mu ); clist[ offset + 0 ] = lerp( scope.palette[ c_offset1 * 3 + 0 ], scope.palette[ c_offset2 * 3 + 0 ], mu ); clist[ offset + 1 ] = lerp( scope.palette[ c_offset1 * 3 + 1 ], scope.palette[ c_offset2 * 3 + 1 ], mu ); clist[ offset + 2 ] = lerp( scope.palette[ c_offset1 * 3 + 2 ], scope.palette[ c_offset2 * 3 + 2 ], mu ); } function VIntY( q, offset, isol, x, y, z, valp1, valp2, c_offset1, c_offset2 ) { const mu = ( isol - valp1 ) / ( valp2 - valp1 ), nc = scope.normal_cache; vlist[ offset + 0 ] = x; vlist[ offset + 1 ] = y + mu * scope.delta; vlist[ offset + 2 ] = z; const q2 = q + scope.yd * 3; nlist[ offset + 0 ] = lerp( nc[ q + 0 ], nc[ q2 + 0 ], mu ); nlist[ offset + 1 ] = lerp( nc[ q + 1 ], nc[ q2 + 1 ], mu ); nlist[ offset + 2 ] = lerp( nc[ q + 2 ], nc[ q2 + 2 ], mu ); clist[ offset + 0 ] = lerp( scope.palette[ c_offset1 * 3 + 0 ], scope.palette[ c_offset2 * 3 + 0 ], mu ); clist[ offset + 1 ] = lerp( scope.palette[ c_offset1 * 3 + 1 ], scope.palette[ c_offset2 * 3 + 1 ], mu ); clist[ offset + 2 ] = lerp( scope.palette[ c_offset1 * 3 + 2 ], scope.palette[ c_offset2 * 3 + 2 ], mu ); } function VIntZ( q, offset, isol, x, y, z, valp1, valp2, c_offset1, c_offset2 ) { const mu = ( isol - valp1 ) / ( valp2 - valp1 ), nc = scope.normal_cache; vlist[ offset + 0 ] = x; vlist[ offset + 1 ] = y; vlist[ offset + 2 ] = z + mu * scope.delta; const q2 = q + scope.zd * 3; nlist[ offset + 0 ] = lerp( nc[ q + 0 ], nc[ q2 + 0 ], mu ); nlist[ offset + 1 ] = lerp( nc[ q + 1 ], nc[ q2 + 1 ], mu ); nlist[ offset + 2 ] = lerp( nc[ q + 2 ], nc[ q2 + 2 ], mu ); clist[ offset + 0 ] = lerp( scope.palette[ c_offset1 * 3 + 0 ], scope.palette[ c_offset2 * 3 + 0 ], mu ); clist[ offset + 1 ] = lerp( scope.palette[ c_offset1 * 3 + 1 ], scope.palette[ c_offset2 * 3 + 1 ], mu ); clist[ offset + 2 ] = lerp( scope.palette[ c_offset1 * 3 + 2 ], scope.palette[ c_offset2 * 3 + 2 ], mu ); } function compNorm( q ) { const q3 = q * 3; if ( scope.normal_cache[ q3 ] === 0.0 ) { scope.normal_cache[ q3 + 0 ] = scope.field[ q - 1 ] - scope.field[ q + 1 ]; scope.normal_cache[ q3 + 1 ] = scope.field[ q - scope.yd ] - scope.field[ q + scope.yd ]; scope.normal_cache[ q3 + 2 ] = scope.field[ q - scope.zd ] - scope.field[ q + scope.zd ]; } } // Returns total number of triangles. Fills triangles. // (this is where most of time is spent - it's inner work of O(n3) loop ) function polygonize( fx, fy, fz, q, isol ) { // cache indices const q1 = q + 1, qy = q + scope.yd, qz = q + scope.zd, q1y = q1 + scope.yd, q1z = q1 + scope.zd, qyz = q + scope.yd + scope.zd, q1yz = q1 + scope.yd + scope.zd; let cubeindex = 0; const field0 = scope.field[ q ], field1 = scope.field[ q1 ], field2 = scope.field[ qy ], field3 = scope.field[ q1y ], field4 = scope.field[ qz ], field5 = scope.field[ q1z ], field6 = scope.field[ qyz ], field7 = scope.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 const bits = edgeTable[ cubeindex ]; if ( bits === 0 ) return 0; const d = scope.delta, fx2 = fx + d, fy2 = fy + d, fz2 = fz + d; // top of the cube if ( bits & 1 ) { compNorm( q ); compNorm( q1 ); VIntX( q * 3, 0, isol, fx, fy, fz, field0, field1, q, q1 ); } if ( bits & 2 ) { compNorm( q1 ); compNorm( q1y ); VIntY( q1 * 3, 3, isol, fx2, fy, fz, field1, field3, q1, q1y ); } if ( bits & 4 ) { compNorm( qy ); compNorm( q1y ); VIntX( qy * 3, 6, isol, fx, fy2, fz, field2, field3, qy, q1y ); } if ( bits & 8 ) { compNorm( q ); compNorm( qy ); VIntY( q * 3, 9, isol, fx, fy, fz, field0, field2, q, qy ); } // bottom of the cube if ( bits & 16 ) { compNorm( qz ); compNorm( q1z ); VIntX( qz * 3, 12, isol, fx, fy, fz2, field4, field5, qz, q1z ); } if ( bits & 32 ) { compNorm( q1z ); compNorm( q1yz ); VIntY( q1z * 3, 15, isol, fx2, fy, fz2, field5, field7, q1z, q1yz ); } if ( bits & 64 ) { compNorm( qyz ); compNorm( q1yz ); VIntX( qyz * 3, 18, isol, fx, fy2, fz2, field6, field7, qyz, q1yz ); } if ( bits & 128 ) { compNorm( qz ); compNorm( qyz ); VIntY( qz * 3, 21, isol, fx, fy, fz2, field4, field6, qz, qyz ); } // vertical lines of the cube if ( bits & 256 ) { compNorm( q ); compNorm( qz ); VIntZ( q * 3, 24, isol, fx, fy, fz, field0, field4, q, qz ); } if ( bits & 512 ) { compNorm( q1 ); compNorm( q1z ); VIntZ( q1 * 3, 27, isol, fx2, fy, fz, field1, field5, q1, q1z ); } if ( bits & 1024 ) { compNorm( q1y ); compNorm( q1yz ); VIntZ( q1y * 3, 30, isol, fx2, fy2, fz, field3, field7, q1y, q1yz ); } if ( bits & 2048 ) { compNorm( qy ); compNorm( qyz ); VIntZ( qy * 3, 33, isol, fx, fy2, fz, field2, field6, qy, qyz ); } cubeindex <<= 4; // re-purpose cubeindex into an offset into triTable let o1, o2, o3, numtris = 0, i = 0; // here is where triangles are created while ( triTable[ cubeindex + i ] != - 1 ) { o1 = cubeindex + i; o2 = o1 + 1; o3 = o1 + 2; posnormtriv( vlist, nlist, clist, 3 * triTable[ o1 ], 3 * triTable[ o2 ], 3 * triTable[ o3 ] ); i += 3; numtris ++; } return numtris; } function posnormtriv( pos, norm, colors, o1, o2, o3 ) { const c = scope.count * 3; // positions scope.positionArray[ c + 0 ] = pos[ o1 ]; scope.positionArray[ c + 1 ] = pos[ o1 + 1 ]; scope.positionArray[ c + 2 ] = pos[ o1 + 2 ]; scope.positionArray[ c + 3 ] = pos[ o2 ]; scope.positionArray[ c + 4 ] = pos[ o2 + 1 ]; scope.positionArray[ c + 5 ] = pos[ o2 + 2 ]; scope.positionArray[ c + 6 ] = pos[ o3 ]; scope.positionArray[ c + 7 ] = pos[ o3 + 1 ]; scope.positionArray[ c + 8 ] = pos[ o3 + 2 ]; // normals if ( scope.material.flatShading === true ) { const nx = ( norm[ o1 + 0 ] + norm[ o2 + 0 ] + norm[ o3 + 0 ] ) / 3; const ny = ( norm[ o1 + 1 ] + norm[ o2 + 1 ] + norm[ o3 + 1 ] ) / 3; const nz = ( norm[ o1 + 2 ] + norm[ o2 + 2 ] + norm[ o3 + 2 ] ) / 3; scope.normalArray[ c + 0 ] = nx; scope.normalArray[ c + 1 ] = ny; scope.normalArray[ c + 2 ] = nz; scope.normalArray[ c + 3 ] = nx; scope.normalArray[ c + 4 ] = ny; scope.normalArray[ c + 5 ] = nz; scope.normalArray[ c + 6 ] = nx; scope.normalArray[ c + 7 ] = ny; scope.normalArray[ c + 8 ] = nz; } else { scope.normalArray[ c + 0 ] = norm[ o1 + 0 ]; scope.normalArray[ c + 1 ] = norm[ o1 + 1 ]; scope.normalArray[ c + 2 ] = norm[ o1 + 2 ]; scope.normalArray[ c + 3 ] = norm[ o2 + 0 ]; scope.normalArray[ c + 4 ] = norm[ o2 + 1 ]; scope.normalArray[ c + 5 ] = norm[ o2 + 2 ]; scope.normalArray[ c + 6 ] = norm[ o3 + 0 ]; scope.normalArray[ c + 7 ] = norm[ o3 + 1 ]; scope.normalArray[ c + 8 ] = norm[ o3 + 2 ]; } // uvs if ( scope.enableUvs ) { const d = scope.count * 2; scope.uvArray[ d + 0 ] = pos[ o1 + 0 ]; scope.uvArray[ d + 1 ] = pos[ o1 + 2 ]; scope.uvArray[ d + 2 ] = pos[ o2 + 0 ]; scope.uvArray[ d + 3 ] = pos[ o2 + 2 ]; scope.uvArray[ d + 4 ] = pos[ o3 + 0 ]; scope.uvArray[ d + 5 ] = pos[ o3 + 2 ]; } // colors if ( scope.enableColors ) { scope.colorArray[ c + 0 ] = colors[ o1 + 0 ]; scope.colorArray[ c + 1 ] = colors[ o1 + 1 ]; scope.colorArray[ c + 2 ] = colors[ o1 + 2 ]; scope.colorArray[ c + 3 ] = colors[ o2 + 0 ]; scope.colorArray[ c + 4 ] = colors[ o2 + 1 ]; scope.colorArray[ c + 5 ] = colors[ o2 + 2 ]; scope.colorArray[ c + 6 ] = colors[ o3 + 0 ]; scope.colorArray[ c + 7 ] = colors[ o3 + 1 ]; scope.colorArray[ c + 8 ] = colors[ o3 + 2 ]; } scope.count += 3; } ///////////////////////////////////// // 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, colors ) { const sign = Math.sign( strength ); strength = Math.abs( strength ); const userDefineColor = ! ( colors === undefined || colors === null ); let ballColor = new Color( ballx, bally, ballz ); if ( userDefineColor ) { try { ballColor = colors instanceof Color ? colors : Array.isArray( colors ) ? new Color( Math.min( Math.abs( colors[ 0 ] ), 1 ), Math.min( Math.abs( colors[ 1 ] ), 1 ), Math.min( Math.abs( colors[ 2 ] ), 1 ) ) : new Color( colors ); } catch ( err ) { ballColor = new Color( ballx, bally, ballz ); } } // 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) const radius = this.size * Math.sqrt( strength / subtract ), zs = ballz * this.size, ys = bally * this.size, xs = ballx * this.size; let min_z = Math.floor( zs - radius ); if ( min_z < 1 ) min_z = 1; let max_z = Math.floor( zs + radius ); if ( max_z > this.size - 1 ) max_z = this.size - 1; let min_y = Math.floor( ys - radius ); if ( min_y < 1 ) min_y = 1; let max_y = Math.floor( ys + radius ); if ( max_y > this.size - 1 ) max_y = this.size - 1; let min_x = Math.floor( xs - radius ); if ( min_x < 1 ) min_x = 1; let 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. let 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 * sign; // optimization // http://www.geisswerks.com/ryan/BLOBS/blobs.html const ratio = Math.sqrt( ( x - xs ) * ( x - xs ) + ( y - ys ) * ( y - ys ) + ( z - zs ) * ( z - zs ) ) / radius; const contrib = 1 - ratio * ratio * ratio * ( ratio * ( ratio * 6 - 15 ) + 10 ); this.palette[ ( y_offset + x ) * 3 + 0 ] += ballColor.r * contrib; this.palette[ ( y_offset + x ) * 3 + 1 ] += ballColor.g * contrib; this.palette[ ( y_offset + x ) * 3 + 2 ] += ballColor.b * contrib; } } } } }; this.addPlaneX = function ( strength, subtract ) { // cache attribute lookups const size = this.size, yd = this.yd, zd = this.zd, field = this.field; let x, y, z, xx, val, xdiv, cxy, 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 ) { // cache attribute lookups const size = this.size, yd = this.yd, zd = this.zd, field = this.field; let x, y, z, yy, val, ydiv, cy, cxy, 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 ) { // cache attribute lookups const size = this.size, yd = this.yd, zd = this.zd, field = this.field; let x, y, z, zz, val, zdiv, cz, cyz, 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.setCell = function ( x, y, z, value ) { const index = this.size2 * z + this.size * y + x; this.field[ index ] = value; }; this.getCell = function ( x, y, z ) { const index = this.size2 * z + this.size * y + x; return this.field[ index ]; }; this.blur = function ( intensity = 1 ) { const field = this.field; const fieldCopy = field.slice(); const size = this.size; const size2 = this.size2; for ( let x = 0; x < size; x ++ ) { for ( let y = 0; y < size; y ++ ) { for ( let z = 0; z < size; z ++ ) { const index = size2 * z + size * y + x; let val = fieldCopy[ index ]; let count = 1; for ( let x2 = - 1; x2 <= 1; x2 += 2 ) { const x3 = x2 + x; if ( x3 < 0 || x3 >= size ) continue; for ( let y2 = - 1; y2 <= 1; y2 += 2 ) { const y3 = y2 + y; if ( y3 < 0 || y3 >= size ) continue; for ( let z2 = - 1; z2 <= 1; z2 += 2 ) { const z3 = z2 + z; if ( z3 < 0 || z3 >= size ) continue; const index2 = size2 * z3 + size * y3 + x3; const val2 = fieldCopy[ index2 ]; count ++; val += intensity * ( val2 - val ) / count; } } } field[ index ] = val; } } } }; this.reset = function () { // wipe the normal cache for ( let i = 0; i < this.size3; i ++ ) { this.normal_cache[ i * 3 ] = 0.0; this.field[ i ] = 0.0; this.palette[ i * 3 ] = this.palette[ i * 3 + 1 ] = this.palette[ i * 3 + 2 ] = 0.0; } }; this.update = function () { this.count = 0; // Triangulate. Yeah, this is slow. const smin2 = this.size - 2; for ( let z = 1; z < smin2; z ++ ) { const z_offset = this.size2 * z; const fz = ( z - this.halfsize ) / this.halfsize; //+ 1 for ( let y = 1; y < smin2; y ++ ) { const y_offset = z_offset + this.size * y; const fy = ( y - this.halfsize ) / this.halfsize; //+ 1 for ( let x = 1; x < smin2; x ++ ) { const fx = ( x - this.halfsize ) / this.halfsize; //+ 1 const q = y_offset + x; polygonize( fx, fy, fz, q, this.isolation ); } } } // set the draw range to only the processed triangles this.geometry.setDrawRange( 0, this.count ); // update geometry data geometry.getAttribute( 'position' ).needsUpdate = true; geometry.getAttribute( 'normal' ).needsUpdate = true; if ( this.enableUvs ) geometry.getAttribute( 'uv' ).needsUpdate = true; if ( this.enableColors ) geometry.getAttribute( 'color' ).needsUpdate = true; // safety check if ( this.count / 3 > maxPolyCount ) console.warn( 'THREE.MarchingCubes: Geometry buffers too small for rendering. Please create an instance with a higher poly count.' ); }; this.init( resolution ); } } ///////////////////////////////////// // Marching cubes lookup tables ///////////////////////////////////// // These tables are straight from Paul Bourke's page: // http://paulbourke.net/geometry/polygonise/ // who in turn got them from Cory Gene Bloyd. const 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 ] ); const 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, - 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