// ----------------------------------------------------------------------------- function minorMatrix(M, m, n, row, col) { var out = new Array(m - 1); for (var i = 0; i < m - 1; i++) { out[i] = new Array(n - 1); var ii = i < row ? i : i + 1; for (var j = 0; j < n - 1; j++) { var jj = j < col ? j : j + 1; out[i][j] = M[ii][jj]; } } return out; } // ----------------------------------------------------------------------------- function scaleMatrix(k, M, m, n) { var out = new Array(m); for (var i = 0; i < m; i++) { out[i] = new Array(n); for (var j = 0; j < n; j++) { out[i][j] = k * M[i][j]; } } return out; } // ----------------------------------------------------------------------------- function scaleMinorMatrix(k, M, m, n, row, col) { return scaleMatrix(k, minorMatrix(M, m, n, row, col), m - 1, n - 1); } // ----------------------------------------------------------------------------- function matricialSum(M1, M2, m, n) { var out = new Array(m); for (var i = 0; i < m; i++) { out[i] = new Array(n); for (var j = 0; j < n; j++) { out[i][j] = M1[i][j] + M2[i][j]; } } return out; } // ----------------------------------------------------------------------------- function levelMatrix(M, m, n, level, strict) { var out = new Array(m); for (var i = 0; i < m; i++) { out[i] = new Array(n); for (var j = 0; j < n; j++) { out[i][j] = (strict ? (M[i][j] > level) : (M[i][j] >= level)) ? 1 : 0; } } return out; } // ----------------------------------------------------------------------------- function toMatrix(A, m, n, k) { var out = new Array(m); for (var i = 0; i < m; i++) { out[i] = new Array(n); for (var j = 0; j < n; j++) { out[i][j] = A[i][j][k]; } } return out; } // ---------------------------------------------------------------------------- function maxArray(A, m, n, p) { var max = null; for (var k = 0; k < p; k++) { for (var i = 0; i < m; i++) { for (var j = 0; j < n; j++) { max = Math.max(max, A[i][j][k]); } } } return max; } // ----------------------------------------------------------------------------- function whichIndicesAndItems(M, m, n) { var out = { indices: [], items: [], length: null }; var k = 0; var ij = 0; for (var j = 0; j < n; j++) { for (var i = 0; i < m; i++) { if (M[i][j] > 0 && M[i][j] < 255) { out.indices.push(ij); out.items.push(M[i][j]); k++; } ij++; } } out.length = k; return out; } // ----------------------------------------------------------------------------- function kro1(M, nx, ny, n) { var out = new Array(nx * n + 1); for (var i = 0; i < nx * n; i++) { out[i] = new Array(ny); for (var j = 0; j < ny; j++) { out[i][j] = M[i % nx][j]; } } out[nx * n] = new Array(ny); for (var j = 0; j < ny; j++) { out[nx * n][j] = 0; } return out; } // ----------------------------------------------------------------------------- function kro2(M, nx, ny, n) { var out = new Array(nx * n + 1); var replicates = new Array(nx * n); var count = 0; for (var i = 0; i < nx; i++) { for (var m = 0; m < n; m++) { replicates[count] = i; count++; } } for (var i = 0; i < nx * n; i++) { out[i] = new Array(ny); for (var j = 0; j < ny; j++) { out[i][j] = M[replicates[i]][j]; } } out[nx * n] = new Array(ny); for (var j = 0; j < ny; j++) { out[nx * n][j] = 0; } return out; } // ----------------------------------------------------------------------------- function replicate(x, counts, n) { var total = 0; for (var i = 0; i < n; i++) { total += counts[i]; } var out = new Array(total); var count = 0; for (var i = 0; i < n; i++) { for (var j = 0; j < counts[i]; j++) { out[count] = x[i]; count++; } } return out; } // ---------------------------------------------------------------------------- function repeach(x, times, n) { var out = new Array(n * times); var count = 0; for (var i = 0; i < n; i++) { for (var j = 0; j < times; j++) { out[count] = x[i]; count++; } } return out; } // concatenate rows of a jagged array ------------------------------------------ function unlist(jagged, jaggedsizes, rows, nrows) { var count = 0; for (var i = 0; i < nrows; i++) { count += jaggedsizes[rows[i]]; } var out = new Array(count); count = 0; for (var i = 0; i < nrows; i++) { for (var j = 0; j < jaggedsizes[rows[i]]; j++) { out[count] = jagged[rows[i]][j]; count++; } } return out; } // R: matrix(M, ncol=ncol, byrow=TRUE) ---------------------------------------- function vector2matrix(M, lengthM, ncol) { var nrow = lengthM / ncol; var out = new Array(nrow); for (var i = 0; i < nrow; i++) { out[i] = new Array(ncol); for (var j = 0; j < ncol; j++) { out[i][j] = M[i * ncol + j]; } } return out; } // ---------------------------------------------------------------------------- function matrix2vectorMinusFirstColumn(M, nrow, ncol) { var out = new Array(nrow * (ncol - 1)); for (var i = 0; i < nrow; i++) { for (var j = 1; j < ncol; j++) { out[i * (ncol - 1) + j - 1] = M[i][j]; } } return out; } // ----------------------------------------------------------------------------- function cbind(M, v1, v2, nrow, ncol) { var out = new Array(nrow); for (var i = 0; i < nrow; i++) { out[i] = new Array(ncol + 2); for (var j = 0; j < ncol; j++) { out[i][j] = M[i][j]; } out[i][ncol] = v1[i]; out[i][ncol + 1] = v2[i]; } return out; } // ----------------------------------------------------------------------------- function subsetMatrix(M, rows, cols, nrows, ncols) { var out = new Array(nrows); for (var i = 0; i < nrows; i++) { out[i] = new Array(ncols); for (var j = 0; j < ncols; j++) { out[i][j] = M[rows[i]][cols[j]]; } } return out; } // ----------------------------------------------------------------------------- function whichEqual(v, x, lv) { var flag = new Array(lv); var count = 0; for (var i = 0; i < lv; i++) { if (v[i] == x) { flag[i] = 1; count++; } else { flag[i] = 0; } } var out = new Array(count); count = 0; for (var i = 0; i < lv; i++) { if (flag[i]) { out[count] = i; count++; } } return out; } // ----------------------------------------------------------------------------- function jthColumn(M, lengthM, ncol, j) { var nrow = lengthM / ncol; var out = new Array(nrow); for (var i = 0; i < nrow; i++) { out[i] = M[i * ncol + j]; } return out; } // ----------------------------------------------------------------------------- function jthColumn2(M, nrow, j) { var out = new Array(nrow); for (var i = 0; i < nrow; i++) { out[i] = M[i][j]; } return out; } // ----------------------------------------------------------------------------- function transpose(M, nrow, ncol) { var out = new Array(ncol); for (var i = 0; i < ncol; i++) { out[i] = new Array(nrow); for (var j = 0; j < nrow; j++) { out[i][j] = M[j][i]; } } return out; } // ----------------------------------------------------------------------------- function vectorialSum(v1, v2, l) { var out = new Array(l); for (var i = 0; i < l; i++) { out[i] = v1[i] + v2[i]; } return out; } // ----------------------------------------------------------------------------- var CaseRotationFlip = [ [1, 24, 1], [2, 19, 1], [2, 17, 1], [3, 17, 1], [2, 24, 1], [4, 24, 1], [3, 24, 1], [6, 10, 1], [2, 15, 1], [3, 19, 1], [4, 17, 1], [6, 9, 1], [3, 9, 1], [6, 8, 1], [6, 1, 1], [9, 23, -1], [2, 20, 1], [3, 18, 1], [4, 7, 1], [6, 16, 1], [5, 24, 1], [7, 5, 1], [7, 24, 1], [12, 9, 1], [4, 20, 1], [6, 22, 1], [8, 24, 1], [10, 24, -1], [7, 9, 1], [15, 24, -1], [13, 20, -1], [6, 20, -1], [2, 21, 1], [4, 6, 1], [3, 16, 1], [6, 4, 1], [4, 16, 1], [8, 23, 1], [6, 14, 1], [10, 23, -1], [5, 21, 1], [7, 10, 1], [7, 16, 1], [15, 9, 1], [7, 2, 1], [13, 8, 1], [12, 23, -1], [6, 6, -1], [3, 6, 1], [6, 17, 1], [6, 18, 1], [9, 18, 1], [7, 4, 1], [13, 17, 1], [15, 18, 1], [6, 13, -1], [7, 6, 1], [12, 16, 1], [13, 18, 1], [6, 2, -1], [11, 24, 1], [7, 3, -1], [7, 12, -1], [3, 12, -1], [2, 23, 1], [5, 23, 1], [4, 23, 1], [7, 1, 1], [3, 14, 1], [7, 14, 1], [6, 21, 1], [15, 23, -1], [4, 15, 1], [7, 19, 1], [8, 19, 1], [13, 23, -1], [6, 11, 1], [12, 17, -1], [10, 19, -1], [6, 23, -1], [4, 12, 1], [7, 18, 1], [8, 22, 1], [13, 16, 1], [7, 13, 1], [11, 23, 1], [13, 21, 1], [7, 15, -1], [8, 21, 1], [13, 22, 1], [14, 24, -1], [8, 15, -1], [13, 11, 1], [7, 7, -1], [8, 12, -1], [4, 22, -1], [3, 23, 1], [7, 23, 1], [6, 24, 1], [12, 18, 1], [6, 7, 1], [13, 19, -1], [9, 24, 1], [6, 19, -1], [7, 21, 1], [11, 18, 1], [13, 24, 1], [7, 20, -1], [15, 16, -1], [7, 22, -1], [6, 15, -1], [3, 22, -1], [6, 3, 1], [15, 17, 1], [10, 22, -1], [6, 12, -1], [12, 24, 1], [7, 11, -1], [6, 5, -1], [3, 15, -1], [13, 10, -1], [7, 8, -1], [8, 20, -1], [4, 9, -1], [7, 17, -1], [5, 22, -1], [4, 18, -1], [2, 22, -1], [2, 22, 1], [4, 18, 1], [5, 22, 1], [7, 17, 1], [4, 9, 1], [8, 20, 1], [7, 8, 1], [13, 10, 1], [3, 15, 1], [6, 5, 1], [7, 11, 1], [12, 24, -1], [6, 12, 1], [10, 22, 1], [15, 17, -1], [6, 3, -1], [3, 22, 1], [6, 15, 1], [7, 22, 1], [15, 16, 1], [7, 20, 1], [13, 24, -1], [11, 18, -1], [7, 21, -1], [6, 19, 1], [9, 24, -1], [13, 19, 1], [6, 7, -1], [12, 18, -1], [6, 24, -1], [7, 23, -1], [3, 23, -1], [4, 22, 1], [8, 12, 1], [7, 7, 1], [13, 11, -1], [8, 15, 1], [14, 24, 1], [13, 22, -1], [8, 21, -1], [7, 15, 1], [13, 21, -1], [11, 23, -1], [7, 13, -1], [13, 16, -1], [8, 22, -1], [7, 18, -1], [4, 12, -1], [6, 23, 1], [10, 19, 1], [12, 17, 1], [6, 11, -1], [13, 23, 1], [8, 19, -1], [7, 19, -1], [4, 15, -1], [15, 23, 1], [6, 21, -1], [7, 14, -1], [3, 14, -1], [7, 1, -1], [4, 23, -1], [5, 23, -1], [2, 23, -1], [3, 12, 1], [7, 12, 1], [7, 3, 1], [11, 24, -1], [6, 2, 1], [13, 18, -1], [12, 16, -1], [7, 6, -1], [6, 13, 1], [15, 18, -1], [13, 17, -1], [7, 4, -1], [9, 18, -1], [6, 18, -1], [6, 17, -1], [3, 6, -1], [6, 6, 1], [12, 23, 1], [13, 8, -1], [7, 2, -1], [15, 9, -1], [7, 16, -1], [7, 10, -1], [5, 21, -1], [10, 23, 1], [6, 14, -1], [8, 23, -1], [4, 16, -1], [6, 4, -1], [3, 16, -1], [4, 6, -1], [2, 21, -1], [6, 20, 1], [13, 20, 1], [15, 24, 1], [7, 9, -1], [10, 24, 1], [8, 24, -1], [6, 22, -1], [4, 20, -1], [12, 9, -1], [7, 24, -1], [7, 5, -1], [5, 24, -1], [6, 16, -1], [4, 7, -1], [3, 18, -1], [2, 20, -1], [9, 23, 1], [6, 1, -1], [6, 8, -1], [3, 9, -1], [6, 9, -1], [4, 17, -1], [3, 19, -1], [2, 15, -1], [6, 10, -1], [3, 24, -1], [4, 24, -1], [2, 24, -1], [3, 17, -1], [2, 17, -1], [2, 19, -1], [1, 24, -1] ]; // ----------------------------------------------------------------------------- var indexArray = [ [0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 1, 0], [0, 0, 1], [1, 0, 1], [1, 1, 1], [0, 1, 1] ]; // ----------------------------------------------------------------------------- var EdgesLengths = [3, 3, 6, 3, 18, 6, 9, 3, 6, 18, 9, 6, 9, 9, 6, 3, 6, 18, 9, 24, 48, 48, 12, 18, 9, 177, 12, 48, 12, 96, 9, 3, 18, 6, 9, 18, 177, 9, 12, 24, 48, 48, 12, 48, 96, 12, 9, 6, 9, 9, 6, 48, 96, 12, 9, 48, 12, 96, 9, 96, 48, 48, 6, 3, 24, 18, 48, 6, 48, 9, 12, 18, 48, 177, 96, 9, 12, 12, 9, 18, 48, 177, 96, 48, 96, 96, 48, 177, 96, 816, 177, 96, 48, 177, 18, 6, 48, 9, 12, 9, 96, 6, 9, 48, 96, 96, 48, 12, 48, 9, 6, 9, 12, 12, 9, 12, 48, 9, 6, 96, 48, 177, 18, 48, 24, 18, 3, 3, 18, 24, 48, 18, 177, 48, 96, 6, 9, 48, 12, 9, 12, 12, 9, 6, 9, 48, 12, 48, 96, 96, 48, 9, 6, 96, 9, 12, 9, 48, 6, 18, 177, 48, 96, 177, 816, 96, 177, 48, 96, 96, 48, 96, 177, 48, 18, 9, 12, 12, 9, 96, 177, 48, 18, 12, 9, 48, 6, 48, 18, 24, 3, 6, 48, 48, 96, 9, 96, 12, 48, 9, 12, 96, 48, 6, 9, 9, 6, 9, 12, 96, 48, 12, 48, 48, 24, 12, 9, 177, 18, 9, 6, 18, 3, 9, 96, 12, 48, 12, 177, 9, 18, 12, 48, 48, 24, 9, 18, 6, 3, 6, 9, 9, 6, 9, 18, 6, 3, 9, 6, 18, 3, 6, 3, 3]; // ----------------------------------------------------------------------------- var EdgePoints = [ [1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 1], [5, 5, 6], [6, 6, 7], [7, 7, 8], [8, 8, 5], [9, 1, 5], [10, 2, 6], [11, 3, 7], [12, 4, 8], [13, 9, 9] ]; // ----------------------------------------------------------------------------- var Edges = [ [4, 9, 1], [1, 10, 2], [9, 10, 4, 10, 2, 4], [2, 11, 3], [2, 11, 3, 4, 9, 1, 2, 11, 1, 11, 9, 1, 11, 4, 9, 11, 3, 4], [10, 11, 1, 11, 3, 1], [4, 9, 3, 3, 9, 11, 9, 10, 11], [12, 4, 3], [12, 9, 3, 9, 1, 3], [1, 10, 2, 3, 12, 4, 1, 10, 4, 10, 12, 4, 10, 3, 12, 10, 2, 3], [3, 12, 2, 2, 12, 10, 12, 9, 10], [4, 2, 12, 2, 11, 12], [2, 11, 1, 1, 11, 9, 11, 12, 9], [1, 10, 4, 4, 10, 12, 10, 11, 12], [11, 9, 10, 11, 12, 9], [8, 5, 9], [5, 1, 8, 1, 4, 8], [10, 2, 1, 9, 8, 5, 10, 2, 5, 2, 8, 5, 2, 9, 8, 2, 1, 9], [10, 2, 5, 5, 2, 8, 2, 4, 8], [2, 11, 3, 9, 8, 5, 2, 9, 3, 9, 8, 3, 11, 3, 8, 2, 11, 5, 2, 5, 9, 11, 8, 5], [4, 8, 1, 8, 5, 1, 2, 11, 3, 4, 8, 3, 8, 11, 3, 8, 5, 11, 2, 11, 5, 2, 5, 1, 4, 1, 2, 4, 2, 3, 3, 2, 11, 4, 8, 3, 8, 11, 3, 8, 5, 11, 2, 11, 5, 2, 5, 1], [10, 11, 1, 11, 3, 1, 9, 8, 5, 10, 11, 5, 11, 8, 5, 11, 3, 8, 9, 8, 3, 9, 3, 1, 10, 1, 9, 10, 9, 5, 5, 9, 8, 10, 11, 5, 11, 8, 5, 11, 3, 8, 9, 8, 3, 9, 3, 1], [3, 4, 8, 3, 8, 10, 3, 10, 11, 8, 5, 10], [8, 5, 9, 4, 3, 12, 8, 5, 12, 5, 3, 12, 5, 4, 3, 5, 9, 4], [8, 5, 12, 12, 5, 3, 5, 1, 3], [2, 1, 10, 4, 3, 12, 9, 8, 5, 2, 1, 10, 4, 5, 9, 4, 3, 5, 8, 5, 3, 8, 3, 12, 4, 3, 12, 2, 1, 9, 2, 9, 8, 2, 5, 10, 2, 8, 5, 9, 8, 5, 2, 3, 12, 2, 12, 10, 10, 12, 4, 10, 4, 1, 2, 13, 10, 10, 13, 5, 8, 5, 13, 8, 13, 12, 12, 13, 3, 4, 3, 13, 4, 13, 9, 9, 13, 1, 2, 1, 13, 2, 13, 10, 2, 13, 3, 12, 13, 3, 8, 13, 12, 8, 5, 13, 9, 5, 13, 4, 13, 9, 4, 1, 13, 10, 13, 1, 8, 5, 13, 10, 13, 5, 2, 13, 10, 2, 3, 13, 12, 13, 3, 4, 13, 12, 4, 1, 13, 9, 13, 1, 9, 8, 13, 2, 3, 12, 2, 12, 5, 2, 5, 10, 8, 5, 12, 4, 1, 9, 2, 3, 1, 4, 1, 3, 4, 3, 12, 4, 12, 8, 4, 8, 9, 9, 8, 5, 9, 5, 1, 10, 1, 5, 2, 1, 10], [2, 5, 10, 2, 3, 8, 2, 8, 5, 8, 3, 12], [4, 2, 12, 2, 11, 12, 8, 5, 9, 4, 2, 9, 2, 5, 9, 2, 11, 5, 8, 5, 11, 8, 11, 12, 4, 12, 8, 4, 8, 9, 9, 8, 5, 4, 2, 9, 2, 5, 9, 2, 11, 5, 8, 5, 11, 8, 11, 12], [2, 11, 12, 2, 12, 5, 2, 5, 1, 8, 12, 5], [8, 5, 12, 5, 10, 12, 4, 1, 9, 12, 10, 11, 8, 4, 9, 8, 12, 4, 4, 11, 12, 4, 1, 11, 5, 10, 1, 5, 1, 9, 8, 5, 9, 1, 10, 11, 8, 5, 13, 5, 9, 13, 4, 13, 9, 1, 10, 13, 4, 1, 13, 11, 13, 10, 12, 13, 11, 8, 12, 13, 1, 9, 13, 8, 13, 9, 8, 5, 13, 5, 10, 13, 11, 13, 10, 12, 11, 13, 4, 13, 12, 4, 1, 13, 8, 5, 9, 4, 1, 10, 4, 10, 12, 12, 10, 11], [8, 5, 12, 5, 10, 12, 12, 10, 11], [6, 10, 5], [5, 6, 10, 1, 4, 9, 5, 6, 9, 6, 4, 9, 6, 1, 4, 6, 10, 1], [1, 5, 2, 5, 6, 2], [5, 6, 9, 9, 6, 4, 6, 2, 4], [10, 5, 6, 11, 3, 2, 10, 5, 2, 5, 3, 2, 5, 11, 3, 5, 6, 11], [6, 10, 5, 2, 11, 3, 1, 4, 9, 6, 10, 5, 2, 9, 1, 2, 11, 9, 4, 9, 11, 4, 11, 3, 2, 11, 3, 6, 10, 1, 6, 1, 4, 6, 9, 5, 6, 4, 9, 1, 4, 9, 6, 11, 3, 6, 3, 5, 5, 3, 2, 5, 2, 10, 6, 13, 5, 5, 13, 9, 4, 9, 13, 4, 13, 3, 3, 13, 11, 2, 11, 13, 2, 13, 1, 1, 13, 10, 6, 10, 13, 6, 13, 5, 6, 13, 11, 3, 13, 11, 4, 13, 3, 4, 9, 13, 1, 9, 13, 2, 13, 1, 2, 10, 13, 5, 13, 10, 4, 9, 13, 5, 13, 9, 6, 13, 5, 6, 11, 13, 3, 13, 11, 2, 13, 3, 2, 10, 13, 1, 13, 10, 1, 4, 13, 6, 11, 3, 6, 3, 9, 6, 9, 5, 4, 9, 3, 2, 10, 1, 6, 11, 10, 2, 10, 11, 2, 11, 3, 2, 3, 4, 2, 4, 1, 1, 4, 9, 1, 9, 10, 5, 10, 9, 6, 10, 5], [11, 3, 6, 6, 3, 5, 3, 1, 5], [6, 9, 5, 6, 11, 4, 6, 4, 9, 4, 11, 3], [6, 10, 5, 12, 4, 3, 6, 12, 5, 12, 4, 5, 10, 5, 4, 6, 10, 3, 6, 3, 12, 10, 4, 3], [1, 3, 9, 3, 12, 9, 5, 6, 10, 1, 3, 10, 3, 6, 10, 3, 12, 6, 5, 6, 12, 5, 12, 9, 1, 9, 5, 1, 5, 10, 10, 5, 6, 1, 3, 10, 3, 6, 10, 3, 12, 6, 5, 6, 12, 5, 12, 9], [1, 5, 2, 5, 6, 2, 3, 12, 4, 1, 5, 4, 5, 12, 4, 5, 6, 12, 3, 12, 6, 3, 6, 2, 1, 2, 3, 1, 3, 4, 4, 3, 12, 1, 5, 4, 5, 12, 4, 5, 6, 12, 3, 12, 6, 3, 6, 2], [3, 6, 2, 3, 9, 6, 3, 12, 9, 5, 9, 6], [11, 12, 2, 12, 4, 2, 10, 5, 6, 11, 12, 6, 12, 5, 6, 12, 4, 5, 10, 5, 4, 10, 4, 2, 11, 2, 10, 11, 10, 6, 6, 10, 5, 11, 12, 6, 12, 5, 6, 12, 4, 5, 10, 5, 4, 10, 4, 2], [2, 11, 1, 1, 11, 9, 6, 10, 5, 11, 12, 9, 2, 10, 6, 2, 6, 11, 6, 11, 12, 6, 12, 5, 1, 5, 9, 1, 10, 5, 2, 10, 1, 5, 12, 9, 2, 13, 1, 1, 13, 10, 6, 10, 13, 5, 13, 9, 6, 13, 5, 12, 9, 13, 11, 12, 13, 2, 13, 11, 5, 13, 10, 2, 10, 13, 2, 13, 1, 1, 13, 9, 12, 9, 13, 11, 13, 12, 6, 11, 13, 6, 13, 5, 2, 10, 1, 6, 9, 5, 6, 11, 9, 11, 12, 9], [6, 1, 5, 6, 12, 1, 6, 11, 12, 1, 12, 4], [5, 6, 9, 6, 11, 9, 9, 11, 12], [8, 6, 9, 6, 10, 9], [1, 4, 10, 10, 4, 6, 4, 8, 6], [9, 8, 1, 1, 8, 2, 8, 6, 2], [4, 8, 6, 4, 6, 2], [10, 9, 6, 9, 8, 6, 11, 3, 2, 10, 9, 2, 9, 3, 2, 9, 8, 3, 11, 3, 8, 11, 8, 6, 10, 6, 11, 10, 11, 2, 2, 11, 3, 10, 9, 2, 9, 3, 2, 9, 8, 3, 11, 3, 8, 11, 8, 6], [1, 4, 10, 10, 4, 6, 3, 2, 11, 4, 8, 6, 1, 2, 3, 1, 3, 4, 3, 4, 8, 3, 8, 11, 10, 11, 6, 10, 2, 11, 1, 2, 10, 11, 8, 6, 1, 13, 10, 10, 13, 2, 3, 2, 13, 11, 13, 6, 3, 13, 11, 8, 6, 13, 4, 8, 13, 1, 13, 4, 11, 13, 2, 1, 2, 13, 1, 13, 10, 10, 13, 6, 8, 6, 13, 4, 13, 8, 3, 4, 13, 3, 13, 11, 1, 2, 10, 3, 6, 11, 3, 4, 6, 4, 8, 6], [9, 3, 1, 9, 6, 3, 9, 8, 6, 11, 6, 3], [11, 3, 6, 3, 4, 6, 6, 4, 8], [8, 6, 9, 6, 10, 9, 4, 3, 12, 8, 6, 12, 6, 3, 12, 6, 10, 3, 4, 3, 10, 4, 10, 9, 8, 9, 4, 8, 4, 12, 12, 4, 3, 8, 6, 12, 6, 3, 12, 6, 10, 3, 4, 3, 10, 4, 10, 9], [10, 1, 3, 10, 3, 8, 10, 8, 6, 3, 12, 8], [9, 8, 1, 1, 8, 2, 12, 4, 3, 8, 6, 2, 9, 4, 12, 9, 12, 8, 12, 8, 6, 12, 6, 3, 1, 3, 2, 1, 4, 3, 9, 4, 1, 3, 6, 2, 9, 13, 1, 1, 13, 4, 12, 4, 13, 3, 13, 2, 12, 13, 3, 6, 2, 13, 8, 6, 13, 9, 13, 8, 3, 13, 4, 9, 4, 13, 9, 13, 1, 1, 13, 2, 6, 2, 13, 8, 13, 6, 12, 8, 13, 12, 13, 3, 9, 4, 1, 12, 2, 3, 12, 8, 2, 8, 6, 2], [3, 12, 2, 12, 8, 2, 2, 8, 6], [2, 11, 4, 10, 9, 6, 6, 9, 8, 11, 12, 4, 2, 11, 6, 2, 6, 10, 6, 11, 12, 6, 12, 8, 4, 12, 9, 9, 12, 8, 2, 10, 9, 2, 9, 4, 2, 10, 13, 2, 13, 4, 4, 13, 12, 11, 12, 13, 6, 11, 13, 6, 13, 8, 9, 8, 13, 10, 9, 13, 4, 13, 9, 2, 13, 4, 2, 11, 13, 11, 12, 13, 8, 13, 12, 6, 13, 8, 10, 13, 6, 10, 9, 13, 2, 10, 4, 10, 9, 4, 6, 11, 12, 6, 12, 8], [6, 11, 8, 8, 11, 12, 2, 10, 1, 6, 10, 8, 8, 10, 1, 8, 1, 12, 2, 12, 1, 2, 11, 12, 6, 2, 11, 6, 10, 2, 10, 1, 2, 6, 10, 8, 8, 10, 1, 8, 1, 12, 2, 12, 1, 2, 11, 12], [12, 8, 11, 11, 8, 6, 9, 4, 1, 12, 4, 11, 11, 4, 1, 11, 1, 6, 9, 6, 1, 9, 8, 6, 12, 9, 8, 12, 4, 9, 4, 1, 9, 12, 4, 11, 11, 4, 1, 11, 1, 6, 9, 6, 1, 9, 8, 6], [12, 8, 11, 11, 8, 6], [6, 7, 11], [6, 7, 11, 1, 4, 9, 6, 1, 11, 1, 4, 11, 7, 11, 4, 6, 7, 9, 6, 9, 1, 7, 4, 9], [6, 7, 11, 2, 1, 10, 6, 7, 10, 7, 1, 10, 7, 2, 1, 7, 11, 2], [2, 4, 10, 4, 9, 10, 6, 7, 11, 2, 4, 11, 4, 7, 11, 4, 9, 7, 6, 7, 9, 6, 9, 10, 2, 10, 6, 2, 6, 11, 11, 6, 7, 2, 4, 11, 4, 7, 11, 4, 9, 7, 6, 7, 9, 6, 9, 10], [2, 6, 3, 6, 7, 3], [2, 6, 3, 6, 7, 3, 4, 9, 1, 2, 6, 1, 6, 9, 1, 6, 7, 9, 4, 9, 7, 4, 7, 3, 2, 3, 4, 2, 4, 1, 1, 4, 9, 2, 6, 1, 6, 9, 1, 6, 7, 9, 4, 9, 7, 4, 7, 3], [6, 7, 10, 10, 7, 1, 7, 3, 1], [6, 7, 3, 6, 3, 9, 6, 9, 10, 4, 3, 9], [12, 4, 3, 11, 6, 7, 12, 4, 7, 4, 6, 7, 4, 11, 6, 4, 3, 11], [12, 9, 3, 9, 1, 3, 11, 6, 7, 12, 9, 7, 9, 6, 7, 9, 1, 6, 11, 6, 1, 11, 1, 3, 12, 3, 11, 12, 11, 7, 7, 11, 6, 12, 9, 7, 9, 6, 7, 9, 1, 6, 11, 6, 1, 11, 1, 3], [4, 3, 12, 2, 1, 10, 11, 6, 7, 4, 3, 12, 2, 7, 11, 2, 1, 7, 6, 7, 1, 6, 1, 10, 2, 1, 10, 4, 3, 11, 4, 11, 6, 4, 7, 12, 4, 6, 7, 11, 6, 7, 4, 1, 10, 4, 10, 12, 12, 10, 2, 12, 2, 3, 4, 13, 12, 12, 13, 7, 6, 7, 13, 6, 13, 10, 10, 13, 1, 2, 1, 13, 2, 13, 11, 11, 13, 3, 4, 3, 13, 4, 13, 12, 4, 13, 1, 10, 13, 1, 6, 13, 10, 6, 7, 13, 11, 7, 13, 2, 13, 11, 2, 3, 13, 12, 13, 3, 6, 7, 13, 12, 13, 7, 4, 13, 12, 4, 1, 13, 10, 13, 1, 2, 13, 10, 2, 3, 13, 11, 13, 3, 11, 6, 13, 4, 1, 10, 4, 10, 7, 4, 7, 12, 6, 7, 10, 2, 3, 11, 4, 1, 3, 2, 3, 1, 2, 1, 10, 2, 10, 6, 2, 6, 11, 11, 6, 7, 11, 7, 3, 12, 3, 7, 4, 3, 12], [6, 7, 10, 7, 12, 10, 2, 3, 11, 10, 12, 9, 6, 2, 11, 6, 10, 2, 2, 9, 10, 2, 3, 9, 7, 12, 3, 7, 3, 11, 6, 7, 11, 3, 12, 9, 6, 7, 13, 7, 11, 13, 2, 13, 11, 3, 12, 13, 2, 3, 13, 9, 13, 12, 10, 13, 9, 6, 10, 13, 3, 11, 13, 6, 13, 11, 6, 7, 13, 7, 12, 13, 9, 13, 12, 10, 9, 13, 2, 13, 10, 2, 3, 13, 6, 7, 11, 2, 3, 12, 2, 12, 10, 10, 12, 9], [12, 4, 7, 7, 4, 6, 4, 2, 6], [1, 12, 9, 1, 6, 12, 1, 2, 6, 12, 6, 7], [4, 7, 12, 4, 1, 6, 4, 6, 7, 6, 1, 10], [6, 7, 10, 7, 12, 10, 10, 12, 9], [7, 11, 6, 5, 9, 8, 7, 11, 8, 11, 9, 8, 11, 5, 9, 11, 6, 5], [5, 1, 8, 1, 4, 8, 7, 11, 6, 5, 1, 6, 1, 11, 6, 1, 4, 11, 7, 11, 4, 7, 4, 8, 5, 8, 7, 5, 7, 6, 6, 7, 11, 5, 1, 6, 1, 11, 6, 1, 4, 11, 7, 11, 4, 7, 4, 8], [8, 5, 9, 6, 7, 11, 10, 2, 1, 8, 5, 9, 6, 1, 10, 6, 7, 1, 2, 1, 7, 2, 7, 11, 6, 7, 11, 8, 5, 10, 8, 10, 2, 8, 1, 9, 8, 2, 1, 10, 2, 1, 8, 7, 11, 8, 11, 9, 9, 11, 6, 9, 6, 5, 8, 13, 9, 9, 13, 1, 2, 1, 13, 2, 13, 11, 11, 13, 7, 6, 7, 13, 6, 13, 10, 10, 13, 5, 8, 5, 13, 8, 13, 9, 8, 13, 7, 11, 13, 7, 2, 13, 11, 2, 1, 13, 10, 1, 13, 6, 13, 10, 6, 5, 13, 9, 13, 5, 2, 1, 13, 9, 13, 1, 8, 13, 9, 8, 7, 13, 11, 13, 7, 6, 13, 11, 6, 5, 13, 10, 13, 5, 10, 2, 13, 8, 7, 11, 8, 11, 1, 8, 1, 9, 2, 1, 11, 6, 5, 10, 8, 7, 5, 6, 5, 7, 6, 7, 11, 6, 11, 2, 6, 2, 10, 10, 2, 1, 10, 1, 5, 9, 5, 1, 8, 5, 9], [10, 2, 5, 5, 2, 8, 11, 6, 7, 2, 4, 8, 10, 6, 11, 10, 11, 2, 11, 2, 4, 11, 4, 7, 5, 7, 8, 5, 6, 7, 10, 6, 5, 7, 4, 8, 10, 13, 5, 5, 13, 6, 11, 6, 13, 7, 13, 8, 11, 13, 7, 4, 8, 13, 2, 4, 13, 10, 13, 2, 7, 13, 6, 10, 6, 13, 10, 13, 5, 5, 13, 8, 4, 8, 13, 2, 13, 4, 11, 2, 13, 11, 13, 7, 10, 6, 5, 11, 8, 7, 11, 2, 8, 2, 4, 8], [7, 3, 6, 3, 2, 6, 5, 9, 8, 7, 3, 8, 3, 9, 8, 3, 2, 9, 5, 9, 2, 5, 2, 6, 7, 6, 5, 7, 5, 8, 8, 5, 9, 7, 3, 8, 3, 9, 8, 3, 2, 9, 5, 9, 2, 5, 2, 6], [6, 7, 2, 5, 1, 8, 8, 1, 4, 7, 3, 2, 6, 7, 8, 6, 8, 5, 8, 7, 3, 8, 3, 4, 2, 3, 1, 1, 3, 4, 6, 5, 1, 6, 1, 2, 6, 5, 13, 6, 13, 2, 2, 13, 3, 7, 3, 13, 8, 7, 13, 8, 13, 4, 1, 4, 13, 5, 1, 13, 2, 13, 1, 6, 13, 2, 6, 7, 13, 7, 3, 13, 4, 13, 3, 8, 13, 4, 5, 13, 8, 5, 1, 13, 6, 5, 2, 5, 1, 2, 8, 7, 3, 8, 3, 4], [6, 7, 10, 10, 7, 1, 8, 5, 9, 7, 3, 1, 6, 5, 8, 6, 8, 7, 8, 7, 3, 8, 3, 9, 10, 9, 1, 10, 5, 9, 6, 5, 10, 9, 3, 1, 6, 13, 10, 10, 13, 5, 8, 5, 13, 9, 13, 1, 8, 13, 9, 3, 1, 13, 7, 3, 13, 6, 13, 7, 9, 13, 5, 6, 5, 13, 6, 13, 10, 10, 13, 1, 3, 1, 13, 7, 13, 3, 8, 7, 13, 8, 13, 9, 6, 5, 10, 8, 1, 9, 8, 7, 1, 7, 3, 1], [8, 7, 4, 4, 7, 3, 6, 5, 10, 8, 5, 4, 4, 5, 10, 4, 10, 3, 6, 3, 10, 6, 7, 3, 8, 6, 7, 8, 5, 6, 5, 10, 6, 8, 5, 4, 4, 5, 10, 4, 10, 3, 6, 3, 10, 6, 7, 3], [6, 7, 11, 8, 5, 9, 12, 4, 3, 6, 7, 11, 8, 3, 12, 8, 5, 3, 4, 3, 5, 4, 5, 9, 8, 5, 9, 6, 7, 12, 6, 12, 4, 6, 3, 11, 6, 4, 3, 12, 4, 3, 6, 5, 9, 6, 9, 11, 11, 9, 8, 11, 8, 7, 6, 13, 11, 11, 13, 3, 4, 3, 13, 4, 13, 9, 9, 13, 5, 8, 5, 13, 8, 13, 12, 12, 13, 7, 6, 7, 13, 6, 13, 11, 6, 13, 5, 9, 13, 5, 4, 13, 9, 4, 3, 13, 12, 3, 13, 8, 13, 12, 8, 7, 13, 11, 13, 7, 4, 3, 13, 11, 13, 3, 6, 13, 11, 6, 5, 13, 9, 13, 5, 8, 13, 9, 8, 7, 13, 12, 13, 7, 12, 4, 13, 6, 5, 9, 6, 9, 3, 6, 3, 11, 4, 3, 9, 8, 7, 12, 6, 5, 7, 8, 7, 5, 8, 5, 9, 8, 9, 4, 8, 4, 12, 12, 4, 3, 12, 3, 7, 11, 7, 3, 6, 7, 11], [8, 5, 12, 12, 5, 3, 6, 7, 11, 5, 1, 3, 8, 7, 6, 8, 6, 5, 6, 5, 1, 6, 1, 11, 12, 11, 3, 12, 7, 11, 8, 7, 12, 11, 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7, 8, 7, 12, 8, 6, 7, 2, 2, 7, 12, 2, 12, 1, 8, 1, 12, 8, 5, 1], [7, 12, 8, 5, 10, 6, 9, 4, 1, 7, 12, 8, 5, 9, 4, 5, 4, 6, 1, 6, 4, 1, 10, 6, 5, 10, 6, 7, 9, 8, 7, 1, 9, 7, 12, 4, 7, 4, 1, 9, 4, 1, 7, 10, 6, 7, 12, 10, 12, 5, 10, 12, 8, 5, 7, 12, 13, 12, 4, 13, 1, 13, 4, 1, 10, 13, 10, 6, 13, 5, 13, 6, 5, 9, 13, 9, 8, 13, 7, 13, 8, 7, 12, 13, 7, 6, 13, 10, 6, 13, 1, 10, 13, 1, 13, 4, 9, 13, 4, 5, 9, 13, 5, 13, 8, 12, 8, 13, 1, 13, 4, 12, 4, 13, 7, 12, 13, 7, 13, 6, 10, 6, 13, 5, 10, 13, 5, 13, 8, 9, 8, 13, 9, 13, 1, 7, 10, 6, 7, 4, 10, 7, 12, 4, 1, 10, 4, 5, 9, 8, 7, 8, 6, 5, 6, 8, 5, 10, 6, 5, 1, 10, 5, 9, 1, 9, 4, 1, 9, 8, 4, 12, 4, 8, 7, 12, 8], [8, 7, 12, 6, 5, 10, 8, 5, 12, 12, 5, 10, 12, 10, 6, 12, 6, 7], [5, 7, 10, 7, 11, 10], [5, 7, 10, 7, 11, 10, 1, 4, 9, 5, 7, 9, 7, 4, 9, 7, 11, 4, 1, 4, 11, 1, 11, 10, 5, 10, 1, 5, 1, 9, 9, 1, 4, 5, 7, 9, 7, 4, 9, 7, 11, 4, 1, 4, 11, 1, 11, 10], [2, 1, 11, 11, 1, 7, 1, 5, 7], [9, 5, 7, 9, 7, 2, 9, 2, 4, 7, 11, 2], [10, 5, 2, 2, 5, 3, 5, 7, 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12, 8, 12, 9, 4, 9, 12, 4, 1, 9, 4, 2, 1, 4, 3, 2, 3, 11, 2, 3, 12, 11, 7, 11, 12, 8, 7, 12], [3, 11, 2, 7, 12, 8, 3, 12, 2, 2, 12, 8, 2, 8, 7, 2, 7, 11], [9, 4, 10, 10, 4, 2, 12, 8, 7, 9, 8, 10, 10, 8, 7, 10, 7, 2, 12, 2, 7, 12, 4, 2, 9, 12, 4, 9, 8, 12, 8, 7, 12, 9, 8, 10, 10, 8, 7, 10, 7, 2, 12, 2, 7, 12, 4, 2], [8, 7, 12, 10, 1, 2, 8, 7, 10, 10, 7, 2, 12, 2, 7, 8, 1, 12, 8, 10, 1, 12, 1, 2], [9, 4, 1, 12, 8, 7, 9, 8, 1, 1, 8, 7, 1, 7, 12, 1, 12, 4], [8, 7, 12], [8, 12, 7], [9, 1, 4, 12, 7, 8, 9, 1, 8, 1, 7, 8, 1, 12, 7, 1, 4, 12], [8, 12, 7, 10, 2, 1, 8, 10, 7, 10, 2, 7, 12, 7, 2, 8, 12, 1, 8, 1, 10, 12, 2, 1], [9, 10, 4, 10, 2, 4, 12, 7, 8, 9, 10, 8, 10, 7, 8, 10, 2, 7, 12, 7, 2, 12, 2, 4, 9, 4, 12, 9, 12, 8, 8, 12, 7, 9, 10, 8, 10, 7, 8, 10, 2, 7, 12, 7, 2, 12, 2, 4], [3, 2, 11, 7, 8, 12, 3, 2, 12, 2, 8, 12, 2, 7, 8, 2, 11, 7], [8, 12, 7, 4, 9, 1, 3, 2, 11, 8, 12, 7, 4, 11, 3, 4, 9, 11, 2, 11, 9, 2, 9, 1, 4, 9, 1, 8, 12, 3, 8, 3, 2, 8, 11, 7, 8, 2, 11, 3, 2, 11, 8, 9, 1, 8, 1, 7, 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6, 11, 13, 8, 12, 7, 6, 11, 3, 6, 3, 5, 5, 3, 1], [6, 11, 7, 8, 9, 5, 12, 3, 4, 6, 11, 7, 8, 12, 3, 8, 3, 5, 4, 5, 3, 4, 9, 5, 8, 9, 5, 6, 12, 7, 6, 4, 12, 6, 11, 3, 6, 3, 4, 12, 3, 4, 6, 9, 5, 6, 11, 9, 11, 8, 9, 11, 7, 8, 6, 11, 13, 11, 3, 13, 4, 13, 3, 4, 9, 13, 9, 5, 13, 8, 13, 5, 8, 12, 13, 12, 7, 13, 6, 13, 7, 6, 11, 13, 6, 5, 13, 9, 5, 13, 4, 9, 13, 4, 13, 3, 12, 13, 3, 8, 12, 13, 8, 13, 7, 11, 7, 13, 4, 13, 3, 11, 3, 13, 6, 11, 13, 6, 13, 5, 9, 5, 13, 8, 9, 13, 8, 13, 7, 12, 7, 13, 12, 13, 4, 6, 9, 5, 6, 3, 9, 6, 11, 3, 4, 9, 3, 8, 12, 7, 6, 7, 5, 8, 5, 7, 8, 9, 5, 8, 4, 9, 8, 12, 4, 12, 3, 4, 12, 7, 3, 11, 3, 7, 6, 11, 7], [8, 4, 7, 4, 3, 7, 6, 10, 5, 8, 4, 5, 4, 10, 5, 4, 3, 10, 6, 10, 3, 6, 3, 7, 8, 7, 6, 8, 6, 5, 5, 6, 10, 8, 4, 5, 4, 10, 5, 4, 3, 10, 6, 10, 3, 6, 3, 7], [6, 10, 7, 10, 1, 7, 8, 9, 5, 7, 1, 3, 6, 8, 5, 6, 7, 8, 8, 3, 7, 8, 9, 3, 10, 1, 9, 10, 9, 5, 6, 10, 5, 9, 1, 3, 6, 10, 13, 10, 5, 13, 8, 13, 5, 9, 1, 13, 8, 9, 13, 3, 13, 1, 7, 13, 3, 6, 7, 13, 9, 5, 13, 6, 13, 5, 6, 10, 13, 10, 1, 13, 3, 13, 1, 7, 3, 13, 8, 13, 7, 8, 9, 13, 6, 10, 5, 8, 9, 1, 8, 1, 7, 7, 1, 3], [6, 2, 7, 5, 8, 1, 8, 4, 1, 7, 2, 3, 6, 8, 7, 6, 5, 8, 8, 3, 7, 8, 4, 3, 2, 1, 3, 1, 4, 3, 6, 1, 5, 6, 2, 1, 6, 13, 5, 6, 2, 13, 2, 3, 13, 7, 13, 3, 8, 13, 7, 8, 4, 13, 1, 13, 4, 5, 13, 1, 2, 1, 13, 6, 2, 13, 6, 13, 7, 7, 13, 3, 4, 3, 13, 8, 4, 13, 5, 8, 13, 5, 13, 1, 6, 2, 5, 5, 2, 1, 8, 3, 7, 8, 4, 3], [7, 6, 3, 3, 6, 2, 5, 8, 9, 7, 8, 3, 3, 8, 9, 3, 9, 2, 5, 2, 9, 5, 6, 2, 7, 5, 6, 7, 8, 5, 8, 9, 5, 7, 8, 3, 3, 8, 9, 3, 9, 2, 5, 2, 9, 5, 6, 2], [10, 5, 2, 5, 8, 2, 11, 7, 6, 2, 8, 4, 10, 11, 6, 10, 2, 11, 11, 4, 2, 11, 7, 4, 5, 8, 7, 5, 7, 6, 10, 5, 6, 7, 8, 4, 10, 5, 13, 5, 6, 13, 11, 13, 6, 7, 8, 13, 11, 7, 13, 4, 13, 8, 2, 13, 4, 10, 2, 13, 7, 6, 13, 10, 13, 6, 10, 5, 13, 5, 8, 13, 4, 13, 8, 2, 4, 13, 11, 13, 2, 11, 7, 13, 10, 5, 6, 11, 7, 8, 11, 8, 2, 2, 8, 4], [8, 9, 5, 6, 11, 7, 10, 1, 2, 8, 9, 5, 6, 10, 1, 6, 1, 7, 2, 7, 1, 2, 11, 7, 6, 11, 7, 8, 10, 5, 8, 2, 10, 8, 9, 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3], [6, 3, 7, 6, 9, 3, 6, 10, 9, 4, 9, 3], [6, 10, 7, 10, 1, 7, 7, 1, 3], [2, 3, 6, 6, 3, 7, 4, 1, 9, 2, 1, 6, 6, 1, 9, 6, 9, 7, 4, 7, 9, 4, 3, 7, 2, 4, 3, 2, 1, 4, 1, 9, 4, 2, 1, 6, 6, 1, 9, 6, 9, 7, 4, 7, 9, 4, 3, 7], [2, 3, 6, 6, 3, 7], [2, 10, 4, 4, 10, 9, 6, 11, 7, 2, 11, 4, 4, 11, 7, 4, 7, 9, 6, 9, 7, 6, 10, 9, 2, 6, 10, 2, 11, 6, 11, 7, 6, 2, 11, 4, 4, 11, 7, 4, 7, 9, 6, 9, 7, 6, 10, 9], [6, 11, 7, 2, 10, 1, 6, 10, 7, 7, 10, 1, 7, 1, 2, 7, 2, 11], [6, 11, 7, 1, 9, 4, 6, 11, 1, 1, 11, 4, 7, 4, 11, 6, 9, 7, 6, 1, 9, 7, 9, 4], [6, 11, 7], [12, 11, 8, 11, 6, 8], [12, 11, 8, 11, 6, 8, 9, 1, 4, 12, 11, 4, 11, 1, 4, 11, 6, 1, 9, 1, 6, 9, 6, 8, 12, 8, 9, 12, 9, 4, 4, 9, 1, 12, 11, 4, 11, 1, 4, 11, 6, 1, 9, 1, 6, 9, 6, 8], [6, 8, 11, 8, 12, 11, 2, 1, 10, 6, 8, 10, 8, 1, 10, 8, 12, 1, 2, 1, 12, 2, 12, 11, 6, 11, 2, 6, 2, 10, 10, 2, 1, 6, 8, 10, 8, 1, 10, 8, 12, 1, 2, 1, 12, 2, 12, 11], [2, 4, 11, 10, 6, 9, 6, 8, 9, 11, 4, 12, 2, 6, 11, 2, 10, 6, 6, 12, 11, 6, 8, 12, 4, 9, 12, 9, 8, 12, 2, 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11, 6, 13, 3, 11, 13, 8, 13, 6, 4, 13, 8, 1, 4, 13, 11, 2, 13, 1, 13, 2, 1, 10, 13, 10, 6, 13, 8, 13, 6, 4, 8, 13, 3, 13, 4, 3, 11, 13, 1, 10, 2, 3, 11, 6, 3, 6, 4, 4, 6, 8], [10, 6, 9, 9, 6, 8, 11, 2, 3, 10, 2, 9, 9, 2, 3, 9, 3, 8, 11, 8, 3, 11, 6, 8, 10, 11, 6, 10, 2, 11, 2, 3, 11, 10, 2, 9, 9, 2, 3, 9, 3, 8, 11, 8, 3, 11, 6, 8], [4, 6, 8, 4, 2, 6], [9, 1, 8, 1, 2, 8, 8, 2, 6], [1, 10, 4, 10, 6, 4, 4, 6, 8], [8, 9, 6, 6, 9, 10], [5, 9, 6, 6, 9, 11, 9, 12, 11], [6, 5, 1, 6, 1, 12, 6, 12, 11, 1, 4, 12], [2, 1, 11, 1, 9, 11, 6, 5, 10, 11, 9, 12, 2, 6, 10, 2, 11, 6, 6, 12, 11, 6, 5, 12, 1, 9, 5, 1, 5, 10, 2, 1, 10, 5, 9, 12, 2, 1, 13, 1, 10, 13, 6, 13, 10, 5, 9, 13, 6, 5, 13, 12, 13, 9, 11, 13, 12, 2, 11, 13, 5, 10, 13, 2, 13, 10, 2, 1, 13, 1, 9, 13, 12, 13, 9, 11, 12, 13, 6, 13, 11, 6, 5, 13, 2, 1, 10, 6, 5, 9, 6, 9, 11, 11, 9, 12], [11, 2, 12, 12, 2, 4, 10, 6, 5, 11, 6, 12, 12, 6, 5, 12, 5, 4, 10, 4, 5, 10, 2, 4, 11, 10, 2, 11, 6, 10, 6, 5, 10, 11, 6, 12, 12, 6, 5, 12, 5, 4, 10, 4, 5, 10, 2, 4], [3, 2, 6, 3, 6, 9, 3, 9, 12, 5, 6, 9], [1, 2, 5, 5, 2, 6, 3, 4, 12, 1, 4, 5, 5, 4, 12, 5, 12, 6, 3, 6, 12, 3, 2, 6, 1, 3, 2, 1, 4, 3, 4, 12, 3, 1, 4, 5, 5, 4, 12, 5, 12, 6, 3, 6, 12, 3, 2, 6], [1, 9, 3, 3, 9, 12, 5, 10, 6, 1, 10, 3, 3, 10, 6, 3, 6, 12, 5, 12, 6, 5, 9, 12, 1, 5, 9, 1, 10, 5, 10, 6, 5, 1, 10, 3, 3, 10, 6, 3, 6, 12, 5, 12, 6, 5, 9, 12], [6, 5, 10, 12, 3, 4, 6, 5, 12, 12, 5, 4, 10, 4, 5, 6, 3, 10, 6, 12, 3, 10, 3, 4], [6, 5, 9, 6, 4, 11, 6, 9, 4, 4, 3, 11], [11, 6, 3, 6, 5, 3, 3, 5, 1], [6, 5, 10, 2, 3, 11, 1, 9, 4, 6, 5, 10, 2, 1, 9, 2, 9, 11, 4, 11, 9, 4, 3, 11, 2, 3, 11, 6, 1, 10, 6, 4, 1, 6, 5, 9, 6, 9, 4, 1, 9, 4, 6, 3, 11, 6, 5, 3, 5, 2, 3, 5, 10, 2, 6, 5, 13, 5, 9, 13, 4, 13, 9, 4, 3, 13, 3, 11, 13, 2, 13, 11, 2, 1, 13, 1, 10, 13, 6, 13, 10, 6, 5, 13, 6, 11, 13, 3, 11, 13, 4, 3, 13, 4, 13, 9, 1, 13, 9, 2, 1, 13, 2, 13, 10, 5, 10, 13, 4, 13, 9, 5, 9, 13, 6, 5, 13, 6, 13, 11, 3, 11, 13, 2, 3, 13, 2, 13, 10, 1, 10, 13, 1, 13, 4, 6, 3, 11, 6, 9, 3, 6, 5, 9, 4, 3, 9, 2, 1, 10, 6, 10, 11, 2, 11, 10, 2, 3, 11, 2, 4, 3, 2, 1, 4, 1, 9, 4, 1, 10, 9, 5, 9, 10, 6, 5, 10], [10, 6, 5, 11, 2, 3, 10, 2, 5, 5, 2, 3, 5, 3, 11, 5, 11, 6], [5, 9, 6, 9, 4, 6, 6, 4, 2], [1, 2, 5, 5, 2, 6], [5, 10, 6, 1, 9, 4, 5, 9, 6, 6, 9, 4, 6, 4, 1, 6, 1, 10], [6, 5, 10], [8, 12, 5, 5, 12, 10, 12, 11, 10], [8, 12, 5, 5, 12, 10, 4, 9, 1, 12, 11, 10, 8, 9, 4, 8, 4, 12, 4, 12, 11, 4, 11, 1, 5, 1, 10, 5, 9, 1, 8, 9, 5, 1, 11, 10, 8, 13, 5, 5, 13, 9, 4, 9, 13, 1, 13, 10, 4, 13, 1, 11, 10, 13, 12, 11, 13, 8, 13, 12, 1, 13, 9, 8, 9, 13, 8, 13, 5, 5, 13, 10, 11, 10, 13, 12, 13, 11, 4, 12, 13, 4, 13, 1, 8, 9, 5, 4, 10, 1, 4, 12, 10, 12, 11, 10], [2, 12, 11, 2, 5, 12, 2, 1, 5, 8, 5, 12], [4, 12, 2, 2, 12, 11, 8, 9, 5, 4, 9, 2, 2, 9, 5, 2, 5, 11, 8, 11, 5, 8, 12, 11, 4, 8, 12, 4, 9, 8, 9, 5, 8, 4, 9, 2, 2, 9, 5, 2, 5, 11, 8, 11, 5, 8, 12, 11], [2, 10, 5, 2, 8, 3, 2, 5, 8, 8, 12, 3], [2, 10, 1, 4, 12, 3, 9, 5, 8, 2, 10, 1, 4, 9, 5, 4, 5, 3, 8, 3, 5, 8, 12, 3, 4, 12, 3, 2, 9, 1, 2, 8, 9, 2, 10, 5, 2, 5, 8, 9, 5, 8, 2, 12, 3, 2, 10, 12, 10, 4, 12, 10, 1, 4, 2, 10, 13, 10, 5, 13, 8, 13, 5, 8, 12, 13, 12, 3, 13, 4, 13, 3, 4, 9, 13, 9, 1, 13, 2, 13, 1, 2, 10, 13, 2, 3, 13, 12, 3, 13, 8, 12, 13, 8, 13, 5, 9, 13, 5, 4, 9, 13, 4, 13, 1, 10, 1, 13, 8, 13, 5, 10, 5, 13, 2, 10, 13, 2, 13, 3, 12, 3, 13, 4, 12, 13, 4, 13, 1, 9, 1, 13, 9, 13, 8, 2, 12, 3, 2, 5, 12, 2, 10, 5, 8, 12, 5, 4, 9, 1, 2, 1, 3, 4, 3, 1, 4, 12, 3, 4, 8, 12, 4, 9, 8, 9, 5, 8, 9, 1, 5, 10, 5, 1, 2, 10, 1], [8, 12, 5, 12, 3, 5, 5, 3, 1], [8, 9, 5, 4, 12, 3, 8, 12, 5, 5, 12, 3, 5, 3, 4, 5, 4, 9], [3, 8, 4, 3, 10, 8, 3, 11, 10, 8, 10, 5], [10, 1, 11, 11, 1, 3, 9, 5, 8, 10, 5, 11, 11, 5, 8, 11, 8, 3, 9, 3, 8, 9, 1, 3, 10, 9, 1, 10, 5, 9, 5, 8, 9, 10, 5, 11, 11, 5, 8, 11, 8, 3, 9, 3, 8, 9, 1, 3], [4, 1, 8, 8, 1, 5, 2, 3, 11, 4, 3, 8, 8, 3, 11, 8, 11, 5, 2, 5, 11, 2, 1, 5, 4, 2, 1, 4, 3, 2, 3, 11, 2, 4, 3, 8, 8, 3, 11, 8, 11, 5, 2, 5, 11, 2, 1, 5], [2, 3, 11, 9, 5, 8, 2, 3, 9, 9, 3, 8, 11, 8, 3, 2, 5, 11, 2, 9, 5, 11, 5, 8], [10, 5, 2, 5, 8, 2, 2, 8, 4], [10, 1, 2, 9, 5, 8, 10, 5, 2, 2, 5, 8, 2, 8, 9, 2, 9, 1], [5, 8, 1, 1, 8, 4], [8, 9, 5], [11, 10, 9, 11, 9, 12], [1, 4, 10, 4, 12, 10, 10, 12, 11], [2, 1, 11, 1, 9, 11, 11, 9, 12], [4, 12, 2, 2, 12, 11], [3, 2, 12, 2, 10, 12, 12, 10, 9], [1, 2, 10, 3, 4, 12, 1, 4, 10, 10, 4, 12, 10, 12, 3, 10, 3, 2], [12, 3, 9, 9, 3, 1], [12, 3, 4], [4, 3, 9, 3, 11, 9, 9, 11, 10], [10, 1, 11, 11, 1, 3], [2, 3, 11, 4, 1, 9, 2, 1, 11, 11, 1, 9, 11, 9, 4, 11, 4, 3], [2, 3, 11], [9, 4, 10, 10, 4, 2], [1, 2, 10], [4, 1, 9] ]; // ----------------------------------------------------------------------------- var Faces = [ [0], [0], [0], [0], [5], [0], [0], [0], [0], [-5], [0], [0], [0], [0], [0], [0], [0], [-1], [0], [7], [5, 7], [-1, 7], [0], [-4], [0], [-5, -1, -4, 7], [0], [-4, 7], [0], [-4, -1, 7], [0], [0], [1], [0], [0], [-2], [-2, 1, 5, -7], [0], [0], [-7], [1, -7], [-5, -7], [0], [-2, -7], [-2, 1, -7], [0], [0], [0], [0], [0], [0], [-2, 7], [5, -2, 7], [0], [0], [-4, -7], [0], [-4, -5, -7], [0], [-2, -4, 7], [2, -7], [4, 7], [0], [0], [7], [2], [2, 7], [0], [5, 7], [0], [0], [3], [3, 7], [-5, 3, 2, 7], [2, 3, 7], [0], [0], [0], [0], [6], [6, 7], [6, -1, 2, -7], [2, 6, 7], [6, 7], [6, 5, 7], [6, -1, 7], [-6, -7], [6, 3, -4, -7], [6, 3, 7], [-5, -1, 6, 3, 2, -4, 7], [-3, -6, -2, 7], [-4, 6, 7], [-6, -7], [-6, 4, 1, 7], [-6], [0], [1, 7], [0], [0], [0], [5, 1, 7], [0], [0], [3, -7], [1, 3, 7], [-5, 3, -7], [-3, 7], [0], [-1, -7], [0], [0], [0], [0], [0], [0], [0], [-5, -7], [0], [0], [-4, 3, -7], [-3, -7], [4, -3, 5, -7], [-3], [4, -7], [-7], [4], [0], [0], [4], [-7], [4, -7], [-3], [4, -3, 5, -7], [-3, -7], [4, -3, -7], [0], [0], [-5, -7], [0], [0], [0], [0], [0], [0], [0], [-1, -7], [0], [-3, 7], [5, -3, 7], [-1, -3, 7], [3, -7], [0], [0], [-5, -1, -7], [0], [0], [0], [1, 7], [0], [-6], [-6, 4, 1, 7], [-6, -7], [4, -6, -7], [-3, -6, -2, 7], [5, 1, -6, -3, -2, 4, 7], [-6, -3, -7], [6, 3, -4, -7], [-6, -7], [-6, 1, -7], [-6, -5, -7], [6, 7], [-2, -6, -7], [6, -1, 2, -7], [6, 7], [6], [0], [0], [0], [0], [-2, -3, 7], [-5, 3, 2, 7], [3, 7], [3], [0], [0], [5, 7], [0], [2, 7], [2], [7], [0], [0], [4, 7], [2, -7], [2, 4, 7], [0], [4, 5, 7], [0], [-4, -7], [0], [0], [-5, 2, -7], [-2, 7], [0], [0], [0], [0], [0], [0], [2, -1, -7], [-2, -7], [0], [-5, -7], [1, -7], [-7], [0], [0], [-2, 1, 5, -7], [-2], [0], [0], [1], [0], [0], [4, 1, 7], [0], [-4, 7], [0], [-5, -1, -4, 7], [0], [-4], [0], [-1, 7], [5, 7], [7], [0], [-1], [0], [0], [0], [0], [0], [0], [0], [-5], [0], [0], [0], [0], [5], [0], [0], [0], [0] ]; // ----------------------------------------------------------------------------- var FacesSizes = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 4, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 3, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 4, 3, 1, 1, 1, 1, 1, 2, 4, 3, 2, 3, 3, 2, 4, 3, 7, 4, 3, 2, 4, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 4, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 4, 2, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 3, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 4, 2, 3, 4, 7, 3, 4, 2, 3, 3, 2, 3, 4, 2, 1, 1, 1, 1, 1, 3, 4, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 3, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 4, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; // ----------------------------------------------------------------------------- var FacePoints = [ [1, 1, 6, 2, 5, 60], [2, 2, 7, 3, 6, 252], [3, 4, 7, 3, 8, 672], [4, 1, 8, 4, 5, 160], [5, 1, 3, 2, 4, 24], [6, 5, 7, 6, 8, 1680] ]; // ----------------------------------------------------------------------------- var special_name = [3, 4, 6, 7, 10, 12, 13]; var special_nface = [1, 1, 2, 4, 3, 3, 7]; var special_nedge = [18, 24, 48, 177, 96, 96, 816]; var special_indSizes = [2, 2, 4, 16, 8, 8, 31]; // ----------------------------------------------------------------------------- var special_ind = [ [0, 1], [0, 1], [0, 2, 1, 3], [0, 8, 4, 12, 2, 10, 1, 9, 6, 14, 5, 13, 3, 11, 15, 7], [0, 4, 1, 5, 2, 6, 3, 7], [0, 4, 2, 6, 1, 5, 3, 7], [0, 1, 2, 4, 8, 16, 32, 3, 9, 17, 33, 6, 18, 34, 12, 20, 36, 24, 40, 35, 25, 22, 44, 19, 41, 38, 28, 83, 105, 102, 92] ]; // ----------------------------------------------------------------------------- var special_pos = [ [ [1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18] ], [ [1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24] ], [ [1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48] ], [ [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54], [55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81], [55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81], [82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108], [82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108], [109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135], [109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135], [136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150], [151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177] ], [ [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84], [85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96], [85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96] ], [ [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84], [85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96], [85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96] ], [ [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66], [67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84], [85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102], [103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120], [121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150], [151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180], [181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210], [211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240], [241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270], [271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300], [301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330], [331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360], [361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390], [391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420], [421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450], [451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480], [481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516], [517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552], [553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588], [589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624], [625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642], [643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660], [661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678], [679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696], [697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726], [727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756], [757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786], [787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816] ] ]; // ----------------------------------------------------------------------------- var special_posSize = [ [6, 12], [6, 18], [9, 24, 15, 15], [9, 9, 15, 15, 15, 15, 15, 15, 27, 27, 27, 27, 27, 27, 15, 27], [12, 24, 24, 24, 24, 24, 12, 12], [12, 24, 24, 24, 24, 24, 12, 12], [12, 18, 18, 18, 18, 18, 18, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 36, 36, 36, 36, 18, 18, 18, 18, 30, 30, 30, 30] ]; // ----------------------------------------------------------------------------- function FacesNo7(faces, p1, values, l, j) { var index = new Array(l); for (var i = 0; i < l; i++) { var f = Math.abs(faces[i]) - 1; var e1 = FacePoints[f][1]; var e2 = FacePoints[f][2]; var e3 = FacePoints[f][3]; var e4 = FacePoints[f][4]; var p = p1[i] - 2; var A = values[p + e1]; var B = values[p + e2]; var C = values[p + e3]; var D = values[p + e4]; var temp = faces[i] > 0 ? 1 : -1; temp *= (A * B - C * D > 0 ? 1 : -1); index[i] = temp == 1 ? 2 ** (j - 1) : 0; } return index; } // ----------------------------------------------------------------------------- function Faces7(faces, p1, values, l, j) { var index = new Array(l); for (var i = 0; i < l; i++) { var p = p1[i] - 1; var A0 = values[p]; var B0 = values[p + 3]; var C0 = values[p + 2]; var D0 = values[p + 1]; var A1 = values[p + 4]; var B1 = values[p + 7]; var C1 = values[p + 6]; var D1 = values[p + 5]; var a = (A1 - A0) * (C1 - C0) - (B1 - B0) * (D1 - D0); var b = C0 * (A1 - A0) + A0 * (C1 - C0) - D0 * (B1 - B0) - B0 * (D1 - D0); var c = A0 * C0 - B0 * D0; var tmax = -b / (2 * a); var maximum = a * tmax * tmax + b * tmax + c; maximum = isNaN(maximum) ? -1 : maximum; var cond1 = a < 0 ? 1 : 0; var cond2 = tmax > 0 ? 1 : 0; var cond3 = tmax < 1 ? 1 : 0; var cond4 = maximum > 0 ? 1 : 0; var totalcond = cond1 * cond2 * cond3 * cond4; var temp = faces[i] > 0 ? 1 : -1; temp *= (totalcond == 1 ? 1 : -1); index[i] = temp == 1 ? 2 ** (j - 1) : 0; } return index; } // ----------------------------------------------------------------------------- function Voxel(f, xmin, xmax, ymin, ymax, zmin, zmax, nx, ny, nz) { var out = new Array(nx); for (var i = 0; i < nx; i++) { out[i] = new Array(ny); for (var j = 0; j < ny; j++) { out[i][j] = new Array(nz); for (var k = 0; k < nz; k++) { out[i][j][k] = f(xmin + (xmax - xmin) * i / (nx - 1), ymin + (ymax - ymin) * j / (ny - 1), zmin + (zmax - zmin) * k / (nz - 1)); } } } return out; } // ----------------------------------------------------------------------------- function faceType(M, m, n, level, max) { var L = levelMatrix(M, m, n, level, level < max); var minorMat = minorMatrix(L, m, n, m - 1, n - 1); var sminorMat2 = scaleMinorMatrix(2, L, m, n, 0, n - 1); var sminorMat4 = scaleMinorMatrix(4, L, m, n, 0, 0); var sminorMat8 = scaleMinorMatrix(8, L, m, n, m - 1, 0); var sum1 = matricialSum(minorMat, sminorMat2, m - 1, n - 1); var sum2 = matricialSum(sminorMat4, sminorMat8, m - 1, n - 1); var out = matricialSum(sum1, sum2, m - 1, n - 1); return out; } // ----------------------------------------------------------------------------- function levCells(A, nx, ny, nz, level, max) { var cells = new Array(nz - 1); var types = new Array(nz - 1); var bottomTypes = faceType(toMatrix(A, nx, ny, 0), nx, ny, level, max); var totallength = 0; var lengths = new Array(nz - 1); for (var k = 0; k < nz - 1; k++) { var topTypes = faceType(toMatrix(A, nx, ny, k + 1), nx, ny, level, max); var cellTypes = matricialSum(bottomTypes, scaleMatrix(16, topTypes, nx - 1, ny - 1), nx - 1, ny - 1); var goodcells01 = whichIndicesAndItems(cellTypes, nx - 1, ny - 1); cells[k] = new Array(goodcells01.length) types[k] = new Array(goodcells01.length) for (var l = 0; l < goodcells01.length; l++) { cells[k][l] = goodcells01.indices[l] + (nx - 1) * (ny - 1) * k + 1; types[k][l] = goodcells01.items[l]; } bottomTypes = topTypes; lengths[k] = goodcells01.length; totallength += goodcells01.length; } var out = new Array(4); out[0] = new Array(totallength); out[1] = new Array(totallength); out[2] = new Array(totallength); out[3] = new Array(totallength); var count = 0; for (var k = 0; k < nz - 1; k++) { for (var l = 0; l < lengths[k]; l++) { var c = cells[k][l] - 1; out[0][count] = c % (nx - 1) + 1; out[1][count] = Math.floor(c / (nx - 1)) % (ny - 1) + 1; out[2][count] = Math.floor(c / ((nx - 1) * (ny - 1))) + 1; out[3][count] = types[k][l]; count++; } } return { out: out, outnrow: totallength }; } // ----------------------------------------------------------------------------- function GetBasic1(R, nR, vivjvk) { var indexPtr = new Array(8); for (var i = 0; i < 8; i++) { indexPtr[i] = new Array(3); for (var j = 0; j < 3; j++) { indexPtr[i][j] = indexArray[i][j]; } } var cube1 = new Array(nR); for (var i = 0; i < nR; i++) { cube1[i] = new Array(3); var vivjvkRi = vivjvk[R[i]]; for (var j = 0; j < 3; j++) { cube1[i][j] = vivjvkRi[j]; } } var k1 = kro1(indexPtr, 8, 3, nR); var k2 = kro2(cube1, nR, 3, 8); var cubeco = matricialSum(k1, k2, 8 * nR + 1, 3); return cubeco; } // ----------------------------------------------------------------------------- function GetBasic2prime(A, level, cubeco, nR) { var values = new Array(8 * nR + 1); for (var i = 0; i < 8 * nR; i++) { values[i] = A[cubeco[i][0] - 1][cubeco[i][1] - 1][cubeco[i][2] - 1] - level; } values[8 * nR] = 0; return values; } // ----------------------------------------------------------------------------- function get_tcase(types, nrow) { var CRF = [1, 2, 2, 3, 2, 4, 3, 6, 2, 3, 4, 6, 3, 6, 6, 9, 2, 3, 4, 6, 5, 7, 7, 12, 4, 6, 8, 10, 7, 15, 13, 6, 2, 4, 3, 6, 4, 8, 6, 10, 5, 7, 7, 15, 7, 13, 12, 6, 3, 6, 6, 9, 7, 13, 15, 6, 7, 12, 13, 6, 11, 7, 7, 3, 2, 5, 4, 7, 3, 7, 6, 15, 4, 7, 8, 13, 6, 12, 10, 6, 4, 7, 8, 13, 7, 11, 13, 7, 8, 13, 14, 8, 13, 7, 8, 4, 3, 7, 6, 12, 6, 13, 9, 6, 7, 11, 13, 7, 15, 7, 6, 3, 6, 15, 10, 6, 12, 7, 6, 3, 13, 7, 8, 4, 7, 5, 4, 2, 2, 4, 5, 7, 4, 8, 7, 13, 3, 6, 7, 12, 6, 10, 15, 6, 3, 6, 7, 15, 7, 13, 11, 7, 6, 9, 13, 6, 12, 6, 7, 3, 4, 8, 7, 13, 8, 14, 13, 8, 7, 13, 11, 7, 13, 8, 7, 4, 6, 10, 12, 6, 13, 8, 7, 4, 15, 6, 7, 3, 7, 4, 5, 2, 3, 7, 7, 11, 6, 13, 12, 7, 6, 15, 13, 7, 9, 6, 6, 3, 6, 12, 13, 7, 15, 7, 7, 5, 10, 6, 8, 4, 6, 3, 4, 2, 6, 13, 15, 7, 10, 8, 6, 4, 12, 7, 7, 5, 6, 4, 3, 2, 9, 6, 6, 3, 6, 4, 3, 2, 6, 3, 4, 2, 3, 2, 2, 1]; out = new Array(nrow); for (var i = 0; i < nrow; i++) { out[i] = CRF[types[i]] - 1; } return out; } // ----------------------------------------------------------------------------- function getR(tcase, nrow) { out = []; for (var i = 0; i < nrow; i++) { var c = tcase[i]; if (c == 1 || c == 2 || c == 5 || c == 8 || c == 9 || c == 11 || c == 14) { out.push(i); } } return out; } // ----------------------------------------------------------------------------- function LambdaMu(x1, n) { var lambdamu = new Array(2); lambdamu[0] = new Array(n); lambdamu[1] = new Array(n); for (var i = 0; i < n; i++) { lambdamu[0][i] = Math.floor(x1[i] / 9); lambdamu[1][i] = 1 - lambdamu[0][i]; } return lambdamu; } function average(lambdamu, w1, w2, n) { var lambda = lambdamu[0]; var mu = lambdamu[1]; var out = new Array(n); for (var i = 0; i < n; i++) { out[i] = mu[i] * w1[i] + lambda[i] * w2[i]; } return out; } function average7(lambdamu, w, n) { var lambda = lambdamu[0]; var mu = lambdamu[1]; var out = new Array(n); for (var i = 0; i < n; i++) { out[i] = mu[i] * w[i] + lambda[i]; } return out; } function average8(lambdamu, w, n) { var lambda = lambdamu[0]; var mu = lambdamu[1]; var out = new Array(n); for (var i = 0; i < n; i++) { out[i] = mu[i] * w[i] - lambda[i]; } return out; } // ----------------------------------------------------------------------------- function GetPoints(cubeco, values, p1, x1, x2, n) { var p1x1 = new Array(n); var p1x2 = new Array(n); for (var i = 0; i < n; i++) { p1x1[i] = p1[i] + x1[i]; p1x2[i] = p1[i] + x2[i]; } var lambdamu = LambdaMu(x1, n); var v1 = new Array(n); var v2 = new Array(n); var v3 = new Array(n); var v4 = new Array(n); var v5 = new Array(n); var v6 = new Array(n); var v7 = new Array(n); var v8 = new Array(n); var w1 = new Array(n); var w2 = new Array(n); var w3 = new Array(n); var w4 = new Array(n); var w5 = new Array(n); var w6 = new Array(n); for (var i = 0; i < n; i++) { v1[i] = cubeco[p1x1[i] - 2][0]; w1[i] = cubeco[p1[i] - 1][0]; v2[i] = cubeco[p1x2[i] - 2][0]; w2[i] = cubeco[p1[i]][0]; v3[i] = cubeco[p1x1[i] - 2][1]; w3[i] = cubeco[p1[i]][1]; v4[i] = cubeco[p1x2[i] - 2][1]; w4[i] = cubeco[p1[i] + 1][1]; v5[i] = cubeco[p1x1[i] - 2][2]; w5[i] = cubeco[p1[i]][2]; v6[i] = cubeco[p1x2[i] - 2][2]; w6[i] = cubeco[p1[i] + 4][2]; v7[i] = values[p1x1[i] - 2]; v8[i] = values[p1x2[i] - 2]; } var out = new Array(8); out[0] = average(lambdamu, v1, w1, n); out[1] = average(lambdamu, v2, w2, n); out[2] = average(lambdamu, v3, w3, n); out[3] = average(lambdamu, v4, w4, n); out[4] = average(lambdamu, v5, w5, n); out[5] = average(lambdamu, v6, w6, n); out[6] = average7(lambdamu, v7, n); out[7] = average8(lambdamu, v8, n); return (out); } // ----------------------------------------------------------------------------- function CalPoints(points, n) { var x1 = points[0]; var x2 = points[1]; var y1 = points[2]; var y2 = points[3]; var z1 = points[4]; var z2 = points[5]; var v1 = points[6]; var v2 = points[7]; var x = new Array(n); var y = new Array(n); var z = new Array(n); for (var i = 0; i < n; i++) { var s = v1[i] / (v1[i] - v2[i]); x[i] = x1[i] + s * (x2[i] - x1[i]); y[i] = y1[i] + s * (y2[i] - y1[i]); z[i] = z1[i] + s * (z2[i] - z1[i]); } var out = new Array(3); out[0] = x; out[1] = y; out[2] = z; return transpose(out, 3, n); } // ----------------------------------------------------------------------------- function computeContour3d(voxel, nx, ny, nz, max, level) { var obj_ijkt = levCells(voxel, nx, ny, nz, level, max); var ijkt = obj_ijkt.out; var nrow = obj_ijkt.outnrow; tcase = get_tcase(ijkt[3], nrow); var R = getR(tcase, nrow); var nR = R.length; if (nR == 0) { return []; } else { var vivjvk = new Array(nrow); for (var i = 0; i < nrow; i++) { vivjvk[i] = new Array(3); for (var j = 0; j < 3; j++) { vivjvk[i][j] = ijkt[j][i]; } } var cubeco = GetBasic1(R, nR, vivjvk); var values = GetBasic2prime(voxel, level, cubeco, nR); var p1 = new Array(nR); for (var i = 0; i < nR; i++) { p1[i] = i * 8 + 1; } var vt = ijkt[3]; var cases = new Array(nR); for (var i = 0; i < nR; i++) { cases[i] = vt[R[i]] - 1; } var edgeslengths = new Array(nR); var totalLength = 0; for (var i = 0; i < nR; i++) { edgeslengths[i] = EdgesLengths[cases[i]]; totalLength += edgeslengths[i]; } var p1rep = replicate(p1, edgeslengths, nR); var edges = new Array(totalLength); var edgeiter = 0; for (var i = 0; i < nR; i++) { for (var j = 0; j < edgeslengths[i]; j++) { edges[edgeiter] = Edges[cases[i]][j]; edgeiter++; } } var x1 = new Array(totalLength); var x2 = new Array(totalLength); for (var i = 0; i < totalLength; i++) { var EPi = EdgePoints[edges[i] - 1]; x1[i] = EPi[1]; x2[i] = EPi[2]; } var points = GetPoints(cubeco, values, p1rep, x1, x2, totalLength); var triangles = CalPoints(points, totalLength); var special = 0; for (var i = 0; i < nrow; i++) { var tc = tcase[i]; if (tc == 3 || tc == 4 || tc == 6 || tc == 7 || tc == 10 || tc == 12 || tc == 13) { special = tc; break; } } if (special) { console.log("there are special cases") } for (var c = 0; c < 7; c++) { var R3 = whichEqual(tcase, special_name[c], nrow); var nR3 = R3.length; if (nR3 > 0) { var cubeco3 = GetBasic1(R3, nR3, vivjvk); var values3 = GetBasic2prime(voxel, level, cubeco3, nR3); var p13 = new Array(nR3); for (var i = 0; i < nR3; i++) { p13[i] = 8 * i + 1; } var cases3 = new Array(nR3); for (var i = 0; i < nR3; i++) { cases3[i] = vt[R3[i]] - 1; } var nedge = special_nedge[c]; var faces3 = unlist(Faces, FacesSizes, cases3, nR3); var outlength3 = faces3.length; var index3; if (c == 0) { index3 = FacesNo7(faces3, p13, values3, nR3, 1); } else if (c == 1) { index3 = Faces7(faces3, p13, values3, nR3, 1); } else { var nface = special_nface[c]; var facelast = jthColumn(faces3, outlength3, nface, nface - 1); index3 = Faces7(facelast, p13, values3, nR3, nface); for (var j = 0; j < nface - 1; j++) { var facej = jthColumn(faces3, outlength3, nface, j); var temp = FacesNo7(facej, p13, values3, nR3, j + 1); index3 = vectorialSum(index3, temp, nR3); } } var unlisted_edges3 = unlist(Edges, EdgesLengths, cases3, nR3); outlength3 = unlisted_edges3.length; var edges3 = vector2matrix(unlisted_edges3, outlength3, nedge); var edgesp1index = cbind(edges3, p13, index3, nR3, nedge); var ind3Size = special_indSizes[c]; var ind3 = new Array(ind3Size); for (var i = 0; i < ind3Size; i++) { ind3[i] = special_ind[c][i]; } for (var j = 0; j < ind3Size; j++) { var wrows = whichEqual(index3, ind3[j], nR3); var lwrows = wrows.length; if (lwrows > 0) { var lwcols = special_posSize[c][j] + 1; var wcols = new Array(lwcols); wcols[0] = nedge; for (var k = 1; k < lwcols; k++) { wcols[k] = special_pos[c][j][k - 1] - 1; } var ed = subsetMatrix(edgesp1index, wrows, wcols, lwrows, lwcols); var col0ed = new Array(lwrows); for (var i = 0; i < lwrows; i++) { col0ed[i] = ed[i][0]; } var col0edrep = repeach(col0ed, lwcols - 1, lwrows); var edge1 = matrix2vectorMinusFirstColumn(ed, lwrows, lwcols); var totalLength3 = lwrows * (lwcols - 1); var xx1 = new Array(totalLength3); var xx2 = new Array(totalLength3); for (var i = 0; i < totalLength3; i++) { var EPi = EdgePoints[edge1[i] - 1]; xx1[i] = EPi[1]; xx2[i] = EPi[2]; } var points3 = GetPoints(cubeco3, values3, col0edrep, xx1, xx2, totalLength3); var triangles3 = CalPoints(points3, totalLength3); for (var i = 0; i < totalLength3; i++) { triangles.push(triangles3[i]); } } } /* end loop for(var j=0; j0) */ } /* end for(var i=0; i<7; i++) (loop over special_name) */ return triangles; } } // ---------------------------------------------------------------------------- function marchingCubes(f, level, xmin, xmax, ymin, ymax, zmin, zmax, nx, ny, nz, max, rescale, logBounds) { // default values if(typeof max === "undefined"){ max = null; } if(typeof rescale === "undefined"){ rescale = true; } if(typeof logBounds === "undefined"){ logBounds = true; } // voxel console.log("Calculate voxel..."); var voxel = Voxel(f, xmin, xmax, ymin, ymax, zmin, zmax, nx, ny, nz); if (max === null) { max = maxArray(voxel, nx, ny, nz); } // marching cubes console.log("Marching cubes..."); var triangles = computeContour3d(voxel, nx, ny, nz, max, level); var nrows = triangles.length; console.log("number of triangles: ", nrows / 3); if (logBounds) { var x = jthColumn2(triangles, nrows, 0); var y = jthColumn2(triangles, nrows, 1); var z = jthColumn2(triangles, nrows, 2); var xm = x.reduce(function (p, v) { return (p < v ? p : v); }); var xM = x.reduce(function (p, v) { // https://stackoverflow.com/a/13440842 return (p > v ? p : v); }); var ym = y.reduce(function (p, v) { return (p < v ? p : v); }); var yM = y.reduce(function (p, v) { return (p > v ? p : v); }); var zm = z.reduce(function (p, v) { return (p < v ? p : v); }); var zM = z.reduce(function (p, v) { return (p > v ? p : v); }); var boundsx = [ xmin + (xmax - xmin) * xm / (nx - 1), xmin + (xmax - xmin) * xM / (nx - 1)]; console.log("x-bounds: ", boundsx); var boundsy = [ ymin + (ymax - ymin) * ym / (ny - 1), ymin + (ymax - ymin) * yM / (ny - 1)]; console.log("y-bounds: ", boundsy); var boundsz = [ zmin + (zmax - zmin) * zm / (nz - 1), zmin + (zmax - zmin) * zM / (nz - 1)]; console.log("z-bounds: ", boundsz); } // rescaling if (rescale) { var rangex = xmax - xmin; var rangey = ymax - ymin; var rangez = zmax - zmin; for (var i = 0; i < nrows; i++) { var vertex = triangles[i]; vertex[0] = xmin + rangex * vertex[0] / (nx - 1); vertex[1] = ymin + rangey * vertex[1] / (ny - 1); vertex[2] = zmin + rangez * vertex[2] / (nz - 1); triangles[i] = vertex; } } // return triangles; } // ----------------------------------------------------------------------------