## C2 macro schemes

It's interesting to construct macro schemes on superspline subspaces of . The dimension of itself is 545. For a macro element it is natural to impose smoothness at the vertices of the macro tetrahedron. The dimension of the subspace of that has that additional smoothness is 529. The number of natural data that need to be imposed is 264. The table below lists all possible combinations of symmetric smoothness conditions that can be imposed while still making it possible to interpolate to the data. (The "count" being 264 indicates that all 264 conditions can be imposed.) The table gives the additional smoothness imposed, and is sorted by increasing dimension. A range of values like(0-4) indicates that any number in that range will cause the dimension to assume the stated value. Thus, for example, there are a total of possible sets of supersmoothness conditions in the first row that give a dimension of 280, and that are all equivalent. Double Clough-Tocher Super Splines
 n V0 V4 V5 E01 E04 E05 E45 F014 F015 F045 dim count 1 2 5 6 0-1 0-2 0-5 1 0-1 280 264 2 2 0-4 6 0-1 0-2 5 1 0-1 280 264 3 2 0-5 0-5 0-1 0-2 5 1 0-1 292 264 4 2 4 6 0-1 0-2 0-4 1 0-1 296 264 5 2 0-3 6 0-1 0-2 4 1 0-1 296 264 6 2 0-3 6 0-1 0-2 0-3 1 0-1 304 264 7 2 5 5 0-1 0-2 0-4 1 1 308 264 8 2 5 5 0-1 2 0-4 1 308 264 9 2 5 5 0-1 0-1 0-4 1 312 264 10 2 5 0-4 0-1 0-2 4 1 1 312 264 11 2 5 0-4 0-1 2 4 1 312 264 12 2 5 6 0-1 0-2 0-5 0-1 314 264 13 2 5 0-4 0-1 0-1 4 1 316 264 14 2 5 0-4 0-1 0-2 0-3 1 1 320 264 15 2 5 0-4 0-1 2 0-3 1 320 264 16 2 0-4 5 0-1 0-2 4 1 1 324 264 17 2 0-4 5 0-1 2 4 1 324 264 18 2 4 6 0-1 0-2 5 0-1 324 264 19 2 5 0-5 0-1 0-2 5 0-1 326 264 20 2 0-4 0-4 0-1 0-2 4 1 1 328 264 21 2 0-4 0-4 0-1 2 4 1 328 264 22 2 0-4 5 0-1 0-1 4 1 328 264 23 2 3 6 0-1 0-2 5 0-1 328 264 24 2 0-2 6 0-1 0-2 5 0-1 329 264 25 2 0-4 0-4 0-1 0-1 4 1 332 264 26 2 4 5 0-1 0-2 0-3 1 1 332 264 27 2 5 0-4 0-1 0-1 3 1 336 264 28 2 4 0-5 0-1 0-2 5 0-1 336 264 29 2 5 4 0-1 0-1 0-2 1 336 264 30 2 4 5 0-1 2 0-3 1 336 264 31 2 0-3 5 0-1 0-2 0-3 1 1 340 264 32 2 3 0-5 0-1 0-2 5 0-1 340 264 33 2 4 5 0-1 0-1 0-3 1 340 264 34 2 4 6 1 0-2 0-4 0-1 340 264 35 2 4 6 0-2 0-4 1 340 264 36 2 0-2 0-5 0-1 0-2 5 0-1 341 264 37 2 5 5 0-1 0-2 0-4 1 342 264 38 2 5 5 0-1 2 0-4 342 264 39 2 4 0-4 0-1 0-2 0-3 1 1 344 264 40 2 0-3 5 0-1 2 3 1 344 264 41 2 3 6 1 0-2 4 0-1 344 264 42 2 3 6 0-2 4 1 344 264 43 2 0-2 6 1 0-2 4 0-1 345 264 44 2 0-2 6 0-2 4 1 345 264 45 2 5 0-4 0-1 0-2 4 1 346 264 46 2 5 0-4 0-1 2 4 346 264 47 2 5 0-3 0-1 0-1 2 1 348 264 48 2 5 3 0-1 0-1 0-1 1 348 264 49 2 0-3 5 0-1 0-1 3 1 348 264 50 2 4 0-4 0-1 2 3 1 348 264 51 2 0-3 5 0-1 2 2 1 348 264 52 2 3 5 0-1 2 0-1 1 348 264 53 2 0-2 5 0-1 2 0-1 1 349 264 54 2 0-3 0-4 0-1 0-2 0-3 1 1 352 264 55 2 5 0-2 0-1 0-1 0-1 1 352 264 56 2 0-3 5 0-1 0-1 2 1 352 264 57 2 3 5 0-1 0-1 0-1 1 352 264 58 2 4 6 0-2 0-4 352 264 59 2 3 6 1 0-2 0-3 0-1 352 264 60 2 3 6 0-2 0-3 1 352 264 61 2 0-2 5 0-1 0-1 0-1 1 353 264 62 2 0-2 6 1 0-2 0-3 0-1 353 264 63 2 0-2 6 0-2 0-3 1 353 264 64 2 5 0-4 0-1 0-2 0-3 1 354 264 65 2 5 0-4 0-1 2 0-3 354 264 66 2 5 5 0-1 0-1 0-4 354 264 67 2 0-3 0-4 0-1 2 3 1 356 264 68 2 3 6 0-2 4 356 264 69 2 0-2 6 0-2 4 357 264 70 2 5 0-4 0-1 0-1 4 358 264 71 2 4 0-4 0-1 2 2 1 360 264 72 2 4 4 0-1 2 0-1 1 360 264 73 2 4 0-3 0-1 2 0-1 1 364 264 74 2 4 0-4 0-1 0-1 3 1 364 264 75 2 4 5 0-1 0-2 4 1 368 264 76 2 4 5 1 2 4 368 264 77 2 0-3 0-4 0-1 0-1 3 1 372 264 78 2 0-3 0-4 0-1 2 2 1 372 264 79 2 4 0-4 0-1 0-2 4 1 372 264 80 2 4 0-4 1 2 4 372 264 81 2 3 5 0-1 0-2 4 1 372 264 82 2 3 5 1 2 4 372 264 83 2 0-2 5 0-1 0-2 4 1 373 264 84 2 0-2 5 1 2 4 373 264 85 2 3 0-4 0-1 0-2 4 1 376 264 86 2 4 4 0-1 0-1 0-2 1 376 264 87 2 3 6 0-2 0-3 376 264 88 2 4 5 0-1 0-2 0-3 1 376 264 89 2 3 4 0-1 2 0-1 1 376 264 90 2 3 0-4 1 2 4 376 264 91 2 0-2 0-4 0-1 0-2 4 1 377 264 92 2 0-2 4 0-1 2 0-1 1 377 264 93 2 0-2 0-4 1 2 4 377 264 94 2 0-2 6 0-2 3 377 264 95 2 5 0-4 0-1 0-1 3 378 264 96 2 5 4 0-1 0-1 0-2 378 264 97 2 3 0-3 0-1 2 0-1 1 380 264 98 2 4 5 1 0-1 4 380 264 99 2 4 5 2 4 380 264 100 2 0-2 0-3 0-1 2 0-1 1 381 264 101 2 4 0-4 1 0-1 4 384 264 102 2 4 0-4 2 4 384 264 103 2 3 5 1 0-1 4 384 264 104 2 3 5 2 4 384 264 105 2 0-2 5 1 0-1 4 385 264 106 2 0-2 5 2 4 385 264 107 2 4 0-4 0-1 0-2 0-3 1 388 264 108 2 4 0-3 0-1 0-1 2 1 388 264 109 2 0-3 4 0-1 0-1 2 1 388 264 110 2 3 0-4 1 0-1 4 388 264 111 2 3 5 0-1 0-2 0-3 1 388 264 112 2 3 0-4 2 4 388 264 113 2 4 5 1 2 0-3 388 264 114 2 0-2 0-4 1 0-1 4 389 264 115 2 0-2 5 0-1 0-2 0-3 1 389 264 116 2 0-2 0-4 2 4 389 264 117 2 2 6 0-2 0-2 389 264 118 2 0-1 6 0-2 2 389 264 119 2 5 0-3 0-1 0-1 2 390 264 120 2 5 3 0-1 0-1 0-1 390 264 121 2 4 3 0-1 0-1 0-1 1 392 264 122 2 3 4 0-1 0-1 0-1 1 392 264 123 2 4 5 0-1 4 392 264 124 2 0-2 4 0-1 0-1 0-1 1 393 264 125 2 0-1 6 0-2 0-1 393 264 126 2 5 0-2 0-1 0-1 0-1 394 264 127 2 4 0-2 0-1 0-1 0-1 1 396 264 128 2 4 0-4 0-1 4 396 264 129 2 3 5 0-1 4 396 264 130 2 0-2 5 0-1 4 397 264 131 2 0-3 0-3 0-1 0-1 2 1 400 264 132 2 3 0-4 0-1 0-2 0-3 1 400 264 133 2 3 0-4 0-1 4 400 264 134 2 4 0-4 1 2 3 400 264 135 2 4 5 1 0-1 0-3 400 264 136 2 4 5 2 0-3 400 264 137 2 3 5 1 2 3 400 264 138 2 0-2 0-4 0-1 0-2 0-3 1 401 264 139 2 0-2 0-4 0-1 4 401 264 140 2 0-2 5 1 2 3 401 264 141 2 3 3 0-1 0-1 0-1 1 408 264 142 2 0-2 3 0-1 0-1 0-1 1 409 264 143 2 3 0-2 0-1 0-1 0-1 1 412 264 144 2 4 0-4 1 2 2 412 264 145 2 4 5 0-1 0-3 412 264 146 2 4 0-4 2 3 412 264 147 2 3 0-4 1 2 3 412 264 148 2 4 4 1 2 0-1 412 264 149 2 3 5 1 2 0-2 412 264 150 2 3 5 1 0-1 3 412 264 151 2 0-2 0-2 0-1 0-1 0-1 1 413 264 152 2 0-2 0-4 1 2 3 413 264 153 2 0-2 5 1 0-1 3 413 264 154 2 0-2 5 1 2 2 413 264 155 2 4 0-3 1 2 0-1 416 264 156 2 0-2 5 1 2 0-1 417 264 157 2 4 0-4 1 0-1 3 424 264 158 2 4 0-4 2 2 424 264 159 2 3 5 1 0-1 0-2 424 264 160 2 4 4 2 0-1 424 264 161 2 3 5 2 3 424 264 162 2 0-2 5 1 0-1 2 425 264 163 2 0-2 5 2 3 425 264 164 2 4 0-3 2 0-1 428 264 165 2 0-2 5 1 0-1 0-1 429 264 166 2 4 0-4 0-1 3 436 264 167 2 3 0-4 1 0-1 3 436 264 168 2 3 0-4 1 2 2 436 264 169 2 3 0-4 2 3 436 264 170 2 4 4 1 0-1 0-2 436 264 171 2 3 5 2 0-2 436 264 172 2 3 5 0-1 3 436 264 173 2 0-2 0-4 1 0-1 3 437 264 174 2 0-2 0-4 1 2 2 437 264 175 2 0-2 0-4 2 3 437 264 176 2 0-2 5 0-1 3 437 264 177 2 3 4 1 2 0-1 440 264 178 2 3 0-3 1 2 0-1 444 264 179 2 0-2 4 1 2 0-1 445 264 180 2 4 0-3 1 0-1 2 448 264 181 2 4 4 0-1 0-2 448 264 182 2 3 5 0-1 0-2 448 264 183 2 0-2 0-3 1 2 0-1 449 264 184 2 0-2 5 2 2 449 264 185 2 4 3 1 0-1 0-1 452 264 186 2 2 5 2 0-1 453 264 187 2 4 0-2 1 0-1 0-1 456 264 188 2 0-1 5 2 0-1 457 264 189 2 4 0-3 0-1 2 460 264 190 2 3 0-4 0-1 3 460 264 191 2 3 0-4 2 2 460 264 192 2 3 4 1 0-1 2 460 264 193 2 0-2 0-4 0-1 3 461 264 194 2 0-2 5 0-1 2 461 264 195 2 0-2 4 1 0-1 2 461 264 196 2 4 3 0-1 0-1 464 264 197 2 3 4 1 0-1 0-1 464 264 198 2 3 4 2 0-1 464 264 199 2 2 5 0-1 0-1 465 264 200 2 4 0-2 0-1 0-1 468 264 201 2 3 0-3 2 0-1 468 264 202 2 0-1 5 0-1 0-1 469 264 203 2 0-2 4 1 0-1 0-1 469 264 204 2 3 0-3 1 0-1 2 472 264 205 2 0-2 0-3 1 0-1 2 473 264 206 2 0-2 0-4 2 2 473 264 207 2 3 3 1 0-1 0-1 480 264 208 2 2 4 2 0-1 481 264 209 2 3 0-2 1 0-1 0-1 484 264 210 2 3 4 0-1 2 484 264 211 2 2 0-3 2 0-1 485 264 212 2 0-2 3 1 0-1 0-1 485 264 213 2 0-1 4 2 0-1 485 264 214 2 3 4 0-1 0-1 488 264 215 2 0-2 0-2 1 0-1 0-1 489 264 216 2 0-1 0-3 2 0-1 489 264 217 2 3 0-3 0-1 2 496 264 218 2 0-2 4 0-1 2 497 264 219 2 3 3 0-1 0-1 504 264 220 2 2 4 0-1 0-1 505 264 221 2 3 0-2 0-1 0-1 508 264 222 2 0-2 0-3 0-1 2 509 264 223 2 0-1 4 0-1 0-1 509 264 224 2 2 3 0-1 0-1 521 264 225 2 2 0-2 0-1 0-1 525 264 226 2 0-1 3 0-1 0-1 525 264 227 2 0-1 0-2 0-1 0-1 529 264 227 0-1 545 264