55:
31:
452:
441:
422:
398:
248:
175:
640:
119:
for their invention and application of subdivision surfaces. DeRose wrote about "efficient, fair interpolation" and character animation. Stam described a technique for a direct evaluation of the limit surface without recursion.
373:
657:
244:
601:
562:
531:
614:
The limit surface of
Catmull–Clark subdivision surfaces can also be evaluated directly, without any recursive refinement. This can be accomplished by means of the technique of
1085:
480:. The new mesh will generally look "smoother" (i.e. less "jagged" or "pointy") than the old mesh. Repeated subdivision results in meshes that are more and more rounded.
1116:
116:
1130:
Manuel
Kraemer (2014). "OpenSubdiv: Interoperating GPU Compute and Drawing". In Martin Watt; Erwin Coumans; George ElKoura; et al. (eds.).
1139:
1047:
1451:
1277:
901:
679:
1194:
1092:
1071:
54:
661:
1446:
603:
819:
895:
906:
830:
319:
764:
650:
1311:
1255:
1025:
939:
804:
623:
202:
39:
1247:
Proceedings of the 25th annual conference on
Computer graphics and interactive techniques - SIGGRAPH '98
1181:
1017:
Proceedings of the 25th annual conference on
Computer graphics and interactive techniques - SIGGRAPH '98
1008:
575:
536:
505:
30:
93:
70:
1316:
1260:
980:
769:
290:, where each edge midpoint is the average of its two endpoint vertices (not to be confused with new
58:
Visual difference between sphere (green) and
Catmull-Clark subdivision surface (magenta) from a cube
1030:
774:
477:
74:
35:
1388:
1342:
451:
440:
421:
397:
247:
174:
1406:
1373:
1329:
1296:
1283:
1219:
1167:
1053:
962:
784:
779:
724:
719:
619:
496:
492:
108:
1021:
1015:
825:
1251:
1245:
1365:
1273:
1135:
1110:
1043:
147:
1430:
1392:
1357:
1321:
1265:
1035:
954:
694:
606:). After one iteration, the number of extraordinary points on the surface remains constant.
856:
809:
799:
569:
935:
502:
It can be shown that the limit surface obtained by this refinement process is at least
85:
1409:: Eurographics 2012 Annex: Short Papers (Eurographics 2012, Cagliary). 2012, pp 41–44.
1382:
1009:"Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values"
1440:
966:
958:
931:
867:
850:
469:
81:
1417:
1377:
1333:
1287:
1238:
1057:
139:
1426:
1407:
Efficient
Evaluation of Semi-Smooth Creases in Catmull-Clark Subdivision Surfaces
639:
77:
1413:
1400:
1207:
1155:
835:
759:
488:
484:
376:
143:
17:
1396:
1325:
872:
794:
789:
739:
129:
66:
1369:
1269:
1039:
495:, although they do go to great lengths to rigorously show that the method
192:
Set each edge point to be the average of the two neighbouring face points
1361:
1004:
940:"Recursively generated B-spline surfaces on arbitrary topological meshes"
877:
861:
845:
754:
749:
744:
618:(1998). This method reformulates the recursive refinement process into a
615:
112:
101:
97:
89:
1343:"Real-Time Creased Approximate Subdivision Surfaces with Displacements"
1297:"Approximating Catmull-Clark subdivision surfaces with bicubic patches"
1214:
1162:
898:- A set of related topological polyhedron and polygonal mesh operators.
840:
714:
709:
699:
664: in this section. Unsourced material may be challenged and removed.
165:
47:
882:
814:
43:
1389:
Feature
Adaptive GPU Rendering of Catmull-Clark Subdivision Surfaces
729:
450:
439:
420:
396:
246:
173:
53:
29:
1423:
Behavior of recursive division surfaces near extraordinary points
1391:", ACM Transactions on Graphics Volume 31 Issue 1, January 2012,
1157:
Meet the
Experts: Pixar Animation Studios, The OpenSubdiv Project
734:
704:
633:
582:
543:
512:
34:
Catmull–Clark level-3 subdivision of a cube with the limit
1387:
Matthias Nießner, Charles Loop, Mark Meyer, Tony DeRose, "
444:
3 new edges per vertex point of shifted original vertices
1350:
1425:, Computer-Aided Design, 10 (6) 356–360 (1978), (
1341:
Kovacs, D.; Mitchell, J.; Drone, S.; Zorin, D. (2010).
438:
of all original edges incident on the original vertex
578:
539:
508:
487:
formula was chosen by
Catmull and Clark based on the
322:
205:
1405:
Nießner, Matthias; Loop, Charles; Greiner, Günther:
294:
above). (Note that from the perspective of a vertex
38:shown below. (Note that although it looks like the
981:"Catmull–Clark subdivision surface - Rosetta Code"
622:problem, which can be solved directly by means of
595:
556:
525:
367:
274:(recently created) face points for faces touching
238:
419:of all original edges defining the original face
926:
924:
922:
1239:"Subdivision surfaces in character animation"
8:
302:is also the number of adjacent faces, hence
853:- Grasshopper 3D Plugin - Weaverbird Plugin
491:of the resulting surfaces rather than on a
286:edge midpoints for original edges touching
1416:also presented as a SIGGRAPH2014 tutorial
1315:
1259:
1237:Derose, T.; Kass, M.; Truong, T. (1998).
1029:
680:Learn how and when to remove this message
587:
581:
580:
577:
548:
542:
541:
538:
517:
511:
510:
507:
323:
321:
206:
204:
107:In 2005/06, Edwin Catmull, together with
1182:"Pixar's OpenSubdiv V2: A detailed look"
368:{\displaystyle {\frac {F+2R+(n-3)P}{n}}}
918:
117:Academy Award for Technical Achievement
1115:: CS1 maint: archived copy as title (
1108:
449:Define new faces as enclosed by edges
820:Power Surfacing add-in for SolidWorks
408:Form edges and faces in the new mesh
7:
1414:Tessellation in Call of Duty: Ghosts
662:adding citations to reliable sources
239:{\displaystyle {\frac {A+F+M+E}{4}}}
570:how many derivatives are continuous
128:Catmull–Clark surfaces are defined
73:to create curved surfaces by using
596:{\displaystyle {\mathcal {C}}^{n}}
557:{\displaystyle {\mathcal {C}}^{2}}
526:{\displaystyle {\mathcal {C}}^{1}}
468:The new mesh will consist only of
298:, the number of edges neighboring
196:and the two endpoints of the edge
25:
1132:Multithreading for Visual Effects
27:Technique in 3D computer graphics
1222:from the original on 2021-12-11.
1170:from the original on 2021-12-11.
638:
1295:Loop, C.; Schaefer, S. (2008).
1134:. CRC Press. pp. 163–199.
649:needs additional citations for
401:New vertex points (green cones)
88:in 1978 as a generalization of
1072:"Subdivision Surface Modifier"
533:at extraordinary vertices and
499:to bicubic B-spline surfaces.
353:
341:
164:Set each face point to be the
1:
902:Doo-Sabin subdivision surface
150:in this mesh shall be called
1304:ACM Transactions on Graphics
959:10.1016/0010-4485(78)90110-0
630:Software using the algorithm
425:New edges, 4 per face point
251:Edge points (magenta cubes)
1468:
1452:Multivariate interpolation
896:Conway polyhedron notation
178:Face points (blue spheres)
730:CATIA (Imagine and Shape)
391:with respective weights (
907:Loop subdivision surface
472:, which in general will
1397:10.1145/2077341.2077347
1326:10.1145/1330511.1330519
1209:OpenSubdiv Blender demo
790:LightWave 3D, version 9
765:DeleD Community Edition
493:mathematical derivation
455:Final faces to the mesh
278:, and take the average
172:for the respective face
69:is a technique used in
624:matrix diagonalization
597:
564:everywhere else (when
558:
527:
483:The arbitrary-looking
456:
445:
426:
402:
369:
252:
240:
185:For each edge, add an
179:
132:, using the following
100:surfaces to arbitrary
59:
51:
46:, an actual sphere is
40:bi-cubic interpolation
1421:D. Doo and M. Sabin:
1270:10.1145/280814.280826
1040:10.1145/280814.280945
947:Computer-Aided Design
598:
559:
528:
454:
443:
424:
400:
370:
250:
241:
177:
158:For each face, add a
57:
33:
1447:3D computer graphics
1362:10.1109/TVCG.2010.31
864:- Requires a Plugin.
658:improve this article
576:
537:
506:
489:aesthetic appearance
320:
266:, take the average (
203:
124:Recursive evaluation
80:. It was devised by
71:3D computer graphics
75:subdivision surface
36:subdivision surface
620:matrix exponential
593:
554:
523:
457:
446:
427:
403:
365:
253:
236:
180:
134:refinement scheme.
60:
52:
1141:978-1-4822-4356-7
1049:978-0-89791-999-9
690:
689:
682:
430:Connect each new
411:Connect each new
363:
234:
16:(Redirected from
1459:
1381:
1347:
1337:
1319:
1301:
1291:
1263:
1243:
1224:
1223:
1204:
1198:
1192:
1186:
1185:
1178:
1172:
1171:
1152:
1146:
1145:
1127:
1121:
1120:
1114:
1106:
1104:
1103:
1097:
1091:. Archived from
1090:
1082:
1076:
1075:
1068:
1062:
1061:
1033:
1013:
1001:
995:
994:
992:
991:
977:
971:
970:
944:
928:
755:Creo (Freestyle)
685:
678:
674:
671:
665:
642:
634:
610:Exact evaluation
602:
600:
599:
594:
592:
591:
586:
585:
563:
561:
560:
555:
553:
552:
547:
546:
532:
530:
529:
524:
522:
521:
516:
515:
374:
372:
371:
366:
364:
359:
324:
245:
243:
242:
237:
235:
230:
207:
142:of an arbitrary
21:
1467:
1466:
1462:
1461:
1460:
1458:
1457:
1456:
1437:
1436:
1412:Wade Brainerd,
1345:
1340:
1317:10.1.1.153.2047
1299:
1294:
1280:
1261:10.1.1.679.1198
1241:
1236:
1233:
1231:Further reading
1228:
1227:
1206:
1205:
1201:
1197:gputechconf.com
1193:
1189:
1180:
1179:
1175:
1154:
1153:
1149:
1142:
1129:
1128:
1124:
1107:
1101:
1099:
1095:
1088:
1086:"Archived copy"
1084:
1083:
1079:
1070:
1069:
1065:
1050:
1011:
1003:
1002:
998:
989:
987:
985:rosettacode.org
979:
978:
974:
942:
930:
929:
920:
915:
892:
887:
760:Daz Studio, 2.0
686:
675:
669:
666:
655:
643:
632:
612:
579:
574:
573:
540:
535:
534:
509:
504:
503:
466:
325:
318:
317:
208:
201:
200:
170:original points
152:original points
126:
28:
23:
22:
15:
12:
11:
5:
1465:
1463:
1455:
1454:
1449:
1439:
1438:
1435:
1434:
1419:
1410:
1403:
1385:
1338:
1292:
1279:978-0897919999
1278:
1232:
1229:
1226:
1225:
1199:
1187:
1173:
1147:
1140:
1122:
1077:
1063:
1048:
1031:10.1.1.20.7798
996:
972:
917:
916:
914:
911:
910:
909:
904:
899:
891:
888:
886:
885:
880:
875:
870:
865:
859:
854:
848:
843:
838:
833:
828:
822:
817:
812:
807:
802:
797:
792:
787:
782:
777:
772:
770:DeleD Designer
767:
762:
757:
752:
747:
742:
737:
732:
727:
722:
717:
712:
707:
702:
697:
691:
688:
687:
646:
644:
637:
631:
628:
611:
608:
590:
584:
572:, we speak of
551:
545:
520:
514:
470:quadrilaterals
465:
462:
461:
460:
459:
458:
447:
428:
406:
405:
404:
395:− 3), 2 and 1)
362:
358:
355:
352:
349:
346:
343:
340:
337:
334:
331:
328:
311:original point
260:original point
256:
255:
254:
233:
229:
226:
223:
220:
217:
214:
211:
183:
182:
181:
125:
122:
115:, received an
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1464:
1453:
1450:
1448:
1445:
1444:
1442:
1432:
1428:
1424:
1420:
1418:
1415:
1411:
1408:
1404:
1402:
1398:
1394:
1390:
1386:
1384:
1379:
1375:
1371:
1367:
1363:
1359:
1356:(5): 742–51.
1355:
1351:
1344:
1339:
1335:
1331:
1327:
1323:
1318:
1313:
1309:
1305:
1298:
1293:
1289:
1285:
1281:
1275:
1271:
1267:
1262:
1257:
1253:
1249:
1248:
1240:
1235:
1234:
1230:
1221:
1217:
1216:
1211:
1210:
1203:
1200:
1196:
1191:
1188:
1184:. 2013-09-18.
1183:
1177:
1174:
1169:
1165:
1164:
1159:
1158:
1151:
1148:
1143:
1137:
1133:
1126:
1123:
1118:
1112:
1098:on 2016-11-23
1094:
1087:
1081:
1078:
1074:. 2020-01-15.
1073:
1067:
1064:
1059:
1055:
1051:
1045:
1041:
1037:
1032:
1027:
1023:
1019:
1018:
1010:
1006:
1000:
997:
986:
982:
976:
973:
968:
964:
960:
956:
952:
948:
941:
937:
933:
927:
925:
923:
919:
912:
908:
905:
903:
900:
897:
894:
893:
889:
884:
881:
879:
876:
874:
871:
869:
868:Softimage XSI
866:
863:
860:
858:
855:
852:
851:Rhinoceros 3D
849:
847:
844:
842:
839:
837:
834:
832:
829:
827:
823:
821:
818:
816:
813:
811:
808:
806:
803:
801:
798:
796:
793:
791:
788:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
692:
684:
681:
673:
663:
659:
653:
652:
647:This section
645:
641:
636:
635:
629:
627:
625:
621:
617:
609:
607:
605:
588:
571:
567:
549:
518:
500:
498:
494:
490:
486:
481:
479:
475:
471:
463:
453:
448:
442:
437:
433:
429:
423:
418:
414:
410:
409:
407:
399:
394:
390:
386:
382:
378:
375:(This is the
360:
356:
350:
347:
344:
338:
335:
332:
329:
326:
316:
312:
308:
307:
305:
301:
297:
293:
289:
285:
281:
277:
273:
269:
265:
261:
257:
249:
231:
227:
224:
221:
218:
215:
212:
209:
199:
195:
191:
190:
188:
184:
176:
171:
167:
163:
162:
161:
157:
156:
155:
153:
149:
145:
141:
138:Start with a
136:
135:
131:
123:
121:
118:
114:
110:
105:
103:
99:
96:
95:
91:
87:
83:
82:Edwin Catmull
79:
76:
72:
68:
65:
64:Catmull–Clark
56:
49:
45:
42:approaches a
41:
37:
32:
19:
18:Catmull-Clark
1422:
1353:
1349:
1307:
1303:
1246:
1213:
1208:
1202:
1190:
1176:
1161:
1156:
1150:
1131:
1125:
1100:. Retrieved
1093:the original
1080:
1066:
1016:
999:
988:. Retrieved
984:
975:
950:
946:
873:Strata 3D CX
676:
667:
656:Please help
651:verification
648:
613:
565:
501:
482:
473:
467:
435:
432:vertex point
431:
416:
412:
392:
388:
384:
380:
315:vertex point
314:
310:
303:
299:
295:
291:
287:
283:
279:
275:
271:
267:
263:
259:
197:
193:
186:
169:
159:
151:
137:
133:
127:
106:
92:
63:
61:
1250:. pp.
1020:. pp.
932:Catmull, E.
805:Metasequoia
436:edge points
434:to the new
417:edge points
415:to the new
313:to the new
292:edge points
130:recursively
109:Tony DeRose
1441:Categories
1102:2016-12-04
990:2022-01-13
953:(6): 350.
913:References
836:Realsoft3D
826:OpenSubdiv
670:April 2013
604:continuity
568:indicates
485:barycenter
464:Properties
413:face point
377:barycenter
309:Move each
187:edge point
160:face point
146:. All the
144:polyhedron
1312:CiteSeerX
1256:CiteSeerX
1026:CiteSeerX
967:121149868
936:Clark, J.
795:Makehuman
740:Cheetah3D
497:converges
348:−
258:For each
86:Jim Clark
67:algorithm
1383:preprint
1378:17138394
1370:20616390
1310:: 1–11.
1220:Archived
1195:AV Media
1168:Archived
1111:cite web
1007:(1998).
1005:Stam, J.
938:(1978).
890:See also
878:Wings 3D
862:SketchUp
824:Pixar's
750:Clara.io
745:Cinema4D
616:Jos Stam
148:vertices
113:Jos Stam
102:topology
98:B-spline
90:bi-cubic
78:modeling
1334:6068564
1288:1221330
1215:YouTube
1163:YouTube
1058:2771758
1022:395–404
841:Remo 3D
785:Houdini
780:Hexagon
725:Carrara
720:Blender
715:AutoCAD
710:Anim8or
700:3D-Coat
695:3ds Max
282:of all
270:of all
168:of all
166:average
94:uniform
48:quadric
1376:
1368:
1332:
1314:
1286:
1276:
1258:
1138:
1056:
1046:
1028:
965:
883:Zbrush
815:Mudbox
775:Hammer
478:planar
44:sphere
1374:S2CID
1346:(PDF)
1330:S2CID
1300:(PDF)
1284:S2CID
1242:(PDF)
1096:(PDF)
1089:(PDF)
1054:S2CID
1012:(PDF)
963:S2CID
943:(PDF)
846:Shade
831:PRMan
198:(M,E)
194:(A,F)
1401:demo
1366:PMID
1274:ISBN
1136:ISBN
1117:link
1044:ISBN
857:Silo
810:MODO
800:Maya
735:CGAL
705:AC3D
387:and
140:mesh
111:and
84:and
62:The
1431:pdf
1427:doi
1393:doi
1358:doi
1322:doi
1266:doi
1036:doi
955:doi
660:by
476:be
474:not
379:of
280:(R)
1443::
1429:,
1399:,
1372:.
1364:.
1354:16
1352:.
1348:.
1328:.
1320:.
1308:27
1306:.
1302:.
1282:.
1272:.
1264:.
1254:.
1252:85
1244:.
1218:.
1212:.
1166:.
1160:.
1113:}}
1109:{{
1052:.
1042:.
1034:.
1024:.
1014:.
983:.
961:.
951:10
949:.
945:.
934:;
921:^
626:.
383:,
306:)
268:F)
264:P)
189:.
154:.
104:.
50:.)
1433:)
1395::
1380:.
1360::
1336:.
1324::
1290:.
1268::
1144:.
1119:)
1105:.
1060:.
1038::
993:.
969:.
957::
683:)
677:(
672:)
668:(
654:.
589:n
583:C
566:n
550:2
544:C
519:1
513:C
393:n
389:F
385:R
381:P
361:n
357:P
354:)
351:3
345:n
342:(
339:+
336:R
333:2
330:+
327:F
304:n
300:P
296:P
288:P
284:n
276:P
272:n
262:(
232:4
228:E
225:+
222:M
219:+
216:F
213:+
210:A
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
