Subdivision Curves V 20 V 10 V 30

Subdivision Curves V 20 V 10 V 30 • Subdivision is a recursive 2 step process – Topological split – Local averaging / smoothing V 40

Subdivision Curves V 2 0 E 20 E 10 V 30 E 40 • Subdivision is a repeated 2 step process – Topological split – Local averaging / smoothing V 40

Subdivision Curves V 2 E 21 0 V 21 V 30 V 31 E 11 E 31 V 10 1 E 41 • Subdivision is a repeated 2 step process – Topological split – Local averaging / smoothing V 41 V 40

Subdivision Curves V 2 E 21 0 V 21 V 30 V 31 E 11 E 31 V 10 1 E 41 • Subdivision is a repeated 2 step process – Topological split – Local averaging / smoothing V 41 V 40

Subdivision Curves V 2 E 21 0 V 21 V 30 V 31 E 11 E 31 V 10 1 E 41 • Subdivision is a repeated 2 step process – Topological split – Local averaging / smoothing V 41 V 40

Subdivision of Bspline Curves 234 341 123 Knots: 412 4 1 2 3 4

Subdivision of Bspline Curves 234 2. 534 33. 54 344. 5 233. 5 341 3. 544. 5 2. 533. 5 44. 51 22. 53 1. 523 123 Knots: 4. 511. 522. 5 122. 5 4 1 4. 512 11. 52 2 3 4 411. 5 1 2 3 412 4

Vi 1 234 233. 5 Vi-1 22. 53 1. 523 123 2. 534 Averaging Rules Vi+1 1 33. 54 344. 5 Vi-11 341 Vi 2 2. 533. 541 3. 544. 5 Vi 2= Vi 1 44. 51 1 1. 522. 5 122. 5 4. 511. 52 4. 512 411. 5 Vi+11 412

Subdivision Curve Summary • Subdivsion is a recursive 2 step process – Topological linear split at midpoints – One local averaging / smoothing operator applied to all points • Double the number of vertices at each step • Subdivision curves are nothing new – Averaging rules chosen so that they are simply uniform Bspline curves