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Subdivision Curves

V 2 0. Subdivision Curves. V 3 0. V 4 0. V 1 0. Subdivision is a recursive 2 step process Topological split Local averaging / smoothing. E 2 0. V 2 0. Subdivision Curves. V 3 0. E 1 0. E 3 0. V 4 0. V 1 0. E 4 0. Subdivision is a repeated 2 step process Topological split

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Subdivision Curves

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  1. V20 Subdivision Curves V30 V40 V10 • Subdivision is a recursive 2 step process • Topological split • Local averaging / smoothing

  2. E20 V20 Subdivision Curves V30 E10 E30 V40 V10 E40 • Subdivision is a repeated 2 step process • Topological split • Local averaging / smoothing

  3. E21 V20 Subdivision Curves V30 V21 V31 E11 E31 V41 V11 V40 V10 E41 • Subdivision is a repeated 2 step process • Topological split • Local averaging / smoothing

  4. E21 V20 Subdivision Curves V30 V21 V31 E11 E31 V41 V11 V40 V10 E41 • Subdivision is a repeated 2 step process • Topological split • Local averaging / smoothing

  5. E21 V20 Subdivision Curves V30 V21 V31 E11 E31 V41 V11 V40 V10 E41 • Subdivision is a repeated 2 step process • Topological split • Local averaging / smoothing

  6. 234 Subdivision of Bspline Curves 341 123 412 Knots: 4 1 2 3 4 1 2 3 4

  7. 2.534 33.54 344.5 234 Subdivision of Bspline Curves 341 233.5 3.541 3.544.5 2.533.5 44.51 22.53 4.511.5 1.522.5 411.5 1.523 123 4.512 122.5 11.52 412 Knots: 4 1 2 3 4 1 2 3 4

  8. Vi1 Vi-11 2.534 Vi+11 33.54 344.5 234 Averaging Rules 341 Vi2 233.5 3.541 2.533.5 3.544.5 Vi2=Vi1 Vi-11 44.51 22.53 411.5 1.523 1.522.5 4.511.5 Vi+11 123 4.512 122.5 11.52 412

  9. 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

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