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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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PowerPoint Slideshow about ' Subdivision Curves' - aaron-martinez


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Subdivision curves

V20

Subdivision Curves

V30

V40

V10

  • Subdivision is a recursive 2 step process

    • Topological split

    • Local averaging / smoothing


Subdivision curves1

E20

V20

Subdivision Curves

V30

E10

E30

V40

V10

E40

  • Subdivision is a repeated 2 step process

    • Topological split

    • Local averaging / smoothing


Subdivision curves2

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


Subdivision curves3

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


Subdivision curves4

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


Subdivision of bspline curves

234

Subdivision of Bspline Curves

341

123

412

Knots:

4

1

2

3

4

1

2

3

4


Subdivision of bspline curves1

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


Averaging rules

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


Subdivision curve summary
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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