B-Spline and Subdivision Surfaces - Stanford University

B-Spline and Subdivision Surfaces

Images from: & sunflow.

Mirela Ben-Chen

Today

? B-Spline surfaces

? NURBS surfaces

? Subdivision surfaces

? Theory ? Zoo

? Recent trends

? Non linear subdivision ? T-Splines

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Images from: , sunflow. ,

Reminder: Bezier & B-Spline Curves

Bezier Curve

Cubic curve, 4 control points: Applet (Curves) Applet (Basis functions)

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Reminder: Bezier & B-Spline Curves

B-Spline Curve

Decouple number of control points from degree of curve

"Glue" a few degree p Bezier curves, with continuity conditions

Applet (Curve)

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Reminder: Bezier & B-Spline Curves

B-Spline Curve

Building blocks:

n + 1 control points Pi

P1

Knot vector U = { u0 , u1 , ... , um } P0

The degree p

m, n, p satisfy m = n + p - 1

P2 P5 P3 P4

P6 P7

Applet (Basis functions)

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