B-Spline and Subdivision Surfaces - Stanford University
B-Spline and Subdivision Surfaces
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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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