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B-Spline
B-Splines
- Is it possible to achieve both $C^{2}$-continuity and local controllability?
- B-splines can do!
- Uniform cubic B-spline basis functions
Uniform B-spline basis functions
- Bell-shaped basis function for each control points
- Overlapping basis functions
- Control points correspond to knot points
Uniform B-splines
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- We have $(n+1)+2$ unknowns.
B-spline Properties
- Variation Diminishing
- $C^{2}$-continuity
- Local Controllability
Demo
B-spline basis functions
B-spline basis functions The equation for k-order B-spline with n+1 control points (P0 , P1 , ... , Pn ) is P(t) = ∑i=0,n Ni,k(t) Pi , tk-1 ≤ t ≤ tn+1 . In a B-spline each control point is associated with a basis function Ni,k which is gi
www.ibiblio.org
Summary
- Polynomial Interpolation
- Lagrange Polynomial
- Oscillation Problem
- Spline Interpolation
- Natural Cubic Spline
- $C^{2}$-continuity
- No Local Controllability
- Catmull-Rom Spline
- $C^{1}$-continuity
- Local Controllability
- B-Spline
- $C^{2}$-continuity
- Local Controllability
- Natural Cubic Spline
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