Smoothing nonlinear subdivision schemes by averaging

2017 ◽  
Vol 77 (2) ◽  
pp. 361-379 ◽  
Author(s):  
Tom Duchamp ◽  
Gang Xie ◽  
Thomas Yu
Keyword(s):  
Subdivision Schemes ◽  
Nonlinear Subdivision

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

Comparison of different interpolation operators including nonlinear subdivision schemes in the simulation of particle trajectories

2013 ◽  
Vol 236 ◽  
pp. 346-366 ◽  
Author(s):  
Bouchra Bensiali ◽  
Kowsik Bodi ◽  
Guido Ciraolo ◽  
Philippe Ghendrih ◽  
Jacques Liandrat
Keyword(s):  
Particle Trajectories ◽  
Subdivision Schemes ◽  
Nonlinear Subdivision ◽  
Interpolation Operators

On a stable family of four-point nonlinear subdivision schemes eliminating the Gibbs phenomenon

2019 ◽  
Vol 354 ◽  
pp. 310-325 ◽  
Author(s):  
Sergio Amat ◽  
Juan Ruiz ◽  
J. Carlos Trillo ◽  
Dionisio F. Yáñez
Keyword(s):  
Gibbs Phenomenon ◽  
Subdivision Schemes ◽  
Nonlinear Subdivision ◽  
Stable Family

Nonlinear Subdivision Schemes on Irregular Meshes

2009 ◽  
Vol 31 (3) ◽  
pp. 395-415 ◽  
Author(s):  
Andreas Weinmann
Keyword(s):  
Subdivision Schemes ◽  
Nonlinear Subdivision ◽  
Irregular Meshes

Weighted-Power p Nonlinear Subdivision Schemes

2012 ◽  
pp. 109-129 ◽  
Author(s):  
Francesc Aràndiga ◽  
Rosa Donat ◽  
Maria Santágueda
Keyword(s):  
Subdivision Schemes ◽  
Nonlinear Subdivision
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