Approximation order/smoothness tradeoff in Hermite subdivision schemes

2001 ◽  
Author(s):  
Thomas P. Yu
Keyword(s):  
Approximation Order ◽  
Subdivision Schemes ◽  
Order Smoothness ◽  
Hermite 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.

scholarly journals Honeycomb and k-fold Hermite subdivision schemes

2005 ◽  
Vol 177 (2) ◽  
pp. 401-425 ◽  
Author(s):  
Yonggang Xue ◽  
Thomas P.-Y. Yu
Keyword(s):  
Subdivision Schemes ◽  
Hermite Subdivision

Design of Hermite Subdivision Schemes Aided by Spectral Radius Optimization

2003 ◽  
Vol 25 (2) ◽  
pp. 643-656 ◽  
Author(s):  
Bin Han ◽  
Michael L. Overton ◽  
Thomas P. Y. Yu
Keyword(s):  
Spectral Radius ◽  
Subdivision Schemes ◽  
Hermite Subdivision

scholarly journals Hermite Subdivision Schemes and Taylor Polynomials

2008 ◽  
Vol 29 (2) ◽  
pp. 219-245 ◽  
Author(s):  
Serge Dubuc ◽  
Jean-Louis Merrien
Keyword(s):  
Subdivision Schemes ◽  
Taylor Polynomials ◽  
Hermite Subdivision

scholarly journals Extended Hermite subdivision schemes

2017 ◽  
Vol 317 ◽  
pp. 343-361 ◽  
Author(s):  
Jean-Louis Merrien ◽  
Tomas Sauer
Keyword(s):  
Subdivision Schemes ◽  
Hermite Subdivision

scholarly journals A New 4-PointC3Quaternary Approximating Subdivision Scheme

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Ghulam Mustafa ◽  
Faheem Khan
Keyword(s):  
Shape Parameter ◽  
Approximation Order ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Approximating Subdivision Scheme

A new 4-pointC3quaternary approximating subdivision scheme with one shape parameter is proposed and analyzed. Its smoothness and approximation order are higher but support is smaller in comparison with the existing binary and ternary 4-point subdivision schemes.

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