scholarly journals Interpolatory blending net subdivision schemes of Dubuc–Deslauriers type

2012 ◽  
Vol 29 (9) ◽  
pp. 722-735 ◽  
Author(s):  
Costanza Conti ◽  
Nira Dyn ◽  
Lucia Romani
Keyword(s):  
Subdivision Schemes

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 Convergence of Vector Subdivision Schemes in Sobolev Spaces

2002 ◽  
Vol 12 (1) ◽  
pp. 128-149 ◽  
Author(s):  
Di-Rong Chen ◽  
Rong-Qing Jia ◽  
S.D Riemenschneider
Keyword(s):  
Sobolev Spaces ◽  
Subdivision Schemes

scholarly journals Totally positive functions through nonstationary subdivision schemes

2007 ◽  
Vol 200 (1) ◽  
pp. 255-265 ◽  
Author(s):  
Costanza Conti ◽  
Laura Gori ◽  
Francesca Pitolli
Keyword(s):  
Subdivision Schemes ◽  
Totally Positive ◽  
Positive Functions

A study on the mask of interpolatory symmetric subdivision schemes

2007 ◽  
Vol 187 (2) ◽  
pp. 609-621 ◽  
Author(s):  
Kwan Pyo Ko ◽  
Byung-Gook Lee ◽  
Gang Joon Yoon
Keyword(s):  
Subdivision Schemes

scholarly journals TERNARY INTERPOLATORY SUBDIVISION SCHEMES ORIGINATED FROM SPLINES

2011 ◽  
Vol 09 (04) ◽  
pp. 611-633 ◽  
Author(s):  
AMIR Z. AVERBUCH ◽  
VALERY A. ZHELUDEV ◽  
GARY B. FATAKHOV ◽  
EDUARD H. YAKUBOV
Keyword(s):  
Arbitrary Order ◽  
Rational Points ◽  
Fast Computation ◽  
Subdivision Schemes ◽  
Rational Symbols ◽  
Interpolatory Subdivision

A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompanied by a detailed description of the design of the refinement masks and by algorithms that verify the convergence of these schemes. In addition, the smoothness of the limit functions is investigated. The ternary subdivision schemes, whose construction is based on continuous splines, become tools for fast computation ofıory s of arbitrary order at triadic rational points.

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