Subdivision schemes with optimal bounded curvature near extraordinary vertices

2018 ◽  
Vol 37 (7) ◽  
pp. 455-467 ◽  
Author(s):  
Yue Ma ◽  
Weiyin Ma
Keyword(s):  
Subdivision Schemes ◽  
Bounded Curvature

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 Remarks on Manifolds with Two-Sided Curvature Bounds

2021 ◽  
Vol 9 (1) ◽  
pp. 53-64
Author(s):  
Vitali Kapovitch ◽  
Alexander Lytchak
Keyword(s):  
Distance Functions ◽  
Cut Locus ◽  
Bounded Curvature ◽  
Curvature Bounds ◽  
Positive Reach

Abstract We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

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 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 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
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