Non-uniform subdivision for B-splines of arbitrary degree

2009 ◽  
Vol 26 (1) ◽  
pp. 75-81 ◽  
Author(s):  
S. Schaefer ◽  
R. Goldman
Keyword(s):  
Arbitrary Degree ◽  
B Splines

scholarly journals Creases and boundary conditions for subdivision curves

2020 ◽  
Author(s):  
J Kosinka ◽  
M Sabin ◽  
Neil Dodgson
Keyword(s):  
Control Points ◽  
Knot Insertion ◽  
Degree Polynomial ◽  
Arbitrary Degree ◽  
B Splines ◽  
Novel Approach ◽  
Low Degree ◽  
Subdivision Curves ◽  
Subspace Selection ◽  
Subdivision Rules

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

scholarly journals Creases and boundary conditions for subdivision curves

2021 ◽  
Author(s):  
J Kosinka ◽  
M Sabin ◽  
Neil Dodgson
Keyword(s):  
Control Points ◽  
Knot Insertion ◽  
Degree Polynomial ◽  
Arbitrary Degree ◽  
B Splines ◽  
Novel Approach ◽  
Low Degree ◽  
Subdivision Curves ◽  
Subspace Selection ◽  
Subdivision Rules

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

scholarly journals Creases and boundary conditions for subdivision curves

2020 ◽  
Author(s):  
J Kosinka ◽  
M Sabin ◽  
Neil Dodgson
Keyword(s):  
Control Points ◽  
Knot Insertion ◽  
Degree Polynomial ◽  
Arbitrary Degree ◽  
B Splines ◽  
Novel Approach ◽  
Low Degree ◽  
Subdivision Curves ◽  
Subspace Selection ◽  
Subdivision Rules

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

scholarly journals Creases and boundary conditions for subdivision curves

2021 ◽  
Author(s):  
J Kosinka ◽  
M Sabin ◽  
Neil Dodgson
Keyword(s):  
Control Points ◽  
Knot Insertion ◽  
Degree Polynomial ◽  
Arbitrary Degree ◽  
B Splines ◽  
Novel Approach ◽  
Low Degree ◽  
Subdivision Curves ◽  
Subspace Selection ◽  
Subdivision Rules

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points. The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points. © 2014 The Authors. Published by Elsevier Inc.

Application of Cubic B-Splines for Synthesis of Selective Signals

2007 ◽  
Vol 66 (12) ◽  
pp. 1047-1056 ◽  
Author(s):  
I. V. Strelkovskaya
Keyword(s):  
B Splines

B-splines on sparse grids for surrogates in uncertainty quantification

2021 ◽  
Vol 209 ◽  
pp. 107430
Author(s):  
Michael F. Rehme ◽  
Fabian Franzelin ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Sparse Grids ◽  
B Splines

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Extended isogeometric analysis using B++ splines for strong discontinuous problems

2021 ◽  
Vol 381 ◽  
pp. 113779
Author(s):  
Wenbin Hou ◽  
Kai Jiang ◽  
Xuefeng Zhu ◽  
Yuanxing Shen ◽  
Ping Hu
Keyword(s):  
Isogeometric Analysis ◽  
B Splines ◽  
Discontinuous Problems

scholarly journals Interpolation and Sampling with Exponential Splines of Real Order

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Peter Massopust
Keyword(s):  
Positive Real ◽  
B Splines

AbstractThe existence of fundamental cardinal exponential B-splines of positive real order $$\sigma $$ σ is established subject to two conditions on $$\sigma $$ σ and their construction is implemented. A sampling result for these fundamental cardinal exponential B-splines is also presented.

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