Composite primal/dual \(\sqrt 3\)-subdivision schemes

DOI10.1016/S0167-8396(03)00026-8zbMath1069.65562OpenAlexW2068264968MaRDI QIDQ2388501

Peter Schröder, Peter Oswald

Publication date: 14 September 2005

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-8396(03)00026-8

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (19)

Highly symmetric \(\sqrt{3}\)-refinement bi-frames for surface multiresolution processing ⋮ BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING ⋮ A generative classification of mesh refinement rules with lattice transformations ⋮ Refinability of splines derived from regular tessellations ⋮ Biorthogonal wavelets with 4-fold axial symmetry for quadrilateral surface multiresolution processing ⋮ Convergence analysis of regular dynamic Loop-like subdivision scheme ⋮ Variations on the four-point subdivision scheme ⋮ Surface subdivision schemes generated by refinable bivariate spline function vectors ⋮ Repeated local operations and associated interpolation properties of dual \(2n\)-point subdivision schemes ⋮ Four-point \(n\)-ary interpolating subdivision schemes ⋮ Subdivision schemes with general dilation in the geometric and nonlinear setting ⋮ Triangular \(\sqrt 7\) and quadrilateral \(\sqrt 5\) subdivision schemes: regular case ⋮ A bivariate \(C^1\) subdivision scheme based on cubic half-box splines ⋮ Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices ⋮ Composite \(\sqrt{2}\) subdivision surfaces ⋮ Quasi-interpolating bivariate dual \(\sqrt{ 2}\)-subdivision using 1D stencils ⋮ Designing composite triangular subdivision schemes ⋮ Matrix-valued symmetric templates for interpolatory surface subdivisions. I: Regular vertices ⋮ Interpolatory ternary subdivision surfaces

Cites Work

• A unified approach to subdivision algorithms near extraordinary vertices
• Regularity of irregular subdivision
• Triangular \(\sqrt 3\)-subdivision schemes: The regular case
• Analyzing the characteristic map of triangular subdivision schemes
• A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
• A Method for Analysis ofC¹-Continuity of Subdivision Surfaces
• Quasi 4--8 subdivision
• On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
• A unified framework for primal/dual quadrilateral subdivision schemes

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