Non-uniform recursive Doo–Sabin surfaces

Huang, Zhangjin; Wang, Guoping

doi:10.1016/j.cad.2011.08.016

Cited by 11 publications

(6 citation statements)

References 9 publications

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“…without letting it fair out, or let the discontinuity to run (smoothly) through it (as in tensor product scenarios)? Our approach can be adapted to work for any other surface subdivision scheme based on B‐splines, e.g. [ZS01; HW11], since basically only knot insertion is required to be supported.…”

Section: Discussionmentioning

confidence: 99%

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Subdivision Surfaces with Creases and Truncated Multiple Knot Lines

Kosinka

Sabin

Dodgson

2013

Computer Graphics Forum

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We deal with subdivision schemes based on arbitrary degree B-splines. We focus on extraordinary knots which exhibit various levels of complexity in terms of both valency and multiplicity of knot lines emanating from such knots. The purpose of truncated multiple knot lines is to model creases which fair out. Our construction supports any degree and any knot line multiplicity and provides a modelling framework familiar to users used to B-splines and NURBS systems.

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Section: Discussionmentioning

confidence: 99%

“…More recently, Huang and Wang [HW11] extended Doo-Sabin subdivision to the non-uniform case, including double knot lines. This construction is limited to degree two only and lacks a complete continuity analysis.…”

Section: Related Workmentioning

confidence: 99%

Subdivision Surfaces with Creases and Truncated Multiple Knot Lines

Kosinka

Sabin

Dodgson

2013

Computer Graphics Forum

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“…Other constructions with crease support include NURSS [SZSS98], the schemes by Müller et al [MRF06, MFR * 10], and extended Doo-Sabin subdivision [HW11]. However, all these constructions are limited to degrees up to three.…”

Section: Related Workmentioning

confidence: 99%

Semi‐sharp Creases on Subdivision Curves and Surfaces

Kosinka

Sabin

Dodgson

2014

Computer Graphics Forum

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We explore a method for generalising Pixar semi-sharp creases from the univariate cubic case to arbitrary degree subdivision curves. Our approach is based on solving simple matrix equations. The resulting schemes allow for greater flexibility over existing methods, via control vectors. We demonstrate our results on several high-degree univariate examples and explore analogous methods for subdivision surfaces.

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“…Motivated by these observations and the fact that sharp rules have so far been limited to low-degree subdivision [7,1,17,15,16,11,10], we investigate a more general setting for introducing sharp creases and boundary interpolation rules in higher-degree spline curves. Our results then extend naturally to tensor-product surfaces and potentially to higher-degree subdivision surfaces, such as those by Stam [24] and Cashman [2].…”

Section: Introductionmentioning

confidence: 99%

Creases and boundary conditions for subdivision curves

Kosinka¹,

Sabin²,

Dodgson³

2021

Preprint

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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.

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Non-uniform recursive Doo–Sabin surfaces

Cited by 11 publications

References 9 publications

Subdivision Surfaces with Creases and Truncated Multiple Knot Lines

Subdivision Surfaces with Creases and Truncated Multiple Knot Lines

Semi‐sharp Creases on Subdivision Curves and Surfaces

Creases and boundary conditions for subdivision curves

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