Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

Cashman, Thomas J.

doi:10.1111/j.1467-8659.2011.02083.x

Cited by 41 publications

(25 citation statements)

References 127 publications

(158 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We refer the reader to a recent survey [Cashman 2012] for a general overview of recent work on subdivision; here we focus on the most closely related work on subdivision schemes allowing nonuniform knot spacing on the one hand, and schemes for constructing smooth surfaces on T-meshes on the other hand.…”

Section: Related Workmentioning

confidence: 99%

Dyadic T-mesh subdivision

Kovacs¹,

Bisceglio

Zorin

2015

ACM Trans. Graph.

View full text Add to dashboard Cite

Meshes with T-joints (T-meshes) and related high-order surfaces have many advantages in situations where flexible local refinement is needed. At the same time, designing subdivision rules and bases for T-meshes is much more difficult, and fewer options are available. For common geometric modeling tasks it is desirable to retain the simplicity and flexibility of commonly used subdivision surfaces, and extend them to handle T-meshes.We propose a subdivision scheme extending Catmull-Clark and NURSS to a special class of quad T-meshes, dyadic T-meshes, which have no more than one T-joint per edge. Our scheme is based on a factorization with the same structure as Catmull-Clark subdivision. On regular T-meshes it is a refinement scheme for a subset of standard T-splines. While we use more variations of subdivision masks compared to Catmull-Clark and NURSS, the minimal size of the stencil is maintained, and all variations in formulas are due to simple changes in coefficients.

show abstract

Section: Related Workmentioning

confidence: 99%

Dyadic T-mesh subdivision

Kovacs¹,

Bisceglio

Zorin

2015

ACM Trans. Graph.

View full text Add to dashboard Cite

show abstract

“…The same idea was also extended to surfaces for refining control meshes of arbitrary topology [Prautzsch 1998;Zorin and Schröder 2001;Warren and Weimer 2001;Stam 2001]. In regular regions, all these schemes can generate tensor-product B-splines of any specified degree [Cashman 2012] and Prautzsch and Chen [2011] proved C 1 continuity at extraordinary vertices in case of midpoint subdivision for all degrees ≥2. Similar methods are also developed for subdivision schemes on triangular meshes with 1-4 splitting [Stam 2001] and √ 3-subdivision [Oswald and Schröder 2003].…”

Section: Introductionmentioning

confidence: 93%

A unified interpolatory subdivision scheme for quadrilateral meshes

Deng

2013

ACM Trans. Graph.

View full text Add to dashboard Cite

For approximating subdivision schemes, there are several unified frameworks for effectively constructing subdivision surfaces generalizing splines of an arbitrary degree. In this article, we present a similar unified framework for interpolatory subdivision schemes. We first decompose the 2n-point interpolatory curve subdivision scheme into repeated local operations. By extending the repeated local operations to quadrilateral meshes, an efficient algorithm can be further derived for interpolatory surface subdivision. Depending on the number n of repeated local operations, the continuity of the limit curve or surface can be of an arbitrary order C L , except in the surface case at a limited number of extraordinary vertices where C 1 continuity with bounded curvature is obtained. Boundary rules built upon repeated local operations are also presented. ACM Reference Format:Deng, C. and Ma, W. 2013. A unified interpolatory subdivision scheme for quadrilateral meshes.

show abstract

“…See recent surveys for more detailed information [Cas12,ZS00]. meshes, while the Loop scheme is a popular subdivision scheme for triangle meshes.…”

Section: Related Workmentioning

confidence: 99%

“…Especially, the Catmull-Clark scheme has been a default standard for the geometric modeling and has surprisingly close-tooptimal properties [Cas12], while it is one of earliest subdivision schemes. Especially, the Catmull-Clark scheme has been a default standard for the geometric modeling and has surprisingly close-tooptimal properties [Cas12], while it is one of earliest subdivision schemes.…”

Section: Introductionmentioning

confidence: 99%

TSS BVHs: Tetrahedron Swept Sphere BVHs for Ray Tracing Subdivision Surfaces

Kim

Yoon

2016

Computer Graphics Forum

View full text Add to dashboard Cite

We present a novel, compact bounding volume hierarchy, TSS BVH, for ray tracing subdivision surfaces computed by the Catmull-Clark scheme. We use Tetrahedron Swept Sphere (TSS) as a bounding volume to tightly bound limit surfaces of such subdivision surfaces given a user tolerance. Geometric coordinates defining our TSS bounding volumes are implicitly computed from the subdivided mesh via a simple vertex ordering method, and each level of our TSS BVH is associated with a single distance bound, utilizing the Catmull-Clark scheme. These features result in a linear space complexity as a function of the tree depth, while many prior BVHs have exponential space complexity. We have tested our method against different benchmarks with path tracing and photon mapping. We found that our method achieves up to two orders of magnitude of memory reduction with a high culling ratio over the prior AABB BVH methods, when we represent models with two to four subdivision levels. Overall, our method achieves three times performance improvement thanks to these results. These results are acquired by our theorem that rigorously computes our TSS bounding volumes.

show abstract

Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

Cited by 41 publications

References 127 publications

Dyadic T-mesh subdivision

Dyadic T-mesh subdivision

A unified interpolatory subdivision scheme for quadrilateral meshes

TSS BVHs: Tetrahedron Swept Sphere BVHs for Ray Tracing Subdivision Surfaces

Contact Info

Product

Resources

About