Curve and surface constructions using rational B-splines
Computer-Aided Design
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Cubic recursive division with bounded curvature
Curves and surfaces
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Fast rendering of subdivision surfaces
Proceedings of the eurographics workshop on Rendering techniques '96
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Combined subdivision schemes for the design of surfaces satisfying boundary conditions
Computer Aided Geometric Design
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Approximate Boolean operations on free-form solids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Rapid evaluation of Catmull-Clark subdivision surfaces
Proceedings of the seventh international conference on 3D Web technology
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Normal bounds for subdivision-surface interference detection
Proceedings of the conference on Visualization '01
Computational Methods for Geometric Processing. Applications to Industry
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
Geometric Modelling, Dagstuhl, Germany, 1996
Eigenanalysis and Continuity of Non-Uniform Doo-Sabin Surfaces
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
ACM SIGGRAPH 2003 Papers
Modeling Subdivision Control Meshes for Creating Cartoon Faces
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
A generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
On the support of recursive subdivision
ACM Transactions on Graphics (TOG)
On C2 triangle/quad subdivision
ACM Transactions on Graphics (TOG)
Differentiable parameterization of Catmull-Clark subdivision surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Second order smoothness over extraordinary vertices
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
Extended subdivision surfaces: Building a bridge between NURBS and Catmull-Clark surfaces
ACM Transactions on Graphics (TOG)
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Computational formula of depth for Catmull-Clark subdivision surfaces
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
Distance between a Catmull-Clark subdivision surface and its limit mesh
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Interpolation by geometric algorithm
Computer-Aided Design
Constructing curvature-continuous surfaces by blending
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Loop subdivision with curvature control
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
ACM Transactions on Graphics (TOG)
Catmull-Clark subdivision for geometry shaders
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Improved error estimate for extraordinary Catmull–Clark subdivision surface patches
The Visual Computer: International Journal of Computer Graphics
On the curvature of guided surfaces
Computer Aided Geometric Design
Approximating Catmull-Clark subdivision surfaces with bicubic patches
ACM Transactions on Graphics (TOG)
Exact Evaluation of Non-Polynomial Subdivision Schemes at Rational Parameter Values
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Computer Aided Geometric Design
ACM SIGGRAPH 2008 papers
GPU conversion of quad meshes to smooth surfaces
Proceedings of the 2008 ACM symposium on Solid and physical modeling
ACM SIGGRAPH Asia 2008 papers
A bound on the approximation of a Catmull--Clark subdivision surface by its limit mesh
Computer Aided Geometric Design
Exact evaluation of limits and tangents for non-polynomial subdivision schemes
Computer Aided Geometric Design
Computer Aided Geometric Design
Subdivision Surfaces
Real-time creased approximate subdivision surfaces
Proceedings of the 2009 symposium on Interactive 3D graphics and games
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
ACM SIGGRAPH 2009 papers
Robustness of Boolean Operations on Subdivision-Surface Models
Numerical Validation in Current Hardware Architectures
Approximating subdivision surfaces with Gregory patches for hardware tessellation
ACM SIGGRAPH Asia 2009 papers
Adjustable speed surface subdivision
Computer Aided Geometric Design
C2 subdivision over triangulations with one extraordinary point
Computer Aided Geometric Design
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Surface interpolation of meshes by geometric subdivision
Computer-Aided Design
The distance of a subdivision surface to its control polyhedron
Journal of Approximation Theory
Efficient substitutes for subdivision surfaces
ACM SIGGRAPH 2009 Courses
G2 tensor product splines over extraordinary vertices
SGP '08 Proceedings of the Symposium on Geometry Processing
A graph based algorithm for intersection of subdivision surfaces
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
An appropriate geometric invariant for the C2-analysis of subdivision surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Parameterizing subdivision surfaces
ACM SIGGRAPH 2010 papers
Bounding the distance between a loop subdivision surface and its limit mesh
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Dinus: Double insertion, nonuniform, stationary subdivision surfaces
ACM Transactions on Graphics (TOG)
Analysis and Design of Univariate Subdivision Schemes
Analysis and Design of Univariate Subdivision Schemes
Analyzing midpoint subdivision
Computer Aided Geometric Design
Subdivision depth computation for extra-ordinary catmull-clark subdivision surface patches
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Fast intersections for subdivision surfaces
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Computing curvature bounds for bounded curvature subdivision
Computer Aided Geometric Design
Trimming for subdivision surfaces
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A unified interpolatory subdivision scheme for quadrilateral meshes
ACM Transactions on Graphics (TOG)
Technical note: A technical note on the geometric representation of a ship hull form
Computer-Aided Design
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
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Subdivision surfaces allow smooth free-form surface modelling without topological constraints. They have become a fundamental representation for smooth geometry, particularly in the animation and entertainment industries. This survey summarizes research on subdivision surfaces over the last 15 years in three major strands: analysis, integration into existing systems and the development of new schemes. We also examine the reason for the low adoption of new schemes with theoretical advantages, explain why Catmull–Clark surfaces have become a de facto standard in geometric modelling, and conclude by identifying directions for future research. © 2012 Wiley Periodicals, Inc.