A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st 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
Matrix computations (3rd ed.)
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Interactive multi-resolution modeling on arbitrary meshes
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
Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Stationary Subdivision
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Progressive compression for lossless transmission of triangle meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Smooth patching of refined triangulations
ACM Transactions on Graphics (TOG)
Hybrid meshes: multiresolution using regular and irregular refinement
Proceedings of the eighteenth annual symposium on Computational geometry
Biorthogonal wavelets for subdivision volumes
Proceedings of the seventh ACM symposium on Solid modeling and applications
A multi-resolution topological representation for non-manifold meshes
Proceedings of the seventh ACM symposium on Solid modeling and applications
Dual/Primal mesh optimization for polygonized implicit surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the 15th annual ACM symposium on User interface software and technology
Refinement operators for triangle meshes
Computer Aided Geometric Design
The refinability of the four point scheme
Computer Aided Geometric Design
Mesh optimization using global error with application to geometry simplification
Graphical Models - Special issue: Processing on large polygonal meshes
Discretization of functionally based heterogeneous objects
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Dynamic remeshing and applications
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Triangular √3-subdivision schemes: the regular case
Journal of Computational and Applied Mathematics
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Non-linear subdivision using local spherical coordinates
Computer Aided Geometric Design
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Wavelet-Based Progressive Compression Scheme for Triangle Meshes: Wavemesh
IEEE Transactions on Visualization and Computer Graphics
A generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Shape from Contours and Multiple Stereo " A Hierarchical, Mesh-Based Approach
CRV '04 Proceedings of the 1st Canadian Conference on Computer and Robot Vision
A unified approach for fairing arbitrary polygonal meshes
Graphical Models
Subdivision scheme tuning around extraordinary vertices
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)
Automatic construction of control triangles for subdivided Powell-Sabin splines
Computer Aided Geometric Design
Planar Ego-Motion Without Correspondences
WACV-MOTION '05 Proceedings of the IEEE Workshop on Motion and Video Computing (WACV/MOTION'05) - Volume 2 - Volume 02
Silhouette and stereo fusion for 3D object modeling
Computer Vision and Image Understanding - Model-based and image-based 3D scene representation for interactive visalization
Proceedings of the 2005 ACM symposium on Solid and physical modeling
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
Real-Time Refinement and Simplification of Adaptive Triangular Meshes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Cloth animation with adaptively refined meshes
ACSC '05 Proceedings of the Twenty-eighth Australasian conference on Computer Science - Volume 38
A pattern-based data structure for manipulating meshes with regular regions
GI '05 Proceedings of Graphics Interface 2005
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
Evolutions of polygons in the study of subdivision surfaces
Computing - Geometric modelling dagstuhl 2002
Incompatible BLOCK: wonders accompanied interface
CHI '06 Extended Abstracts on Human Factors in Computing Systems
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Local subdivision of Powell-Sabin splines
Computer Aided Geometric Design
Jet subdivision schemes on the k-regular complex
Computer Aided Geometric Design
Refinable bivariate quartic and quintic C2-splines for quadrilateral subdivisions
Journal of Computational and Applied Mathematics
Towards fast and smooth subdivision surface reconstruction
International Journal of Computers and Applications
A mesh refinement library based on generic design
Proceedings of the 43rd annual Southeast regional conference - Volume 1
Parametrizations for triangular Gk spline surfaces of low degree
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2006 Courses
Meshing skin surfaces with certified topology
Computational Geometry: Theory and Applications
Modeling sphere-like manifolds with spherical Powell--Sabin B-splines
Computer Aided Geometric Design
Shape and View Independent Reflectance Map from Multiple Views
International Journal of Computer Vision
Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains
Journal of Computational and Applied Mathematics
Composite 2 subdivision surfaces
Computer Aided Geometric Design
ACM SIGGRAPH 2007 courses
Subdivision schemes and attractors
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Selectively refinable subdivision meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Interpolatory √3 subdivision with harmonic interpolation
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Towards flattenable mesh surfaces
Computer-Aided Design
Incremental subdivision for triangle meshes
International Journal of Computational Science and Engineering
Triangulation of hierarchical hexagon meshes
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Multiresolution sphere packing tree: a hierarchical multiresolution 3D data structure
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
Towards Efficiency in Cloth Simulation
AMDO '08 Proceedings of the 5th international conference on Articulated Motion and Deformable Objects
Exact evaluation of limits and tangents for non-polynomial subdivision schemes
Computer Aided Geometric Design
Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes
Computer Aided Geometric Design
Robust and scalable transmission of arbitrary 3D models over wireless networks
Journal on Image and Video Processing - 3D Image and Video Processing
Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems
ACM SIGGRAPH 2009 papers
Technical Section: Ternary butterfly subdivision
Computers and Graphics
Deriving Box-Spline Subdivision Schemes
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Loop subdivision surfaces interpolating B-spline curves
Computer-Aided Design
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Local subdivision of Powell--Sabin splines
Computer Aided Geometric Design
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
Jet subdivision schemes on the k-regular complex
Computer Aided Geometric Design
Subdivision surfaces for CAD-an overview
Computer-Aided Design
Computer Aided Geometric Design
Orthogonal and biorthogonal √3-refinement wavelets for hexagonal data processing
IEEE Transactions on Signal Processing
Progressive lossless mesh compression via incremental parametric refinement
SGP '09 Proceedings of the Symposium on Geometry Processing
Powell--Sabin spline based multilevel preconditioners for the biharmonic equation
Applied Numerical Mathematics
A novel adaptive algorithm of Catmull-Clark subdivision surfaces
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 5
Adaptive LOD editing of quad meshes
Proceedings of the 7th International Conference on Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa
Proceedings of the 9th ACM SIGGRAPH Conference on Virtual-Reality Continuum and its Applications in Industry
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Advances in Computational Mathematics
ACM Transactions on Graphics (TOG)
SMI 2011: Full Paper: Cyclic twill-woven objects
Computers and Graphics
Exact evaluation of limits and tangents for interpolatory subdivision surfaces at rational points
Journal of Computational and Applied Mathematics
Journal of Approximation Theory
Virtual interventions for image-based blood flow computation
Computer-Aided Design
Multi-step subdivision algorithm for chaikin curves
CIS'04 Proceedings of the First international conference on Computational and Information Science
A modified nielson's side-vertex triangular mesh interpolation scheme
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
A topological lattice refinement descriptor for subdivision schemes
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
An heuristic analysis of the classification of bivariate subdivision schemes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
A marching method for computing intersection curves of two subdivision solids
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Insight for practical subdivision modeling with discrete gauss-bonnet theorem
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Composite √2 subdivision surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Proceedings of the 7th international conference on Curves and Surfaces
OpenFlipper: an open source geometry processing and rendering framework
Proceedings of the 7th international conference on Curves and Surfaces
SMI 2012: Full Interpolating an arbitrary number of joint B-spline curves by Loop surfaces
Computers and Graphics
An alternative method for constructing interpolatory subdivision from approximating subdivision
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
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Isoparametric finite element analysis for Doo-Sabin subdivision models
Proceedings of Graphics Interface 2012
An overview of procedures for refining triangulations
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
A new progressive mesh with adaptive subdivision for LOD models
ICEC'07 Proceedings of the 6th international conference on Entertainment Computing
ACM: atlas of connectivity maps for semiregular models
Proceedings of Graphics Interface 2013
Technical Section: Adaptive cloth simulation using corotational finite elements
Computers and Graphics
A practical algorithm for rendering interreflections with all-frequency BRDFs
ACM Transactions on Graphics (TOG)
Special Section on Graphics Interface: Atlas of connectivity maps
Computers and Graphics
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
Connectivity editing for quad-dominant meshes
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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A new stationary subdivision scheme is presented which performs slower topological refinement than the usual dyadic split operation. The number of triangles increases in every step by a factor of 3 instead of 4. Applying the subdivision operator twice causes a uniform refinement with tri-section of every original edge (hence the name √3-subdivision) while two dyadic splits would quad-sect every original edge. Besides the finer gradation of the hierarchy levels, the new scheme has several important properties: The stencils for the subdivision rules have minimum size and maximum symmetry. The smoothness of the limit surface is C2 everywhere except for the extraordinary points where it is C1. The convergence analysis of the scheme is presented based on a new general technique which also applies to the analysis of other subdivision schemes. The new splitting operation enables locally adaptive refinement under built-in preservation of the mesh consistency without temporary crack-fixing between neighboring faces from different refinement levels. The size of the surrounding mesh area which is affected by selective refinement is smaller than for the dyadic split operation. We further present a simple extension of the new subdivision scheme which makes it applicable to meshes with boundary and allows us to generate sharp feature lines.