Cubic recursive division with bounded curvature
Curves and surfaces
Simple regularity criteria for subdivision schemes
SIAM Journal on Mathematical Analysis
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Box splines
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
A variational approach to subdivision
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
Compactly supported tight affine spline frames in L2Rd
Mathematics of Computation
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Fine level feature editing for subdivision surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
Edge and vertex insertion for a class of C1 subdivision surfaces
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
Cut-and-paste editing of multiresolution surfaces
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Tutorials on Multiresolution in Geometric Modelling: Summer School Lectures Notes
Tutorials on Multiresolution in Geometric Modelling: Summer School Lectures Notes
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
A cascadic geometric filtering approach to subdivision
Computer Aided Geometric Design
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
Improved Triangular Subdivision Schemes
CGI '98 Proceedings of the Computer Graphics International 1998
Mesh mutation in programmable graphics hardware
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
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
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
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
Interpolatory quad/triangle subdivision schemes for surface design
Computer Aided Geometric Design
Deriving Box-Spline Subdivision Schemes
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Fast parallel construction of smooth surfaces from meshes with tri/quad/pent facets
SGP '08 Proceedings of the Symposium on Geometry Processing
Bi-frames with 4-fold axial symmetry for quadrilateral surface multiresolution processing
Journal of Computational and Applied Mathematics
Artifact analysis on B-splines, box-splines and other surfaces defined by quadrilateral polyhedra
Computer Aided Geometric Design
Artifact analysis on triangular box-splines and subdivision surfaces defined by triangular polyhedra
Computer Aided Geometric Design
An heuristic analysis of the classification of bivariate subdivision schemes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Artifacts in box-spline surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
An alternative method for constructing interpolatory subdivision from approximating subdivision
Computer Aided Geometric Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Mathematics and Computers in Simulation
A new interpolation subdivision scheme for triangle/quad mesh
Graphical Models
| Hi-index | 0.00 |
4-3 direction subdivision combines quad and triangle meshes. On quad submeshes it applies a 4-direction alternative to Catmull-Clark subdivision and on triangle submeshes a modification of Loop's scheme. Remarkably, 4-3 surfaces can be proven to be C1 and have bounded curvature everywhere. In regular mesh regions, they are C2 and correspond to two closely-related box-splines of degree four. The box-spline in quad regions has a smaller stencil than Catmull-Clark and defines the unique scheme with a 3 × 3 stencil that can model constant features without ripples both aligned with the quad grid and diagonal to it. From a theoretical point of view, 4-3 subdivision near extraordinary points is remarkable in that the eigenstructure of the local subdivision matrix is easy to determine and a complete analysis is possible. Without tweaking the rules artificially to force a specific spectrum, the leading eigenvalues ordered by modulus of all local subdivision matrices are 1, 1/2, 1/2, 1/4 where the multiplicity of the eigenvalue 1/4 depends on the valence of the extraordinary point and the number of quads surrounding it. This implies equal refinement of the mesh, regardless of the number of neighbors of a mesh node.