Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A variational approach to subdivision
Computer Aided Geometric Design
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computing vertex normals from polygonal facets
Journal of Graphics Tools
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
High-pass quantization for mesh encoding
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
ACM Transactions on Graphics (TOG)
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Direct manipulation of subdivision surfaces on GPUs
ACM SIGGRAPH 2007 papers
Loop subdivision with curvature control
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Tangent driven interpolative subdivision
Computers and Graphics
A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
Computers & Mathematics with Applications
Real-time gradient-domain painting
ACM SIGGRAPH 2008 papers
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
International Journal of Computer Applications in Technology
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH Asia 2008 papers
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
ACM SIGGRAPH 2009 papers
Normal based subdivision scheme for curve design
Computer Aided Geometric Design
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Subdivision surfaces for CAD-an overview
Computer-Aided Design
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Traditional subdivision schemes are applied on Euclidean coordinates (the spatial geometry of the control mesh). Although the subdivision limit surfaces are almost everywhere C^2 continuous, their mean-curvature normals are only C^0. In order to generate higher quality surfaces with better-distributed mean-curvature normals, we propose a novel framework to apply subdivision for shape modeling, which combines subdivision with differential shape processing. Our framework contains two parts: subdivision on differential coordinates (a kind of differential geometry of the control mesh), and mutual conversions between Euclidean coordinates and differential coordinates. Further discussions about various strategies in both parts include a special subdivision method for mean-curvature normals, additional surface editing options, and a version of our framework for curve design. Finally, we demonstrate the improvement on surface quality by comparing the results between our framework and traditional subdivision methods.