Polyhedral subdivision methods for free-form surfaces
ACM Transactions on Graphics (TOG)
Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th 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
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
G2 surface modeling using minimal mean-curvature-variation flow
Computer-Aided Design
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes
Computers & Mathematics with Applications
Construction of minimal catmull-clark's subdivision surfaces with given boundaries
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Construction of subdivision surfaces by fourth-order geometric flows with G1 boundary conditions
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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We present a scheme that combines the subdivision technique and the geometric partial differential equations method which provides us an efficient algorithm for designing high-quality surfaces with arbitrary topology structure. We use several fourth-order geometric partial differential equations to construct Catmull-Clark's subdivision surfaces with prescribed G^1 boundary conditions where a mixed finite element method is based on the modified Catmull-Clark's subdivision scheme. Our approach can uniformly handle surface construction both with specified boundary normals and with interior sharp edges, which is a powerful tool for designing the shape of surfaces.