A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Representing PDE surfaces in terms of B-splines
Computer-Aided Design
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
A variational approach to subdivision
Computer Aided Geometric Design
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A novel FEM-based dynamic framework for subdivision surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
G2 surface modeling using minimal mean-curvature-variation flow
Computer-Aided Design
Approximating Catmull-Clark subdivision surfaces with bicubic patches
ACM Transactions on Graphics (TOG)
Construction of minimal subdivision surface with a given boundary
Computer-Aided Design
Discrete bi-Laplacians and biharmonic b-splines
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Can Mean-Curvature Flow be Modified to be Non-singular?
Computer Graphics Forum
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Surface subdivision gains popularity in surface design owing to its flexible applications for geometry with complicated topology and simple computational scheme, and the geometric partial differential equation (GPDE) method is an advanced technology for constructing high-quality smooth surfaces. In this paper, we composite these two ingredients to form a unified method for freeform surface design. We choose the mean curvature flow and Willmore flow as our driven GPDEs, and the finite element method coupled with a hybrid Loop and Catmull-Clark subdivision algorithm as the numerical simulation method. This research presents a novel technique to evaluate the finite element basis functions and the first attempt for constructing the GPDE subdivision surface with hybrid control meshes consisting of triangles and quadrilaterals. Numerical experiments show that the construction method is efficient and robust, yielding high-quality hybrid subdivision surfaces.