Area and Length Preserving Geometric Invariant Scale-Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Generating Fair Meshes with G1 Boundary Conditions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
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
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
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In this paper, we present a method for constructing Loop's subdivision surface patches with given G1 boundary conditions and a given topology of control polygon, using several fourth-order geometric partial differential equations. These equations are solved by a mixed finite element method in a function space defined by the extended Loop's subdivision scheme. The method is flexible to the shape of the boundaries, and there is no limitation on the number of boundary curves and on the topology of the control polygon. Several properties for the basis functions of the finite element space are developed.