A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
A G1 triangular spline surface of arbitrary topological type
Computer Aided Geometric Design
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Modelings surfaces from meshes of arbitrary topology
Computer Aided Geometric Design
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Curves and surfaces for CAGD: a practical guide
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A generic approach to free form surface generation
Proceedings of the seventh ACM symposium on Solid modeling and applications
Modeling with Triangular B-Splines
IEEE Computer Graphics and Applications
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Modeling surfaces of arbitrary topology using manifolds
Modeling surfaces of arbitrary topology using manifolds
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Graphical Models - Special issue on SPM 05
Parametrizations for triangular Gk spline surfaces of low degree
ACM Transactions on Graphics (TOG)
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Manifold splines with a single extraordinary point
Computer-Aided Design
Computer Aided Geometric Design
Computer Aided Geometric Design
C∞ smooth freeform surfaces over hyperbolic domains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Surface creation on unstructured point sets using neural networks
Computer-Aided Design
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We introduce a new manifold-based construction for fitting a smooth surface to a triangle mesh of arbitrary topology. Our construction combines in novel ways most of the best features of previous constructions and, thus, it fills the gap left by them. We also introduce a theoretical framework that provides a sound justification for the correctness of our construction. Finally, we demonstrate the effectiveness of our manifold-based construction with a few concrete examples.