A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
On calculating normalized Powell-Sabin B-splines
Computer Aided Geometric Design
Subdivision of uniform Powell—Sabin splines
Computer Aided Geometric Design
Modelings surfaces from meshes of arbitrary topology
Computer Aided Geometric Design
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Computer Aided Geometric Design
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Developments in bivariate spline interpolation
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Proceedings of the seventh ACM symposium on Solid modeling and applications
Polynomial Surfaces Interpolating Arbitrary Triangulations
IEEE Transactions on Visualization and Computer Graphics
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Automatic construction of control triangles for subdivided Powell-Sabin splines
Computer Aided Geometric Design
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Proceedings of the 2007 ACM symposium on Solid and physical modeling
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Manifold splines with a single extraordinary point
Computer-Aided Design
Computer-Aided Design
Quasi-hierarchical Powell--Sabin B-splines
Computer Aided Geometric Design
Harmonic 1-form based skeleton extraction from examples
Graphical Models
Technical Section: Geometry-aware domain decomposition for T-spline-based manifold modeling
Computers and Graphics
A normalized basis for quintic Powell--Sabin splines
Computer Aided Geometric Design
On the local approximation power of quasi-hierarchical powell-sabin splines
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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Converting point samples and/or triangular meshes to a more compact spline representation for arbitrarily topology is both desirable and necessary for computer vision and computer graphics. This paper presents a C1 manifold interpolatory spline that can exactly pass through all the vertices and interpolate their normals for data input of complicated topological type. Starting from the Powell-Sabin spline as a building block, we integrate the concepts of global parametrization, affine atlas, and splines defined over local, open domains to arrive at an elegant, easy-to-use spline solution for complicated datasets. The proposed global spline scheme enables the rapid surface reconstruction and facilitates the shape editing and analysis functionality.