A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Interpolatory "2-Subdivision Surfaces
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
Exact evaluation of limits and tangents for non-polynomial subdivision schemes
Computer Aided Geometric Design
Parameterizing subdivision surfaces
ACM SIGGRAPH 2010 papers
Dinus: Double insertion, nonuniform, stationary subdivision surfaces
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Uniform interpolation curves and surfaces based on a family of symmetric splines
Computer Aided Geometric Design
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To avoid the potential distortion problem in curve and surface design, a set of improved basis functions is introduced to construct interpolatory curves and surfaces passing through given data points. Compared with the basis functions used in Zhang and Ma (2011) [33], the accuracy of the partition of unity of the improved basis functions exceeds the computation limit of the floating-point in common computers. Various properties, such as interpolatory property and infinite continuity, are still valid for the improved basis functions, and local support and linear precision are valid under a small tolerance. The method can not only prevent the Runge phenomenon, but also retains various desired operation properties, such as connecting different smooth curves or surfaces easily, constructing closed curves and surfaces conveniently, adjusting the shape of the curves or surfaces locally, etc. An interpolatory curve or surface constructed can be expressed by one equation, and is C^~ continuous. The method may be applied to the graphics community and other related fields.