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
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
Localization of the generalized sampling series and its numerical application
SIAM Journal on Numerical Analysis
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
Uniform interpolation curves and surfaces based on a family of symmetric splines
Computer Aided Geometric Design
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An efficient scheme is introduced to construct interpolatory curves and surfaces passing through a set of given scattered data points. The scheme is based on an interpolatory basis derived from the sinc function with a Guassian multiplier previously applied in other fields for signal or function reconstruction. In connection with its application addressed in this article for spatial curve and surface construction, the interpolatory basis possesses various nice properties, such as partition of unity, linear precision, and local support, etc., under a small tolerance. By using these basis functions, free-form curves and surfaces can be conveniently constructed. A designer can adjust the shape of the constructed curve and surface by moving some interpolating points or by inserting new interpolating points. The resulting interpolatory curves and surfaces are C&infty; continuous. Smooth connection between curves or surfaces can easily be achieved. Closed curves and surfaces can also be expressed using the proposed interpolatory basis functions.