A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
A generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Concentric tessellation maps and curvature continuous guided surfaces
Computer Aided Geometric Design
Computer Aided Geometric Design
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Recent methods for tuning a subdivision scheme create a concentric wave pattern around the extraordinary vertex (EV). We explain it as resulting from the antagonism between the rules which would create a nice limit surface at the EV and the ordinary rules used in the surrounding regular surface. We show that even a scheme which fulfils the most recently proposed conditions for good convergence at the EV may still produce this wave pattern. Then, in order to smooth this antagonism, we define any new vertex as a convex combination of the ideal new vertex from the EV point of view and the one defined with ordinary rules. The weight of the extraordinary rules decreases as the new vertex is topologically farther from the EV. The concentric wave pattern shades off whereas the expected conditions are not too much spoiled. This tuning method remains simple and useful, involving no optimisation process.