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AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Procedural modeling facilities for hierarchical object generation
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AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Composite 2 subdivision surfaces
Computer Aided Geometric Design
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Computer Aided Geometric Design
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
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Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
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Composite √2 subdivision surfaces
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This paper presents a $\sqrt2$ subdivision scheme for quadrilateral meshes that can be regarded as an extension of a 4-8 subdivision with new subdivision rules and improved capability and performance. The proposed scheme adopts a so-called $\sqrt2$ split operator to refine a control mesh such that the face number of the refined mesh generally equals the edge number and is thus about twice the face number of the coarse mesh. Smooth rules are designed in reference to the 4-8 subdivision, while a new set of weights is developed to balance the flatness of surfaces at vertices of different valences. Compared to the 4-8 subdivision, the presented scheme can be naturally generalized for arbitrary control nets and is more efficient in both space and computing time management. Analysis shows that limit surfaces produced by the scheme are C4 continuous for regular control meshes and G1 continuous at extraordinary vertices.