A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A closed algebraic interpolation curve
Computer Aided Geometric Design
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Proceedings of the conference on Visualization '01
A subdivision algorithm for computer display of curved surfaces.
A subdivision algorithm for computer display of curved surfaces.
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A variation on the interpolatory subdivision scheme [Labsik and Greiner 2000] is presented based on √3 subdivision and harmonic interpolation. Harmonic interpolation is generalized to triangle meshes based on a distance representation of the basis functions. The harmonic surface is approximated by limiting the support of the basis functions and the resulting surface is shown to satisfy necessary conditions for continuity. We provide subdivision rules for vertices of valence 3, 4 and 6 that can be applied directly to obtain a smooth surface. Other valences are handled as described in the literature. The resulting algorithm is easily implemented due to √3 subdivision and the simplicity of the stencils involved.