Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Free-form deformations with lattices of arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A new solid subdivision scheme based on box splines
Proceedings of the seventh ACM symposium on Solid modeling and applications
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Efficient mesh deformation using tetrahedron control mesh
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Subdivision schemes for the fair discretization of the spherical motion group
Journal of Computational and Applied Mathematics
Efficient mesh deformation using tetrahedron control mesh
Computer Aided Geometric Design
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We describe a new subdivision scheme for unstructured tetrahedral meshes. Previous tetrahedral schemes based on generalizations of box splines have encoded arbitrary directional preferences in their associated subdivision rules that were not reflected in tetrahedral base mesh. Our method avoids this choice of preferred directions resulting a scheme that is simple to implement via repeated smoothing. In an extended appendix, we analyze this tetrahedral scheme and prove that the scheme generates C2 deformations everywhere except along edges of the tetrahedral base mesh. Along edges shared by four or more tetrahedra in the base mesh, we present strong evidence that the scheme generates C1 deformations.