Computer Aided Geometric Design - Special issue: Topics in CAGD
Local corner cutting and the smoothness of the limiting curve
Computer Aided Geometric Design
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution hierarchies on unstructured triangle meshes
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Local Control for Mesh Morphing
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Technical Section: Smooth reverse subdivision
Computers and Graphics
Smooth reverse Loop and Catmull-Clark subdivision
Graphical Models
A discrete approach to multiresolution curves and surfaces
Transactions on Computational Science VI
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
Special Section on Graphics Interface: Atlas of connectivity maps
Computers and Graphics
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Local fairing techniques are extensively used in the geometry processing of curves and surfaces. They also play an important role in the multiresolution shape editing and synthesis applications. However, due to the inter-dependency of the vertices after applying the current fairing techniques, their inverses are not local. Finding a local fairing operation with local inverse provides a well-defined relationship between the smooth vertices and the initial vertices. This paper introduces a new fairing operation for curves and surfaces that is smoothing and local but with a local inverse. In the curve domain, we find a class of banded smoothing matrices with banded inverses. Then, using the geometric interpretation of the corresponding local operation, this class is extended to surfaces. We discuss the advantages of using this new fairing operation in different applications. Also, the resulting operation is used to find novel subdivision schemes with well-defined reverse subdivisions.