SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Reversing subdivision rules: local linear conditions and observations on inner products
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Curvature and the Fairness of Curves and Surfaces
IEEE Computer Graphics and Applications
Area preserving deformation of multiresolution curves
Computer Aided Geometric Design
Sketch-based modeling with few strokes
Proceedings of the 21st spring conference on Computer graphics
Iris synthesis: a reverse subdivision application
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
A multi-level filtering approach for fairing planar cubic B-spline curves
Computer Aided Geometric Design
Technical Section: Multiresolution for curves and surfaces based on constraining wavelets
Computers and Graphics
Contextual void patching for digital elevation models
The Visual Computer: International Journal of Computer Graphics
Polygonal silhouette error correction: a reverse subdivision approach
International Journal of Computational Science and Engineering
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Technical Section: A multiresolution approach to iris synthesis
Computers and Graphics
Smooth reverse Loop and Catmull-Clark subdivision
Graphical Models
Local fairing with local inverse
Proceedings of Graphics Interface 2013
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In this paper we present a new multiresolution framework that takes into consideration reducing the coarse points' energy during decomposition. We start from initial biorthogonal filters to include energy minimization in multiresolution. Decomposition and reconstruction are main operations for any multiresolution representation. We formulate decomposition as smooth reverse subdivision, based on a least squares problem. Both approximation of overall shape and energy are taken into account in the least squares formulation through different weights. Using this method, significant smoothness in decomposition of curves and tensor product surfaces can be achieved; while their overall shape is preserved. Having smooth coarse points yields details with maximum characteristics. Our method works well with synthesizing applications in which re-using high-energy details is important. We use our method for finding the smooth reverse of three common subdivision schemes. We also provide examples of our method in curve synthesis and terrain synthesis applications.