Multirate systems and filter banks
Multirate systems and filter banks
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Matrix computations (3rd ed.)
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th 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
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Multirate Digital Signal Processing
Multirate Digital Signal Processing
Optimal Surface Smoothing as Filter Design
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
A Discrete Spring Model for Generating Fair Curves and Surfaces
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Fast, robust, and faithful methods for detecting crest lines on meshes
Computer Aided Geometric Design
A new digital watermarking scheme for 3D triangular mesh models
Signal Processing
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The dual of a 2-manifold polygonal mesh without boundary is commonly defined as another mesh with the same topology (genus) but different connectivity (vertex-face incidence), in which faces and vertices occupy complementary locations and the position of each dual vertex is computed as the center of mass (barycenter or centroid) of the vertices that support the corresponding face. This barycenter dual mesh operator is connectivity idempotent but not geometrically idempotent for any choice of vertex positions, other than constants. In this paper we construct a new resampling dual mesh operator that is geometrically idempotent for the largest possible linear subspace of vertex positions. We look at the primal and dual mesh connectivities as irregular sampling spaces and at the rules to determine dual vertex positions as the result of a resampling process that minimizes signal loss. Our formulation, motivated by the duality of Platonic solids, requires the solution of a simple least-squares problem. We introduce a simple and efficient iterative algorithm closely related to Laplacian smoothing and with the same computational cost. We also characterize the configurations of vertex positions where signal loss does and does not occur during dual mesh resampling and the asymptotic behavior of iterative dual mesh resampling in the general case. Finally, we describe the close relation existing with discrete fairing and variational subdivision, and define a new primal-dual interpolatory recursive subdivision scheme.