Using particles to sample and control implicit surfaces
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
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
SMI '03 Proceedings of the Shape Modeling International 2003
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Edge-sharpener: recovering sharp features in triangulations of non-adaptively re-meshed surfaces
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Direct Anisotropic Quad-Dominant Remeshing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics
Mesh massage: A versatile mesh optimization framework
The Visual Computer: International Journal of Computer Graphics
ACM SIGGRAPH 2009 papers
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Feature aligned quad dominant remeshing using iterative local updates
Computer-Aided Design
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Lp Centroidal Voronoi Tessellation and its applications
ACM SIGGRAPH 2010 papers
Piecewise Linear Orthogonal Approximation
SIAM Journal on Numerical Analysis
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Remeshing aims to produce a more regular mesh from a given input mesh, while representing the original geometry as accurately as possible. Many existing remeshing methods focus on where to place new mesh vertices; these samples are placed exactly on the input mesh. However, considering the output mesh as a piecewise linear approximation of some geometry, this simple scheme leads to significant systematic error in non-planar regions. Here, we use parameterised meshes and the recent mathematical development of orthogonal approximation using Sobolev-type inner products to develop a novel sampling scheme which allows vertices to lie in space near the input surface, rather than exactly on it. The algorithm requires little extra computational effort and can be readily incorporated into many remeshing approaches. Experimental results show that on average, approximation error can be reduced by 40% with the same number of vertices.