Polygonization of implicit surfaces
Computer Aided Geometric Design
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Approximation by superposition of sigmoidal and radial basis functions
Advances in Applied Mathematics
Proceedings of the sixth ACM symposium on Solid modeling and applications
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Proceedings of the conference on Visualization '01
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Shape-Preserving MQ-B-Splines Quasi-Interpolation
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
ACM SIGGRAPH 2004 Papers
Spectral surface reconstruction from noisy point clouds
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
3D scattered data interpolation and approximation with multilevel compactly supported RBFs
Graphical Models - Special issue on SMI 2003
Reconstructing multi-scale variational partition of unity implicit surfaces with attributes
Graphical Models - Special issue on SMI 2004
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
ACM SIGGRAPH 2007 papers
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Constructive approximate interpolation by neural networks
Journal of Computational and Applied Mathematics
Quasi-interpolation for data fitting by the radial basis functions
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
SMI 2011: Full Paper: Localized Cocone surface reconstruction
Computers and Graphics
Iterative Consolidation of Unorganized Point Clouds
IEEE Computer Graphics and Applications
Quasi-interpolation for surface reconstruction from scattered data with radial basis function
Computer Aided Geometric Design
Screened poisson surface reconstruction
ACM Transactions on Graphics (TOG)
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Based on the Hermite variational implicit surface reconstruction presented in Pan et al. (Science in China Series F: Information Sciences 52(2):308---315, 2009), we propose a multi-level interpolation method to overcome the problems resulted from using compactly supported radial basis functions (CSRBFs). In addition, we present a multi-level quasi-interpolation method which directly uses normal vectors to construct non-zero constraints and avoids solving any linear system, a common step of variational surface reconstruction, and leads to a fast and stable surface reconstruction from scattered points. With adaptive support size, our approach is robust and can successfully reconstruct surfaces on non-uniform and noisy point sets. Moreover, as the computation of quasi-interpolation is independent for each point, it can be easily parallelized on multi-core CPUs.