Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
An implicit surface polygonizer
Graphics gems IV
Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Dual/Primal mesh optimization for polygonized implicit surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Dual contouring of hermite data
Proceedings of the 29th 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
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
ACM SIGGRAPH 2004 Papers
Context-based surface completion
ACM SIGGRAPH 2004 Papers
A meshless hierarchical representation for light transport
ACM SIGGRAPH 2008 papers
Computers & Mathematics with Applications
Duplex fitting of zero-level and offset surfaces
Computer-Aided Design
Robust mesh reconstruction from unoriented noisy points
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Topology- and error-driven extension of scalar functions from surfaces to volumes
ACM Transactions on Graphics (TOG)
Technical Section: Orienting unorganized points for surface reconstruction
Computers and Graphics
Invariant image reconstruction from irregular samples and hexagonal grid splines
Image and Vision Computing
Proceedings of the 7th International Conference on Computer Graphics, Virtual Reality, Visualisation and Interaction in Africa
Radial basis functions interpolation and applications: an incremental approach
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
A new approach for shape preserving interpolating curves
Computers & Mathematics with Applications
Defining, contouring, and visualizing scalar functions on point-sampled surfaces
Computer-Aided Design
Quasi-interpolation for surface reconstruction from scattered data with radial basis function
Computer Aided Geometric Design
Scattered data interpolation in N-dimensional space
SITE'12 Proceedings of the 11th international conference on Telecommunications and Informatics, Proceedings of the 11th international conference on Signal Processing
A Global Parity Measure for Incomplete Point Cloud Data
Computer Graphics Forum
A benchmark for surface reconstruction
ACM Transactions on Graphics (TOG)
Multi-level hermite variational interpolation and quasi-interpolation
The Visual Computer: International Journal of Computer Graphics
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Hi-index | 0.00 |
In this paper, we propose a hierarchical approach to 3D scattered data interpolation and approximation with compactly supported radial basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarse-to-fine hierarchy makes our method insensitive to the density of scattered data and allows us to restore large parts of missed data. Given a point cloud distributed over a surface, we first use spatial down sampling to construct a coarse-to-fine hierarchy of point sets. Then we interpolate (approximate) the sets starting from the coarsest level. We interpolate (approximate) a point set of the hierarchy, as an offsetting of the interpolating function computed at the previous level. The resulting fitting procedure is fast, memory efficient, and easy to implement.