Multivariate interpolation of large sets of scattered data
ACM Transactions on Mathematical Software (TOMS)
Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Free-form blending: a technique for creating piecewise implicit surfaces
Topics in surface modeling
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
An implicit surface polygonizer
Graphics gems IV
Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
Zippered polygon meshes from range images
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Implicit reconstruction of solids from cloud point sets
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th 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
Hierarchical scattered data filtering for multilevel interpolation schemes
Mathematical Methods for Curves and Surfaces
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
A Particle-Partition of Unity Method--Part III: A Multilevel Solver
SIAM Journal on Scientific Computing
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Proceedings of the conference on Visualization '01
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
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Progressive point set surfaces
ACM Transactions on Graphics (TOG)
Computing - Geometric Modelling, Dagstuhl 2008
Surface-normal estimation with neighborhood reorganization for 3D reconstruction
CIARP'07 Proceedings of the Congress on pattern recognition 12th Iberoamerican conference on Progress in pattern recognition, image analysis and applications
Multi-level partition of unity algebraic point set surfaces
Journal of Computer Science and Technology
SMI 2011: Full Paper: Harmonic point cloud orientation
Computers and Graphics
Wavelet frame based surface reconstruction from unorganized points
Journal of Computational Physics
Co-abstraction of shape collections
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
A Simulation System Based on OGRE and PhysX for Flexible Aircraft Assembly
PADS '12 Proceedings of the 2012 ACM/IEEE/SCS 26th Workshop on Principles of Advanced and Distributed Simulation
A Global Parity Measure for Incomplete Point Cloud Data
Computer Graphics Forum
SIGGRAPH Asia 2013 Technical Briefs
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We present a new shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape.Our approach gives us considerable flexibility in the choice of local shape functions, and in particular we can accurately represent sharp features such as edges and corners by selecting appropriate shape functions. An error-controlled subdivision leads to an adaptive approximation whose time and memory consumption depends on the required accuracy. Due to the separation of local approximation and local blending, the representation is not global and can be created and evaluated rapidly. Because our surfaces are described using implicit functions, operations such as shape blending, offsets, deformations and CSG are simple to perform.