Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Dynamic triangulation of variational implicit surfaces using incremental Delaunay tetrahedralization
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
Point-based modelling and rendering using radial basis functions
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Robust Creation of Implicit Surfaces from Polygonal Meshes
IEEE Transactions on Visualization and Computer Graphics
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit Snakes: Active Constrained Implicit Models
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Interactive shape design using volumetric implicit PDEs
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Surface reconstruction based on compactly supported radial basis functions
Geometric modeling
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
Interactive modelling from sketches using spherical implicit functions
AFRIGRAPH '04 Proceedings of the 3rd international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
VIS '04 Proceedings of the conference on Visualization '04
Surface Reconstruction of Noisy and Defective Data Sets
VIS '04 Proceedings of the conference on Visualization '04
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
3D scattered data interpolation and approximation with multilevel compactly supported RBFs
Graphical Models - Special issue on SMI 2003
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Reconstructing multi-scale variational partition of unity implicit surfaces with attributes
Graphical Models - Special issue on SMI 2004
Interactive editing of segmented volumetric datasets in a hybrid 2D/3D virtual environment
Proceedings of the ACM symposium on Virtual reality software and technology
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
Modelling with implicit surfaces that interpolate
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Some notes on radial basis functions and thin plate splines
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
A shape design system using volumetric implicit PDEs
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Multi-level partition of unity implicits
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Interpolating and approximating implicit surfaces from polygon soup
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Active contours using a constraint-based implicit representation
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
An extended level set method for shape and topology optimization
Journal of Computational Physics
Efficient preconditioning for image reconstruction with radial basis functions
Advances in Engineering Software
Technical Section: Stochastic visualization of intersection curves of implicit surfaces
Computers and Graphics
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A randomized knot insertion algorithm for outline capture of planar images using cubic spline
Proceedings of the 2007 ACM symposium on Applied computing
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Ridge based curve and surface reconstruction
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
EURASIP Journal on Applied Signal Processing
Technical Section: Progressive refinement rendering of implicit surfaces
Computers and Graphics
Efficient Surface Reconstruction using Generalized Coulomb Potentials
IEEE Transactions on Visualization and Computer Graphics
Implicit Surface Reconstruction from Scattered Point Data with Noise
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
Spectral moving removal of non-isolated surface outlier clusters
Computer-Aided Design
Duplex fitting of zero-level and offset surfaces
Computer-Aided Design
On surface reconstruction: A priority driven approach
Computer-Aided Design
Topology- and error-driven extension of scalar functions from surfaces to volumes
ACM Transactions on Graphics (TOG)
A hierarchical sampling approach for polygonizing variational implicit surfaces
Computers and Graphics
Efficient surface reconstruction from noisy data using regularized membrane potentials
IEEE Transactions on Image Processing
3D face model reconstruction from single 2D frontal image
Proceedings of the 8th International Conference on Virtual Reality Continuum and its Applications in Industry
LS-RBF network based 3D surface reconstruction method
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
Point sampled surface reconstruction based on local geometry
Edutainment'07 Proceedings of the 2nd international conference on Technologies for e-learning and digital entertainment
A system for reconstruction of solid models from large point clouds
Machine Graphics & Vision International Journal
Functional modelling of large scattered data sets using neural networks
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Narrow-band based radial basis functions implicit surface reconstruction
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Automation of the volumetric models construction
Heterogeneous objects modelling and applications
Geometric transformation of the RBF implicit surface
Proceedings of the 9th ACM SIGGRAPH Conference on Virtual-Reality Continuum and its Applications in Industry
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
Multi-level partition of unity algebraic point set surfaces
Journal of Computer Science and Technology
FIMH'11 Proceedings of the 6th international conference on Functional imaging and modeling of the heart
Orthogonal least square RBF based implicit surface reconstruction methods
VSMM'06 Proceedings of the 12th international conference on Interactive Technologies and Sociotechnical Systems
Practical boolean operations on point-sampled models
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Implicit surface boolean operations based cut-and-paste algorithm for mesh models
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Kd-tree based OLS in implicit surface reconstruction with radial basis function
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Hierarchically partitioned implicit surfaces for interpolating large point set models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
Journal of Computational Physics
Robust estimation of surface properties and interpolation of shadow/specularity components
Image and Vision Computing
Interactively visualizing procedurally encoded scalar fields
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Efficient surface reconstruction from noisy data using regularized membrane potentials
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Voronoi rasterization of sparse point sets
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
Efficient and prioritized point subsampling for CSRBF compression
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
Variational volumetric surface reconstruction from unorganized points
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
Journal of Scientific Computing
Multi-resolutive sparse approximations of d-dimensional data
Computer Vision and Image Understanding
Multi-level hermite variational interpolation and quasi-interpolation
The Visual Computer: International Journal of Computer Graphics
Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints
The Visual Computer: International Journal of Computer Graphics
Least-squares hermite radial basis functions implicits with adaptive sampling
Proceedings of Graphics Interface 2013
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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We describe algebraic methods for creating implicit surfaces using linear combinations of radial basis interpolants to form complex models from scattered surface points. Shapes with arbitrary topology are easily represented without the usual interpolation or aliasing errors arising from discrete sampling. These methods were first applied to implicit surfaces by Savchenko, et al. and later developed independently by Turk and O'Brien as a means of performing shape interpolation. Earlier approaches were limited as a modeling mechanism because of the order of the computational complexity involved. We explore and extend these implicit interpolating methods to make them suitable for systems of large numbers of scattered surface points by using compactly supported radial basis interpolants. The use of compactly supported elements generates a sparse solution space, reducing the computational complexity and making the technique practical for large models. The local nature of compactly supported radial basis functions permits the use of computational techniques and data structures such as k-d trees for spatial subdivision, promoting fast solvers and methods to divide and conquer many of the subproblems associated with these methods. Moreover, the representation of complex models permits the exploration of diverse surface geometry. This reduction in computational complexity enables the application of these methods to the study of shape properties of large complex shapes.