Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Estimating surface normals in noisy point cloud data
Proceedings of the nineteenth annual symposium on Computational geometry
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Hierarchical Clustering for Unstructured Volumetric Scalar Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
IEEE Computer Graphics and Applications
Interpolating and approximating implicit surfaces from polygon soup
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Harmonic volumetric mapping for solid modeling applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
ACM SIGGRAPH 2007 papers
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
User-controllable polycube map for manifold spline construction
Proceedings of the 2008 ACM symposium on Solid and physical modeling
MLS-based scalar fields over triangle meshes and their application in mesh processing
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Surface Mapping Using Consistent Pants Decomposition
IEEE Transactions on Visualization and Computer Graphics
Technical Section: Computing smooth approximations of scalar functions with constraints
Computers and Graphics
Topology- and error-driven extension of scalar functions from surfaces to volumes
ACM Transactions on Graphics (TOG)
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Polyhedral finite elements using harmonic basis functions
SGP '08 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Technical Section: Feature-aligned harmonic volumetric mapping using MFS
Computers and Graphics
ACM Transactions on Graphics (TOG)
Template based shape descriptor
EG 3DOR'09 Proceedings of the 2nd Eurographics conference on 3D Object Retrieval
Interactively visualizing procedurally encoded scalar fields
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Uncertainty and variability in point cloud surface data
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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In this paper, we tackle the problem of computing a map that locally interpolates or approximates the values of a scalar function, which have been sampled on a surface or a volumetric domain. We propose a local approximation with radial basis functions, which conjugates different features such as locality, independence of any tessellation of the sample points, and approximation accuracy. The proposed approach handles maps defined on both 3D shapes and volumetric data and has extrapolation capabilities higher than linear precision methods and moving least-squares techniques with polynomial functions. It is also robust with respect to data discretization and computationally efficient through the solution of a small and well-conditioned linear system. With respect to previous work, it allows an easy control on the preservation of local details and smoothness through both interpolating and least-squares constraints. The main application we consider is the approximation of maps defined on grids, 3D shapes, and volumetric data.