Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Robust ray intersection with interval arithmetic
Proceedings on Graphics interface '90
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)
Surface fitting to scattered data by a sum of Gaussians
Computer Aided Geometric Design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st 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
Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Fast Evaluation of Radial Basis Functions: Moment-Based Methods
SIAM Journal on Scientific Computing
The approximation power of moving least-squares
Mathematics of Computation
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Surfels: surface elements as rendering primitives
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Delaunay based shape reconstruction from large data
PVG '01 Proceedings of the IEEE 2001 symposium on parallel and large-data visualization and graphics
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Real-time 3D model acquisition
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)
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Adaptive thinning for bivariate scattered data
Journal of Computational and Applied Mathematics
Ray Tracing Point Sampled Geometry
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Proceedings of the 12th Eurographics Workshop on Rendering Techniques
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
3L Fitting of Higher Degree Implicit Polynomials
WACV '96 Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (WACV '96)
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Consensus Surfaces for Modeling 3D Objects from Multiple Range Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
ACM SIGGRAPH 2004 Papers
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Point based animation of elastic, plastic and melting objects
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Adaptive sampling of intersectable models exploiting image and object-space coherence
Proceedings of the 2005 symposium on Interactive 3D graphics and games
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Point-based multiscale surface representation
ACM Transactions on Graphics (TOG)
Reconstructing multi-scale variational partition of unity implicit surfaces with attributes
Graphical Models - Special issue on SMI 2004
A real time human grasp simulation with deformable fingertips
MS'06 Proceedings of the 17th IASTED international conference on Modelling and simulation
Provably good moving least squares
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
An effective condition for sampling surfaces with guarantees
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
ACM SIGGRAPH 2007 papers
Direct visibility of point sets
ACM SIGGRAPH 2007 papers
Non-conforming surface representations
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Provably good moving least squares
ACM Transactions on Algorithms (TALG)
Real-Time Point-Based Rendering Using Visibility Map
IEICE - Transactions on Information and Systems
Generating parametric models of tubes from laser scans
Computer-Aided Design
Point cloud surfaces using geometric proximity graphs
Computers and Graphics
Dynamic surfel set refinement for high-quality rendering
Computers and Graphics
A survey of point-based techniques in computer graphics
Computers and Graphics
Surface processing methods for point sets using finite elements
Computers and Graphics
Narrow-band based radial basis functions implicit surface reconstruction
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
Defining, contouring, and visualizing scalar functions on point-sampled surfaces
Computer-Aided Design
SMI 2011: Full Paper: Geometric models with weigthed topology
Computers and Graphics
Graph-based representations of point clouds
Graphical Models
Bayesian mesh reconstruction from noisy point data
ICAT'06 Proceedings of the 16th international conference on Advances in Artificial Reality and Tele-Existence
Curvature estimation of point-sampled surfaces and its applications
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Hardware-accelerated extraction and rendering of point set surfaces
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Uncertainty and variability in point cloud surface data
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Proximity graphs for defining surfaces over point clouds
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Finite elements on point based surfaces
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Interactive ray tracing of point-based models
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
A sampling theorem for MLS surfaces
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
Computing variation modes for point set surfaces
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
Splat/mesh blending, perspective rasterization and transparency for point-based rendering
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
A benchmark for surface reconstruction
ACM Transactions on Graphics (TOG)
SMI 2013: Adequate inner bound for geometric modeling with compact field functions
Computers and Graphics
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Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted co-variances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zero-set is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted co-variances are well defined in a tubular neighborhood of the surface. For certain, well-chosen weight functions we can show that well-sampled surfaces lead to smooth distance fields with non-zero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute ray-surface intersections for fast ray casting and ray tracing of the surface.