Surfaces over Dirichlet Tessellations
Computer Aided Geometric Design
Interpolation of scattered data on closed surfaces
Computer Aided Geometric Design
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Realistic, hardware-accelerated shading and lighting
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Physically-based visual simulation on graphics hardware
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Visualizing and Modeling Scattered Multivariate Data
IEEE Computer Graphics and Applications
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Using modern graphics architectures for general-purpose computing: a framework and analysis
Proceedings of the 35th annual ACM/IEEE international symposium on Microarchitecture
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Linear algebra operators for GPU implementation of numerical algorithms
ACM SIGGRAPH 2003 Papers
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Hierarchical Clustering for Unstructured Volumetric Scalar Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Interactively visualizing procedurally encoded scalar fields
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
A combined tactical and strategic hierarchical learning framework in multi-agent games
Sandbox '08 Proceedings of the 2008 ACM SIGGRAPH symposium on Video games
Gaussian KD-trees for fast high-dimensional filtering
ACM SIGGRAPH 2009 papers
GPU-based refraction and caustics rendering on depth textures
Proceedings of the 8th International Conference on Virtual Reality Continuum and its Applications in Industry
Scattered data interpolation and approximation for computer graphics
ACM SIGGRAPH ASIA 2010 Courses
Applying natural neighbor coordinates for electromagnetic tracker calibration
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
Issues and implementation of C1 and C2 natural neighbor interpolation
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Direct isosurface extraction from scattered volume data
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
On visualization and reconstruction from non-uniform point sets using B-splines
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d{\hbox{-}}\rm dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds.