Generalized stochastic subdivision
ACM Transactions on Graphics (TOG)
Generalized Hermite interpolation via matrix-valued conditionally positive definite functions
Mathematics of Computation
A comparison of four algorithms for estimating 3-D rigid transformations
BMVC '95 Proceedings of the 1995 British conference on Machine vision (Vol. 1)
Synthesizing realistic facial expressions from photographs
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Scattered data fitting on the sphere
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Solving partial differential equations by collocation using radial basis functions
Applied Mathematics and Computation
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
On-line locomotion generation based on motion blending
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Learning controls for blend shape based realistic facial animation
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
ACM SIGGRAPH 2003 Papers
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Radial Basis Functions
Modeling deformable human hands from medical images
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
Geostatistical motion interpolation
ACM SIGGRAPH 2005 Papers
Anisotropic point set surfaces
AFRIGRAPH '06 Proceedings of the 4th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
IEEE Transactions on Visualization and Computer Graphics
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Short note: A kernel independent fast multipole algorithm for radial basis functions
Journal of Computational Physics
Reflectance Sharing: Predicting Appearance from a Sparse Set of Images of a Known Shape
IEEE Transactions on Pattern Analysis and Machine Intelligence
Locally controllable stylized shading
ACM SIGGRAPH 2007 papers
Multi-scale capture of facial geometry and motion
ACM SIGGRAPH 2007 papers
Stability results for approximation by positive definite functions on SO (3)
Journal of Approximation Theory
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
Divergence-Free Kernel Methods for Approximating the Stokes Problem
SIAM Journal on Numerical Analysis
Radial basis collocation methods for elliptic boundary value problems
Computers & Mathematics with Applications
SIAM Journal on Numerical Analysis
Reduced surface point selection options for efficient mesh deformation using radial basis functions
Journal of Computational Physics
Efficient basis decomposition for scattered reflectance data
EGSR'07 Proceedings of the 18th Eurographics conference on Rendering Techniques
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
Proceedings of the 2011 SIGGRAPH Asia Conference
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The goal of scattered data interpolation techniques is to construct a (typically smooth) function from a set of unorganized samples. These techniques have a wide range of applications in computer graphics. For instance they can be used to model a surface from a set of sparse samples, to reconstruct a BRDF from a set of measurements, to interpolate motion capture data, or to compute the physical properties of a fluid. This course will survey and compare scattered interpolation algorithms and describe their applications in computer graphics. Although the course is focused on applying these techniques, we will introduce some of the underlying mathematical theory and briefly mention numerical considerations.