Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
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
Using a Fast Multipole Method to Accelerate Spline Evaluations
IEEE Computational Science & Engineering
The Integrated Delivery of Large-Scale Data Mining: The ACSys Data Mining Project
Revised Papers from Large-Scale Parallel Data Mining, Workshop on Large-Scale Parallel KDD Systems, SIGKDD
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode
SIAM Journal on Scientific Computing
A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters
SIAM Journal on Scientific Computing
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This paper presents a new method for the fast evaluation of univariate radial basis functions of the form $s(x) = \sum_{n=1}^N d_n \phi ( | x -x_n | ) $ to within accuracy $\epsilon$. The method can be viewed as a generalization of the fast multipole method in which calculations with far field expansions are replaced by calculations involving moments of the data. The method has the advantage of being adaptive to changes in $\phi$. That is, with this method changing to a new $\phi$ requires only coding a one- or two-line function for the (slow) evaluation of $\phi$. In contrast, adapting the usual fast multipole method to a new $\phi$ involves much mathematical analysis of appropriate series expansions and corresponding translation operators, followed by a substantial amount of work expressing this mathematics in code.