8,672 research outputs found
A trivariate interpolation algorithm using a cube-partition searching procedure
In this paper we propose a fast algorithm for trivariate interpolation, which
is based on the partition of unity method for constructing a global interpolant
by blending local radial basis function interpolants and using locally
supported weight functions. The partition of unity algorithm is efficiently
implemented and optimized by connecting the method with an effective
cube-partition searching procedure. More precisely, we construct a cube
structure, which partitions the domain and strictly depends on the size of its
subdomains, so that the new searching procedure and, accordingly, the resulting
algorithm enable us to efficiently deal with a large number of nodes.
Complexity analysis and numerical experiments show high efficiency and accuracy
of the proposed interpolation algorithm
Two-dimensional interpolation using a cell-based searching procedure
In this paper we present an efficient algorithm for bivariate interpolation,
which is based on the use of the partition of unity method for constructing a
global interpolant. It is obtained by combining local radial basis function
interpolants with locally supported weight functions. In particular, this
interpolation scheme is characterized by the construction of a suitable
partition of the domain in cells so that the cell structure strictly depends on
the dimension of its subdomains. This fact allows us to construct an efficient
cell-based searching procedure, which provides a significant reduction of CPU
times. Complexity analysis and numerical results show such improvements on the
algorithm performances
Surface Reconstruction from Scattered Point via RBF Interpolation on GPU
In this paper we describe a parallel implicit method based on radial basis
functions (RBF) for surface reconstruction. The applicability of RBF methods is
hindered by its computational demand, that requires the solution of linear
systems of size equal to the number of data points. Our reconstruction
implementation relies on parallel scientific libraries and is supported for
massively multi-core architectures, namely Graphic Processor Units (GPUs). The
performance of the proposed method in terms of accuracy of the reconstruction
and computing time shows that the RBF interpolant can be very effective for
such problem.Comment: arXiv admin note: text overlap with arXiv:0909.5413 by other author
Rapid evaluation of radial basis functions
Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example. the direct evaluation at M locations of a radial basis function interpolant with N centres requires O(M N) floating-point operations. In this paper we introduce a fast evaluation method based on the Fast Gauss Transform and suitable quadrature rules. This method has been applied to the Hardy multiquadric, the inverse multiquadric and the thin-plate spline to reduce the computational complexity of the interpolant evaluation to O(M + N) floating point operations. By using certain localisation properties of conditionally negative definite functions this method has several performance advantages against traditional hierarchical rapid summation methods which we discuss in detail
- …