The approximation power of moving least-squares
Mathematics of Computation
The use of positional information in the modeling of plants
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Moving Least Squares via Orthogonal Polynomials
SIAM Journal on Scientific Computing
Error Bounds for Least Squares Gradient Estimates
SIAM Journal on Scientific Computing
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Surface interpolation finds application in many aspects of science and technology. Two specific areas of interest are surface reconstruction techniques for plant architecture and approximating cell face fluxes in the finite volume discretisation strategy for solving partial differential equations numerically. An important requirement of both applications is accurate local gradient estimation. In surface reconstruction this gradient information is used to increase the accuracy of the local interpolant, while in the finite volume framework accurate gradient information is essential to ensure second order spatial accuracy of the discretisation. In this work two different least squares strategies for approximating these local gradients are investigated and the errors associated with each analysed. It is shown that although the two strategies appear different, they produce the same least squares error. Some carefully chosen case studies are used to elucidate this finding.