Questions tagged [interpolation]
Interpolation is the process of estimating the values of a function, when the function's values are known only at a particular set of points. Questions on interpolation in one or more dimensions, as well as algorithms for doing so, should have this tag.
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B-Spline basis on a 3D mesh
I need to interpolate some (sparse) data scattered on a 3D manifold mesh. In other words, I have a scattered interpolation problem where the input values are defined for some vertices of the mesh. ...
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Interpolation constant on triangles
There are quite a few references regarding the estimation for the interpolation error for the piece-wise affine finite elements. I find one particular estimate interesting (and useful in my case), ...
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Extending Matlab's pchip to 2D
In The Matlab Guide, chapter 3, section 4, Moler describes a piecewise cubic Hermite interpolator $i$ which
Never leaves the data bounds on each subinterval, e.g. $t \in [t_k, t_{k+1}] \implies i(t) \...
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Nodal functionals in finite element analysis
I have a quintic Hermite basis functions [-1,1] for FEM applications, I wanted to check if it's nodal functionals are proper. Could someone explain nodal functionals in details and give an example of ...
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Quintic Hermite shape functions
I am trying to use quintic Hermite basis functions for FEM applications, could someone please direct me to the general formula that would help me generate quintic Hermite shape functions?
In natural ...
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shape functions of interpolating a piecewise polynomial with continuous 0-th and 1-st derivatives
shape functions are the basis functions that interpolate a function in a subdomain using polynomials. linear interpolation is probably the most convenient approach which results in so-called "...
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Why weighted harmonic mean for pchip slopes leads to monotone interpolator
In Fritsch and Carlson's paper on monotone interpolation, they identify numerous conditions under which a cubic Hermite interpolator will be monotone. For example: On the subinterval $[t_i, t_{i+1}]$ ...
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Conservative interpolation from a 1D grid to another 1D grid
I am given with a function $f(x)$ on a grid $X_{old}\in \{x_{min},x_{max}\}$ with a non uniform spacing.
I need to interpolate that function on a new log-spaced grid $X_{new}\in\{x^{\prime}_{min},x^{\...
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Chebyshev/Lagrange polynomials in spectral methods
I am currently trying to familiarise myself with (Pseudo-)Spectral Methods for solving differential equations. Now, I am struggling to understand some obviously crucial concept of this approach. The ...
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Interpolating 2D data on a hemisphere in order to have $C^2$ function but no overshoot
I am interpolating a 2D dataset on a hemisphere, and I am currently using scipy.Rbf that I like for its simplicity.
I am defining the norm of the interpolator with ...
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If FEM is exact at the nodes, why do first and second-order elements give very different results?
I'm looking at the solution to a structural mechanics problem that is modeled with first-order elements and then as a comparison with second-order elements. It is clear that the first-order elements ...
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Is 'natural neighbor' interpolation better than linear for unstructured function interpolation?
Natural neighbor interpolation is defined here, it is an intriguing method that uses voronoi diagrams. Notably it is smooth almost everywhere whereas linear interpolation is only piecewise linear. I ...
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Modal representations of nodal tensor product Galerkin elements
Nodal discontinuous Galerkin methods on simplices, like those described in Hesthaven and Warburton, have the nice property that the number of nodes is equal to the minimum number needed to represent a ...
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Integral from function approximations
I have some data which I cannot manage to model and fit with a known function, so let’s say that they are a sample from the unknow function $f(x)$, which look a sort of skewed bell-shaped distribution....
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Fitting a monotonically increasing spline function
I want to fit a monotonically increasing smooth spline function for a dataset
Code:
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