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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Cressman interpolation and objective analysis

I have read this question and answer – Interpolation of scattered data to a regular grid in python and I am doing something similar as I have temperature values of the atmosphere at different heights ...
gansub's user avatar
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Integrating highly oscillatory functions

I have a logarithmic grid, upon which i have two functions that are similar to this one (this is only the last 100 points): These are essentially very similar to a Sin function at this point. I need ...
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Padua-type pointset for functions singular on line $x=y$

The Padua points $\mathrm{Pad}_{n} \subset [-1,1]^{2}$ are a unisolvent pointset with optimal growth of Lebesgue constant, described in detail here. With some work they can be used to generate a ...
user14717's user avatar
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How to optimally choose points for multivariable Hermite interpolation?

I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input. I would like to create interpolation polynomial for it. In one-dimensional case ...
Moonwalker's user avatar
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How do I perform chebyshev interpolation from a to b with custom angle range?

Typically Chebyshev interpolation from $-1$ to $1$ with angle from $0$ to $\pi$: $\xi_j=\cos \left ({\pi j \over N}\right )$ $x_j=(1+\xi_j) * {L \over 2}$ $w$: $w_0=\pi/(2N)$ $w_{1,...,N-1}=\pi/(N)$...
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Can I make this numerical integration continuously differentiable?

Suppose I have the discrete values $f(x_i)$ for every discrete value $x_i$ greater than some $\varepsilon$, and I want to numerically calculate the following integral: \begin{equation} n = \int_\...
Maziar Noei's user avatar
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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 $[t_i, t_{i+1}]$ ...
user14717's user avatar
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Derivative of Whittaker-Shannon interpolant

Last time we looked at how to improve the accuracy of Whittaker-Shannon interpolation, where user njuffa demonstrated that judicious use of sin_pi could greatly ...
user14717's user avatar
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WENO5 scheme in a staggered grid

I'm trying to use the finite-difference WENO scheme to solve the 2D density conservation law with axial symmetry (coordinates $r,z$): $\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho \vec{v}) = \...
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1D irregular interpolation with $O(1)$ or $O(\log(N))$ evaluation

In Floater's paper on barycentric rational interpolation, he shows that a stable interpolant using irregularly space points can be evaluated in $O(N)$ operations. For equally spaces samples, cubic b-...
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Gradients of non-uniformly sampled data in 3D space

I have measurements of magnetic field on a 3d grid. My measurements are distributed on four x-y planes similar to what is shown in the image below. The measurements roughly follow a Cartesian grid but ...
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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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How can I reduce the artifact in "Thin Plate Spline" interpolation?

At the Top "right", there is the 2D-density plot of the recorded data (actual), fewer in number. Recorded data has been sampled a on the 8 arms of a regular octagon. These 8 arms are placed ...
Subhadip Saha's user avatar
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Are planar 2nd order NURBS curve segments exactly the segments of conic sections?

I think it is well known that 2nd order NURBS curve can describe any segment of a conic section. Such a segment has 7 degrees of freedom, take an ellipse arc for example: the ellipse itself has 5 ...
Thomas Klimpel's user avatar
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1-D local interpolation of sampled function that is polynomial in 1/x

I have a number of evenly-spaced samples of functions that are polynomial in $1/x$ where $x$ is a continuous variable on $x\in\left[a,b\right]$, i.e. $$f(x_i)=\sum_{n=0}^{N} f_n x_i^{-n}.$$ I want to ...
coolguy1000000's user avatar
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trigonometric interpolation with non-equidistant sampling

I want to interpolate a periodic function on a non-equidistant grid and have implemented it the using the Lagrangian formula described in wikipedia. For an odd number of data points, this takes the ...
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Choosing suitable polynomial degree based on information in advection stencil

I'm working on a finite volume advection scheme for unstructured meshes which uses a multidimensional polynomial weighted least squares fit for interpolating from cell centres onto faces. In 2D, the ...
hertzsprung's user avatar
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NURBS surface fitting for a closed region on mesh

I'm developing a tool that allows users to select a closed boundary (a polygon) on the triangle mesh and then from this boundary, generate a NURBS surface fitting the original mesh surface. My idea ...
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How do I implement thin plate splines with barriers?

I want to implement thin spline interpolation of scattered elevation data $ \{z_i(x_i,y_i)\}_{i=1..n} $ in C++. This seems fairly simple using Radial Basis Functions: $$ z(x,y) = p(x,y) + \sum_i l_i\...
Andy's user avatar
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Propogated Error in Mesh Interpolation

I am working with a code that solves diffusion/reaction equations on a 2D unstructured mesh. Due to the stiffness of some of the processes, I start with time steps near 1e-13, and end with a final ...
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Resampling of values between body fitted and cartesian grids

Assuming there exist two 2D grids on the same domain, one of them is a cartesian one while the other is curvilinear (body fitted regular grid, with curved coordinate lines). I am looking for a way to ...
user44010's user avatar
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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 "...
Hosein Javanmardi's user avatar
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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....
Stefano Barone's user avatar
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Generate polynomial basis through a sequence of SVD

I need help to understand how to use the result given by an algorithm for constructing an orthonormal polynomial basis over $L^{2}(X)$, where $X\subset\mathbb{R}^2$, with respect to the inner product $...
Raibyo's user avatar
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Spline interpolation for vector-valued data in 3D space

I have output from a 3D linear elasticity finite element simulation which uses linear tetrahedral elements, such that the displacement is continuous over the nodes but the gradient is not ($C_0$ ...
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Interpolate location based on triangular sensor array

There are 3 sensors (A, B, C) on a plane, located in the corners of a (known) equilateral triangle. I want to calculate the (2D) location of an object (X) inside that triangle. One sensor returns one ...
Prima's user avatar
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Interpolation of a Concave Mesh

I would like to have an algorithm that interpolates the values attached to nodes in a concave mesh mesh. To be me precise, assume we have a point cloud P (e.g. in 3 dimensions) and a list of edges E ...
ls.'s user avatar
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How to approach geographic data interpolation by distance?

let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order. Now I'm ...
poindls's user avatar
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Grid Data Interpolation

What are the most sophisticated methods for interpolating a scalar field say Electric or Magnetic Field on a 3-D grid? I have scalar data on a meshgrid with equal spacing. I would like to use an ...
Kostis Papadakis's user avatar
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Find B-spline coefficients from values on collocation points

The context of my question is how to compute high order derivates on direct numerical simulation of turbulent channel flow. It is of particular interest for fluid dynamics and turbulence research. I ...
Hydro Guy's user avatar
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Numerical integral of oscillating function with known zeros

I have a function that I need to numerically integrate from $0$ to $+\infty$, given by: $$I = \int_0^{+\infty} \mathrm{d}x\,x\,T^2(x)f(x)$$ where $T^2$ is an interpolated function that goes to $1$ ...
HR_8938's user avatar
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Polynomial approximation - Vandermonde matrix creation - precision

I am trying to fit a polynomial through 340 points in a 3D space, i.e. $$f(x,y,z) = k$$ I asked previously about the theory behind polynomial interpolation here -> Polynomial interpolation Few ...
federico's user avatar
1 vote
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376 views

How to perform Taylor series expansion consisting of cell averaged derivatives in a computational element?

I have encountered the term cell "Cell averaged derivatives" and "Taylor series expansion using cell averaged derivatives about centroid" in the context of polynomial representation in any cell (...
Manish's user avatar
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computational tool for higher order Lagrangian interpolation for finite element

In finite element, I can calculate the Lagrangian interpolation shape functions for each degree of freedom in an element, from the the number of nodal degrees of freedom and the number of nodes ...
user294664's user avatar
1 vote
0 answers
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Sensitivity Analysis -- Total Variation for a function with categorical arguments?

I have an application in sensitivity analysis of complex system models with moderately nonlinear interactions between arguments Arguments potentially dozens or hundreds in number Arguments mostly ...
plucky_underdog's user avatar
1 vote
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178 views

C1 continuous spline on regular 2D-grid with quadratic 1D cuts

I want some scalar spline function defined on regular 2D grid $F(x,y)$ with continuous first derivative which is easy to intersect with arbitrary ray/line ${\vec l}(t) = (c_x t,c_y t,c_z t)$. ...
Prokop Hapala's user avatar
1 vote
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A linear polynomial that is the minimax (best) approximation to $f(x)$ on the interval $[-1,1]$

Suppose you have the following analytical information about a function $f(x)$ on $[-1,1]$: \begin{align*} f(x) &= \frac{1}{x+3}\\ f'(x) & = -\frac{1}{(x+3)^2}\\ f^{''}(x) &= \frac{2}{(x+3)...
Wolfy's user avatar
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linearly interpolate and determine gradients for data on non-uniform grid

I have measurements of a quantity on a 3d grid. My measurements are distributed on four x-y planes similar to what is shown in the image below. The measurements roughly follow a Cartesian grid but ...
jensv's user avatar
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1 vote
0 answers
386 views

Calculating lagrange polynomial for 100 points?

I need to calculate the lagrange polynomial which approximates $e^x$ at $101$ points, the points $\frac{k}{101^2}$ for $k\in\{0,1,2\dots 100\}$. I tried the following code: ...
user avatar
1 vote
0 answers
226 views

End conditions on cubic splines interpolation

I'm currently working on cubic splines interpolation. My question has to do with the end conditions. Instead of using natural or clamped cubic splines, I am asked to use the following condition : $S_{...
Alinwo's user avatar
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Comparison between of higher order interpolations

A while ago I came up with an algorithm which can be used to numerically solve optimal control problems, which basically came down to discretizing the control input $u(t)$ and interpolating this to ...
fibonatic's user avatar
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Gauss Integration over Zero Order Element

I'm working with the Boundary Element Method and want to integrate an expression over a triangular region. I would like to use Gauss Integration to do this, but I'm having trouble since the triangular ...
Grady F. Mathews Iv's user avatar
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823 views

Fast way to compute barycentric lagrange interpolation

Is there any fast way to compute the barycentric Lagrange interpolation using matlab? something more faster than using repmat instead of for loops
user3482383's user avatar
1 vote
0 answers
64 views

Mass-conservative reprojection (on a sphere)

I have a 2D distribution of mass on a sphere given as a matrix of masses in latitude-longitude grid cells. I need these masses projected to another grid on the same sphere with different location of ...
Roux's user avatar
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Combining trend estimation and constrained Marquart fit

This title certainly needs some clarification: I need to compute parameters $a_i$ for a helper function $f(\vec{a};k)$ (for grid interpolation) which is fitted to a number of values $y_k$ which are ...
highsciguy's user avatar
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Advance a Interpolation

Note; No special knowledge of Pykrige is needed to answer the question, as I already mention examples in the question! Hi I would like to use Universal Kriging in my code. For this I have data that ...
Weiss's user avatar
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Interpolation question

I have a set of data $(x_i,y_i,y'_i)$, $i=1,\dots,N$ and I want to fit an interpolating curve $f(x)$ which matches both the data $y_i$ and the first derivatives $y'_i$ at the nodes $x_i$, \begin{align}...
vibe's user avatar
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How to interpolate stress at unknown points from the stress values available based on geometrical position for constant load?

I am working on a combined contact, bending, and torsion problem. I have data on geometrical points and their instantaneous stress components. However, based on the available data, I have to ...
Srikumar Gopalakrishnan's user avatar
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extrapolation/interpolation in fmincg.m

Can you tell me these equations come from where in MATLAB fmincg.m? ...
lightmoon2076's user avatar
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52 views

Cardinal B-Splines with derivative information

Have Schoenberg's cardinal B-splines been extended to accept derivative information at each knot, similar to how Lagrange interpolation can be improved by Hermite interpolation?
user14717's user avatar
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