Questions tagged [interpolation]
Questions on the interpolation functions in Mathematica (InterpolatingFunction[], Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)
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What's inside InterpolatingFunction[{{1., 4.}}, <>]?
I'm curious what's inside the InterpolationFunction object?
For example:
...
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How can the behavior of InterpolationOrder->0 be controlled?
In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
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How does Interpolation really work?
I'm looking for some explanation or advice, not help in solving something. Recently I finished my program and my supervisor said "Ok, now it's time for your first paper: write a scientific text about ...
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How to splice together several instances of InterpolatingFunction?
I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
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Extracting the function from InterpolatingFunction object
I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers.
...
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No warning when extrapolating with Plot
One of the most annoying "features" of Mathematica is that the Plot family does extrapolation on InterpolatingFunctions without ...
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Joining and interpolating data points
I wonder what is the best practice for interpolating curves? Usually, I'm using BSplineCurve and adjusting SplineWeights so it ...
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How can I adaptively simplify a curved shape?
For the purposes of creating a publication-quality plot marker I wish to convert a font glyph into a simplified Polygon where points are taken adaptively according ...
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Arbitrary precision spline interpolation
The current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang says here that "it is not hard to implement it ...
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Finding the intersection of a curve with an interpolation function
There are no issues trying to find the intersection points of two defined curves.
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Data interpolation and ListContourPlot
I am fairly new to Mathematica and I have two quick questions on using it for a Hydrology and Hydrogeology class. One is about data interpolation and interpolating without any data defined in an area. ...
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How to integrate functions of linearly interpolated data?
At first, consider integration of pure InterpolatingFunction.
Importing some data (works in v.9, for earlier versions one can use this link to download zipped <...
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How to reduce the InterpolatingFunction building overhead?
I want a linear interpolation from the following example list:
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ListContourPlot interpolation fails if x and y axes have different scales
To summarize what is below:
ListContourPlot doesn't work when the domain has different x and y scales (fails when x/y~10^4, which seems surprisingly small).
Is it possible to call ListContourPlot on ...
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Easy way to plot ODE solutions from NDSolve?
Inspired by the closed question Beautify a NDSolve Graph ! and a comment someone made to me not too long ago:
Is there some quick way to plot NDSolve results ...
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Mismatch between Mathematica and COMSOL in 3D FEM problem
I would like to solve an advection-diffusion problem on a torus domain. There are three Dirichlet conditions: One at the inlet (concentration $c=0$), one at the outlet ($c=0.5$) and one at the wall ($...
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Getting the interpolation function from a list plot
I have conducted a chemistry experiment and obtained a list of concentrations of a reactant against time. I plot a graph of this using Mathematica's ListPlot ...
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Monotone, periodic 1d-interpolation with continuous 1st order derivative
Lately, we had this thread about interpolation where J. M. linked two interpolation methods. The background for my question is that I estimated a parameter in polar coordinates with dependence on the ...
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Parametric Interpolation of 2D data
I want to create an interpolation through the following 2dim data points:
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Higher order periodic interpolation (curve fitting)
I have a list of points in 3D, and I want to get a smooth interpolation or curve fit (it is more for illustration) of these points such that the first and second derivatives at the start and end ...
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Interpolating data with a step
Suppose I have some data with a step in it:
data = {{1, 1}, {2, 2}, {3, 3}, {3, 4}, {4, 5}, {5, 6}};
Interpolation will complain about this and not give you an ...
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How to fix broken InterpolatingFunction?
Bug introduced in 8.0 and fixed in 9.0.0
I have an InterpolatingFunction based on irregularly-gridded data, like this:
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Object separation from a 2.5D surface
I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
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interpolation of 3D data
I have a 3D surface given in data-points of the form ${x,y,z}$. What is the easiest way to get the interpolated value $z=f(X,Y)$ for given coordinates ${X,Y}$ (which are of course not in the data list)...
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Find maximum value of interpolation function - obviously wrong result
Minimizing and maximizing interpolation function has already been asked and answered, see here for example.
Yet, I observe a strange behaviour. Well, I can understand that the wrong guess of ...
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Fast Spherical Linear Interpolation of list of quaternions
An accurate way to interpolate between two quaternions is to use Spherical Linear Interpolation (Slerp) because it preserves the unit length, whereas straightforward linear interpolation does not, as ...
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How can I smooth a 3D surface generated by RegionBoundary?
I have a set of points that belong to the surface of an object. I would like to approximate a surface to which I can compute the distance. of other points. With the nice code of this post, I was able ...
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Inflection point and curvature
Through a coordinates list and then interpolating them I got a $f[x]$.
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Adding Regularisation to Built-in Interpolation function
tl;tr; How to improve performance of regularised Interpolation?
Context
Since Version 12, Mathematica now incorporates a range of (underrated IMHO) regularisation ...
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Creating a 3D List Line Plot From Discrete Points
Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
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Quirk in VertexColors interpolation when displaying Polygon
When using VertexColors, the docs state:
The interior of the polygon is colored by interpolating between the colors specified by ...
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Improved interpolation of mostly-structured 3d data
This question arose in response to a comment by Leonid to my answer for this question. He noted that for unstructured grids, Interpolation can only use ...
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2D smoothing spline interpolation
Does Mathematica have 2D smoothing spline interpolation built in?
I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
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Getting an InterpolatingFunction from a ContourPlot
I have a function, say
minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β);
I want to find its critical points in $\epsilon$ for a given ...
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Interpolation on a regular square grid spanning a triangular domain
Bug introduced in 10.0 and fixed in 10.1
Context
I am trying to identify contours of a function which is sampled on
a cartesian grid within an irregular (triangular) region.
Here is the data
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How do I prevent NIntegrate::inumr errors within other functions?
I believe this question is best illustrated with a simple example. If I run
FunctionInterpolation[NIntegrate[a + b, {a, 0, 1}], {b, 0, 1}]
I get errors of the ...
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The only usage for the option InterpolationOrder in NDSolve is to be set to All?
We know that changing the option InterpolationOrder in ListLinePlot、ListPlot3D、...
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Finite Element Method and ElementMeshInterpolation issue in v10.3
Bug introduced in 10.3
I recently installed Mathematica v10.3 and checked a project I was working on few months ago under Mathematica v10.1.
In this project I solve a PDE with ...
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Changing the `ExtrapolationHandler` Function in Any Interpolation
This is a related question to What's inside InterpolatingFunction[{{1., 4.}}, <>]? and Suppress extrapolation of interpolating function in a ContourPlot.
When interpolating a set of points,...
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Temporal database reconstruction in mathematica
<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
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Suppress extrapolation of interpolating function in a ContourPlot
I have defined an interpolating function, myfcn[x], valid on the domain x = 0 to 1.5. I am then using ...
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Make an offset curve (parallel curve)
I have a polynomial curve that I got through interpolation.
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How to add an interpolating point to InterpolatingFunction?
Suppose I have an InterpolatingFunction object defined on $[\epsilon,1]$; let's call it f. What is the best way to construct a ...
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Data extraction from a picture of a graph
How can I extract data from this picture of a graph?
i = Import["http://i.stack.imgur.com/Ac8m0.png"];
The caption of the picture reads: " Two-dimensional ...
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Joining points into 3D surface
This seems like a simple problem, but I can't find any questions like it here so I'm making a new one. Apologies if I missed one.
I have a list of points contained in a file which can be visualized ...
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Why does LogLinearPlot sample its argument outside the specified domain?
Bug introduced in 6.0 and fixed in 9.0.0
I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created ...
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Curve fit based on minimal data
Inspired by the fantastic answers here and here, I would like to ask a questions along similar lines.
I have 6 curve types
that follow these rules:
Type A: If point 1 is positive and point 2 is ...
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Subtracting two plots from each other after shifting one
I have the following lists representing energy spectra that need to be subtracted from each other to produce a difference spectrum.
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Custom interpolation on unstructured grid (2D, 3D)
as I'm not satisfied with the way Mathematica interpolates data on unstructured grids, I would like to implement my own interpolation. I will aim for Crouzeix - Raviart type of (quadratic) triangular ...
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