Questions tagged [interpolation]

Questions on the interpolation functions in Mathematica (InterpolatingFunction[], Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)

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59 votes
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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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45 votes
5 answers
2k views

How can the behavior of InterpolationOrder->0 be controlled?

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
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42 votes
5 answers
15k views

My Girlfriend is going to prison...Save her with Math

Salacious title, but true story. ...
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42 votes
2 answers
7k views

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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40 votes
6 answers
6k views

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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  • 735
35 votes
7 answers
9k views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
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  • 453
35 votes
3 answers
2k views

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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34 votes
2 answers
6k views

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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  • 7,075
31 votes
6 answers
13k views

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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  • 9,128
30 votes
3 answers
3k views

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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29 votes
4 answers
2k views

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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27 votes
4 answers
7k views

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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24 votes
4 answers
5k views

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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24 votes
2 answers
2k views

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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24 votes
1 answer
837 views

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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23 votes
4 answers
2k views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
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  • 6,475
23 votes
2 answers
2k views

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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22 votes
4 answers
10k views

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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22 votes
3 answers
3k views

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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  • 111k
21 votes
2 answers
3k views

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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  • 541
21 votes
1 answer
625 views

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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  • 4,941
21 votes
2 answers
818 views

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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  • 441
20 votes
3 answers
3k views

Parametric Interpolation of 2D data

I want to create an interpolation through the following 2dim data points: ...
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  • 303
20 votes
2 answers
9k views

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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  • 13.6k
20 votes
2 answers
3k views

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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  • 4,941
20 votes
1 answer
987 views

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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  • 3,258
19 votes
2 answers
18k views

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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  • 1,547
19 votes
2 answers
3k views

Inflection point and curvature

Through a coordinates list and then interpolating them I got a $f[x]$. ...
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  • 9,055
19 votes
2 answers
570 views

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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  • 21.7k
18 votes
3 answers
9k views

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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18 votes
4 answers
1k views

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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  • 14.6k
18 votes
4 answers
3k views

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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  • 14k
18 votes
2 answers
2k views

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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  • 7,289
17 votes
3 answers
2k views

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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  • 13.4k
17 votes
2 answers
3k views

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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17 votes
2 answers
2k views

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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  • 21.7k
17 votes
1 answer
13k views

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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  • 4,721
16 votes
2 answers
760 views

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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  • 6,903
16 votes
2 answers
2k views

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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  • 291
16 votes
2 answers
455 views

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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  • 558
15 votes
3 answers
6k views

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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15 votes
2 answers
1k views

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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  • 12.4k
15 votes
2 answers
2k views

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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  • 633
15 votes
2 answers
1k views

The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
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  • 51.4k
15 votes
2 answers
1k views

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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  • 625
15 votes
1 answer
609 views

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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  • 6,976
14 votes
3 answers
5k views

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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14 votes
3 answers
1k views

Make an offset curve (parallel curve)

I have a polynomial curve that I got through interpolation. ...
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  • 9,055
14 votes
1 answer
1k views

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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  • 2,234
14 votes
1 answer
1k views

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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