# 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.

196 questions
Filter by
Sorted by
Tagged with
1 vote
135 views

### 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 ...
136 views

### 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 ...
1 vote
66 views

### 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 "...
2k views

### Interpolation by Solving a Minimization Problem (Optimization)

I will try to give the motivation behind this problem and later the math formality. Given a grayscale image (1 Channel - $M \times N$ Matrix). Someone marks some pixels as anchors. Now, you need to ...
1 vote
224 views

### Finding weighted average of curves

This is related to my previous post here I have a dataset with values of multiple curves. An example plot is shown below. I want to scale the curves (move up/down) so that all curves overlap. The ...
168 views

### Automatic differentiation of barycentric rational functions

By a barycentric rational interpolant we understand a function of the form \begin{align*} r(t) := \frac{\sum_{i=0}^{n-1} \frac{w_i y_i}{t-t_i} }{ \sum_{i=0}^{n-1} \frac{w_i}{t-t_i}} \end{align*} In ...
4k views

### Three dimensional irregular grid data interpolation to regular grid

I have three-dimensional radar reflectivity data obtained as voxels (scans, rays, altitudes). The data has been sampled at irregular spacings and I want to convert this into a regular grid. In ...
93 views

### 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 $[t_i, t_{i+1}]$ ...
132 views

294 views

1 vote
110 views

57 views

### Projecting nodal solution to gauss points with certain accuracy

I am having a problem that was also mentioned at the accepted answer to this question by Wolfgang Bangerth. I need to calculate, as it was specified at the question at the link, F1 integral and for ...
1 vote
130 views

### 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 ($C_0$ ...
139 views

### At which stage to interpolate?

Assume I have a multidimensional grid $G$. I consider two functions $f(x)$ and $g(x)$. I have solved the values for the functions over all grid points $x \in G$. Let me now be interested in some third ...
259 views

### Finite element interpolation

I have a finite element solver that I implemented in MATLAB. I am calculating a specific potential function that is constant in each tetrahedral element. The question is, I want to be able to ...
1 vote
48 views

### 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 ...
725 views

### Interpolation using compactly supported radial basis function

I have been struggling for two days with the following problem. I would like to do a $d$-dimensional interpolation over some data. I tried first to use polyharmonic splines, but when the size of data ...
1 vote
169 views

### 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 ...
161 views

### Getting torsion and curvature out of ODE solution skeleton

Suppose I have solved an ODE $v'(t) = f(t,x)$ via some adaptive stepper, such as RK4 or Dormand-Prince, generating a list of points $\{(t_i, v_i, v_i' = f(t_i, v_i))\}_{i=0}^{n-1}$. I wish to use this ...
1 vote
466 views

### Factorization of cubic spline interpolation matrix

In cubic spline interpolation, we use the set of knots and function values $(x_i,y_i),i=1,...,n$ to construct a (tridiagonal) system of equations for the unknowns $\sigma_i$:  h_{i-1}\sigma_{i-1} + ...
665 views

### What are the best ways to interpolate a vector field inside (convex) polygons?

I want to interpolate a vector field inside convex polygons in a polygonal mesh. For triangular meshes the scheme uses a piecewise constant interpolation in the triangle, discretized at the center of ...
1 vote
2k views

### What is the relationship between shape functions, interpolation functions, and degrees of freedom?

I am a newbie in FEM. I would like to get clarity regarding a few questions on shape functions in this post (please use as simple language as possible). What is the relation between Shape function ...
2k views

### Minimal surface solution in Python

Note: this question was also posted in StackOverflow and math.stackexchange. I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane ...