# 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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### 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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### 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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### 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 ...
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### 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 ...
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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 ...
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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 ...
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 ...